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https://github.com/UberGames/GtkRadiant.git
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git-svn-id: svn://svn.icculus.org/gtkradiant/GtkRadiant@1 8a3a26a2-13c4-0310-b231-cf6edde360e5
13236 lines
526 KiB
C
13236 lines
526 KiB
C
#define ANSI_DECLARATORS
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/*****************************************************************************/
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/* */
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/* 888888888 ,o, / 888 */
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/* 888 88o88o " o8888o 88o8888o o88888o 888 o88888o */
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/* 888 888 888 88b 888 888 888 888 888 d888 88b */
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/* 888 888 888 o88^o888 888 888 "88888" 888 8888oo888 */
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/* 888 888 888 C888 888 888 888 / 888 q888 */
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/* 888 888 888 "88o^888 888 888 Cb 888 "88oooo" */
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/* "8oo8D */
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/* */
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/* A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator. */
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/* (triangle.c) */
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/* */
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/* Version 1.3 */
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/* July 19, 1996 */
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/* */
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/* Copyright 1996 */
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/* Jonathan Richard Shewchuk */
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/* School of Computer Science */
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/* Carnegie Mellon University */
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/* 5000 Forbes Avenue */
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/* Pittsburgh, Pennsylvania 15213-3891 */
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/* jrs@cs.cmu.edu */
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/* */
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/* This program may be freely redistributed under the condition that the */
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/* copyright notices (including this entire header and the copyright */
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/* notice printed when the `-h' switch is selected) are not removed, and */
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/* no compensation is received. Private, research, and institutional */
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/* use is free. You may distribute modified versions of this code UNDER */
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/* THE CONDITION THAT THIS CODE AND ANY MODIFICATIONS MADE TO IT IN THE */
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/* SAME FILE REMAIN UNDER COPYRIGHT OF THE ORIGINAL AUTHOR, BOTH SOURCE */
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/* AND OBJECT CODE ARE MADE FREELY AVAILABLE WITHOUT CHARGE, AND CLEAR */
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/* NOTICE IS GIVEN OF THE MODIFICATIONS. Distribution of this code as */
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/* part of a commercial system is permissible ONLY BY DIRECT ARRANGEMENT */
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/* WITH THE AUTHOR. (If you are not directly supplying this code to a */
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/* customer, and you are instead telling them how they can obtain it for */
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/* free, then you are not required to make any arrangement with me.) */
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/* */
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/* Hypertext instructions for Triangle are available on the Web at */
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/* */
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/* http://www.cs.cmu.edu/~quake/triangle.html */
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/* */
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/* Some of the references listed below are marked [*]. These are available */
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/* for downloading from the Web page */
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/* */
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/* http://www.cs.cmu.edu/~quake/triangle.research.html */
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/* */
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/* A paper discussing some aspects of Triangle is available. See Jonathan */
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/* Richard Shewchuk, "Triangle: Engineering a 2D Quality Mesh Generator */
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/* and Delaunay Triangulator," First Workshop on Applied Computational */
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/* Geometry, ACM, May 1996. [*] */
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/* */
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/* Triangle was created as part of the Archimedes project in the School of */
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/* Computer Science at Carnegie Mellon University. Archimedes is a */
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/* system for compiling parallel finite element solvers. For further */
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/* information, see Anja Feldmann, Omar Ghattas, John R. Gilbert, Gary L. */
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/* Miller, David R. O'Hallaron, Eric J. Schwabe, Jonathan R. Shewchuk, */
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/* and Shang-Hua Teng, "Automated Parallel Solution of Unstructured PDE */
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/* Problems." To appear in Communications of the ACM, we hope. */
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/* */
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/* The quality mesh generation algorithm is due to Jim Ruppert, "A */
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/* Delaunay Refinement Algorithm for Quality 2-Dimensional Mesh */
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/* Generation," Journal of Algorithms 18(3):548-585, May 1995. [*] */
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/* */
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/* My implementation of the divide-and-conquer and incremental Delaunay */
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/* triangulation algorithms follows closely the presentation of Guibas */
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/* and Stolfi, even though I use a triangle-based data structure instead */
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/* of their quad-edge data structure. (In fact, I originally implemented */
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/* Triangle using the quad-edge data structure, but switching to a */
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/* triangle-based data structure sped Triangle by a factor of two.) The */
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/* mesh manipulation primitives and the two aforementioned Delaunay */
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/* triangulation algorithms are described by Leonidas J. Guibas and Jorge */
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/* Stolfi, "Primitives for the Manipulation of General Subdivisions and */
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/* the Computation of Voronoi Diagrams," ACM Transactions on Graphics */
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/* 4(2):74-123, April 1985. */
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/* */
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/* Their O(n log n) divide-and-conquer algorithm is adapted from Der-Tsai */
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/* Lee and Bruce J. Schachter, "Two Algorithms for Constructing the */
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/* Delaunay Triangulation," International Journal of Computer and */
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/* Information Science 9(3):219-242, 1980. The idea to improve the */
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/* divide-and-conquer algorithm by alternating between vertical and */
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/* horizontal cuts was introduced by Rex A. Dwyer, "A Faster Divide-and- */
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/* Conquer Algorithm for Constructing Delaunay Triangulations," */
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/* Algorithmica 2(2):137-151, 1987. */
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/* */
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/* The incremental insertion algorithm was first proposed by C. L. Lawson, */
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/* "Software for C1 Surface Interpolation," in Mathematical Software III, */
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/* John R. Rice, editor, Academic Press, New York, pp. 161-194, 1977. */
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/* For point location, I use the algorithm of Ernst P. Mucke, Isaac */
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/* Saias, and Binhai Zhu, "Fast Randomized Point Location Without */
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/* Preprocessing in Two- and Three-dimensional Delaunay Triangulations," */
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/* Proceedings of the Twelfth Annual Symposium on Computational Geometry, */
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/* ACM, May 1996. [*] If I were to randomize the order of point */
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/* insertion (I currently don't bother), their result combined with the */
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/* result of Leonidas J. Guibas, Donald E. Knuth, and Micha Sharir, */
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/* "Randomized Incremental Construction of Delaunay and Voronoi */
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/* Diagrams," Algorithmica 7(4):381-413, 1992, would yield an expected */
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/* O(n^{4/3}) bound on running time. */
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/* */
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/* The O(n log n) sweepline Delaunay triangulation algorithm is taken from */
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/* Steven Fortune, "A Sweepline Algorithm for Voronoi Diagrams", */
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/* Algorithmica 2(2):153-174, 1987. A random sample of edges on the */
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/* boundary of the triangulation are maintained in a splay tree for the */
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/* purpose of point location. Splay trees are described by Daniel */
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/* Dominic Sleator and Robert Endre Tarjan, "Self-Adjusting Binary Search */
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/* Trees," Journal of the ACM 32(3):652-686, July 1985. */
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/* */
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/* The algorithms for exact computation of the signs of determinants are */
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/* described in Jonathan Richard Shewchuk, "Adaptive Precision Floating- */
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/* Point Arithmetic and Fast Robust Geometric Predicates," Technical */
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/* Report CMU-CS-96-140, School of Computer Science, Carnegie Mellon */
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/* University, Pittsburgh, Pennsylvania, May 1996. [*] (Submitted to */
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/* Discrete & Computational Geometry.) An abbreviated version appears as */
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/* Jonathan Richard Shewchuk, "Robust Adaptive Floating-Point Geometric */
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/* Predicates," Proceedings of the Twelfth Annual Symposium on Computa- */
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/* tional Geometry, ACM, May 1996. [*] Many of the ideas for my exact */
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/* arithmetic routines originate with Douglas M. Priest, "Algorithms for */
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/* Arbitrary Precision Floating Point Arithmetic," Tenth Symposium on */
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/* Computer Arithmetic, 132-143, IEEE Computer Society Press, 1991. [*] */
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/* Many of the ideas for the correct evaluation of the signs of */
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/* determinants are taken from Steven Fortune and Christopher J. Van Wyk, */
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/* "Efficient Exact Arithmetic for Computational Geometry," Proceedings */
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/* of the Ninth Annual Symposium on Computational Geometry, ACM, */
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/* pp. 163-172, May 1993, and from Steven Fortune, "Numerical Stability */
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/* of Algorithms for 2D Delaunay Triangulations," International Journal */
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/* of Computational Geometry & Applications 5(1-2):193-213, March-June */
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/* 1995. */
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/* */
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/* For definitions of and results involving Delaunay triangulations, */
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/* constrained and conforming versions thereof, and other aspects of */
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/* triangular mesh generation, see the excellent survey by Marshall Bern */
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/* and David Eppstein, "Mesh Generation and Optimal Triangulation," in */
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/* Computing and Euclidean Geometry, Ding-Zhu Du and Frank Hwang, */
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/* editors, World Scientific, Singapore, pp. 23-90, 1992. */
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/* */
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/* The time for incrementally adding PSLG (planar straight line graph) */
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/* segments to create a constrained Delaunay triangulation is probably */
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/* O(n^2) per segment in the worst case and O(n) per edge in the common */
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/* case, where n is the number of triangles that intersect the segment */
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/* before it is inserted. This doesn't count point location, which can */
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/* be much more expensive. (This note does not apply to conforming */
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/* Delaunay triangulations, for which a different method is used to */
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/* insert segments.) */
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/* */
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/* The time for adding segments to a conforming Delaunay triangulation is */
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/* not clear, but does not depend upon n alone. In some cases, very */
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/* small features (like a point lying next to a segment) can cause a */
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/* single segment to be split an arbitrary number of times. Of course, */
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/* floating-point precision is a practical barrier to how much this can */
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/* happen. */
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/* */
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/* The time for deleting a point from a Delaunay triangulation is O(n^2) in */
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/* the worst case and O(n) in the common case, where n is the degree of */
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/* the point being deleted. I could improve this to expected O(n) time */
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/* by "inserting" the neighboring vertices in random order, but n is */
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/* usually quite small, so it's not worth the bother. (The O(n) time */
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/* for random insertion follows from L. Paul Chew, "Building Voronoi */
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/* Diagrams for Convex Polygons in Linear Expected Time," Technical */
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/* Report PCS-TR90-147, Department of Mathematics and Computer Science, */
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/* Dartmouth College, 1990. */
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/* */
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/* Ruppert's Delaunay refinement algorithm typically generates triangles */
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/* at a linear rate (constant time per triangle) after the initial */
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/* triangulation is formed. There may be pathological cases where more */
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/* time is required, but these never arise in practice. */
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/* */
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/* The segment intersection formulae are straightforward. If you want to */
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/* see them derived, see Franklin Antonio. "Faster Line Segment */
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/* Intersection." In Graphics Gems III (David Kirk, editor), pp. 199- */
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/* 202. Academic Press, Boston, 1992. */
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/* */
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/* If you make any improvements to this code, please please please let me */
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/* know, so that I may obtain the improvements. Even if you don't change */
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/* the code, I'd still love to hear what it's being used for. */
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/* */
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/* Disclaimer: Neither I nor Carnegie Mellon warrant this code in any way */
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/* whatsoever. This code is provided "as-is". Use at your own risk. */
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/* */
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/*****************************************************************************/
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/* For single precision (which will save some memory and reduce paging), */
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/* define the symbol SINGLE by using the -DSINGLE compiler switch or by */
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/* writing "#define SINGLE" below. */
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/* */
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/* For double precision (which will allow you to refine meshes to a smaller */
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/* edge length), leave SINGLE undefined. */
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/* */
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/* Double precision uses more memory, but improves the resolution of the */
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/* meshes you can generate with Triangle. It also reduces the likelihood */
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/* of a floating exception due to overflow. Finally, it is much faster */
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/* than single precision on 64-bit architectures like the DEC Alpha. I */
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/* recommend double precision unless you want to generate a mesh for which */
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/* you do not have enough memory. */
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#define SINGLE
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#ifdef SINGLE
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#define REAL float
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#else /* not SINGLE */
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#define REAL double
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#endif /* not SINGLE */
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/* If yours is not a Unix system, define the NO_TIMER compiler switch to */
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/* remove the Unix-specific timing code. */
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#define NO_TIMER
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/* To insert lots of self-checks for internal errors, define the SELF_CHECK */
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/* symbol. This will slow down the program significantly. It is best to */
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/* define the symbol using the -DSELF_CHECK compiler switch, but you could */
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/* write "#define SELF_CHECK" below. If you are modifying this code, I */
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/* recommend you turn self-checks on. */
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/* #define SELF_CHECK */
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/* To compile Triangle as a callable object library (triangle.o), define the */
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/* TRILIBRARY symbol. Read the file triangle.h for details on how to call */
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/* the procedure triangulate() that results. */
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#define TRILIBRARY
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/* It is possible to generate a smaller version of Triangle using one or */
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/* both of the following symbols. Define the REDUCED symbol to eliminate */
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/* all features that are primarily of research interest; specifically, the */
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/* -i, -F, -s, and -C switches. Define the CDT_ONLY symbol to eliminate */
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/* all meshing algorithms above and beyond constrained Delaunay */
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/* triangulation; specifically, the -r, -q, -a, -S, and -s switches. */
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/* These reductions are most likely to be useful when generating an object */
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/* library (triangle.o) by defining the TRILIBRARY symbol. */
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#define REDUCED
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#define CDT_ONLY
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/* On some machines, the exact arithmetic routines might be defeated by the */
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/* use of internal extended precision floating-point registers. Sometimes */
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/* this problem can be fixed by defining certain values to be volatile, */
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/* thus forcing them to be stored to memory and rounded off. This isn't */
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/* a great solution, though, as it slows Triangle down. */
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/* */
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/* To try this out, write "#define INEXACT volatile" below. Normally, */
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/* however, INEXACT should be defined to be nothing. ("#define INEXACT".) */
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#define INEXACT /* Nothing */
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/* #define INEXACT volatile */
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/* Maximum number of characters in a file name (including the null). */
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#define FILENAMESIZE 512
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/* Maximum number of characters in a line read from a file (including the */
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/* null). */
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#define INPUTLINESIZE 512
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/* For efficiency, a variety of data structures are allocated in bulk. The */
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/* following constants determine how many of each structure is allocated */
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/* at once. */
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#define TRIPERBLOCK 4092 /* Number of triangles allocated at once. */
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#define SHELLEPERBLOCK 508 /* Number of shell edges allocated at once. */
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#define POINTPERBLOCK 4092 /* Number of points allocated at once. */
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#define VIRUSPERBLOCK 1020 /* Number of virus triangles allocated at once. */
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/* Number of encroached segments allocated at once. */
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#define BADSEGMENTPERBLOCK 252
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/* Number of skinny triangles allocated at once. */
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#define BADTRIPERBLOCK 4092
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/* Number of splay tree nodes allocated at once. */
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#define SPLAYNODEPERBLOCK 508
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/* The point marker DEADPOINT is an arbitrary number chosen large enough to */
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/* (hopefully) not conflict with user boundary markers. Make sure that it */
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/* is small enough to fit into your machine's integer size. */
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#define DEADPOINT -1073741824
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/* The next line is used to outsmart some very stupid compilers. If your */
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/* compiler is smarter, feel free to replace the "int" with "void". */
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/* Not that it matters. */
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#define VOID int
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/* Two constants for algorithms based on random sampling. Both constants */
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/* have been chosen empirically to optimize their respective algorithms. */
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/* Used for the point location scheme of Mucke, Saias, and Zhu, to decide */
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/* how large a random sample of triangles to inspect. */
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#define SAMPLEFACTOR 11
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/* Used in Fortune's sweepline Delaunay algorithm to determine what fraction */
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/* of boundary edges should be maintained in the splay tree for point */
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/* location on the front. */
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#define SAMPLERATE 10
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/* A number that speaks for itself, every kissable digit. */
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#define PI 3.141592653589793238462643383279502884197169399375105820974944592308
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/* Another fave. */
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#define SQUAREROOTTWO 1.4142135623730950488016887242096980785696718753769480732
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/* And here's one for those of you who are intimidated by math. */
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#define ONETHIRD 0.333333333333333333333333333333333333333333333333333333333333
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#include <stdio.h>
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#include <string.h>
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#include <math.h>
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#ifndef NO_TIMER
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#include <sys/time.h>
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#endif /* NO_TIMER */
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#ifdef TRILIBRARY
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#include "triangle.h"
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#endif /* TRILIBRARY */
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/* The following obscenity seems to be necessary to ensure that this program */
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/* will port to Dec Alphas running OSF/1, because their stdio.h file commits */
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/* the unpardonable sin of including stdlib.h. Hence, malloc(), free(), and */
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/* exit() may or may not already be defined at this point. I declare these */
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/* functions explicitly because some non-ANSI C compilers lack stdlib.h. */
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#ifndef _STDLIB_H_
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extern void *malloc();
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extern void free();
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extern void exit();
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extern double strtod();
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extern long strtol();
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#endif /* _STDLIB_H_ */
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/* A few forward declarations. */
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void poolrestart();
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#ifndef TRILIBRARY
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char *readline();
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char *findfield();
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#endif /* not TRILIBRARY */
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/* Labels that signify whether a record consists primarily of pointers or of */
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/* floating-point words. Used to make decisions about data alignment. */
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enum wordtype {POINTER, FLOATINGPOINT};
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/* Labels that signify the result of point location. The result of a */
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/* search indicates that the point falls in the interior of a triangle, on */
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/* an edge, on a vertex, or outside the mesh. */
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enum locateresult {INTRIANGLE, ONEDGE, ONVERTEX, OUTSIDE};
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/* Labels that signify the result of site insertion. The result indicates */
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/* that the point was inserted with complete success, was inserted but */
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/* encroaches on a segment, was not inserted because it lies on a segment, */
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/* or was not inserted because another point occupies the same location. */
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enum insertsiteresult {SUCCESSFULPOINT, ENCROACHINGPOINT, VIOLATINGPOINT,
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DUPLICATEPOINT};
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/* Labels that signify the result of direction finding. The result */
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/* indicates that a segment connecting the two query points falls within */
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/* the direction triangle, along the left edge of the direction triangle, */
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/* or along the right edge of the direction triangle. */
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enum finddirectionresult {WITHIN, LEFTCOLLINEAR, RIGHTCOLLINEAR};
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/* Labels that signify the result of the circumcenter computation routine. */
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/* The return value indicates which edge of the triangle is shortest. */
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enum circumcenterresult {OPPOSITEORG, OPPOSITEDEST, OPPOSITEAPEX};
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/*****************************************************************************/
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/* */
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/* The basic mesh data structures */
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/* */
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/* There are three: points, triangles, and shell edges (abbreviated */
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/* `shelle'). These three data structures, linked by pointers, comprise */
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/* the mesh. A point simply represents a point in space and its properties.*/
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/* A triangle is a triangle. A shell edge is a special data structure used */
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/* to represent impenetrable segments in the mesh (including the outer */
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/* boundary, boundaries of holes, and internal boundaries separating two */
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/* triangulated regions). Shell edges represent boundaries defined by the */
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/* user that triangles may not lie across. */
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/* */
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/* A triangle consists of a list of three vertices, a list of three */
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/* adjoining triangles, a list of three adjoining shell edges (when shell */
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/* edges are used), an arbitrary number of optional user-defined floating- */
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/* point attributes, and an optional area constraint. The latter is an */
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/* upper bound on the permissible area of each triangle in a region, used */
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/* for mesh refinement. */
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/* */
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/* For a triangle on a boundary of the mesh, some or all of the neighboring */
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/* triangles may not be present. For a triangle in the interior of the */
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/* mesh, often no neighboring shell edges are present. Such absent */
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/* triangles and shell edges are never represented by NULL pointers; they */
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/* are represented by two special records: `dummytri', the triangle that */
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/* fills "outer space", and `dummysh', the omnipresent shell edge. */
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/* `dummytri' and `dummysh' are used for several reasons; for instance, */
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/* they can be dereferenced and their contents examined without causing the */
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/* memory protection exception that would occur if NULL were dereferenced. */
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/* */
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/* However, it is important to understand that a triangle includes other */
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/* information as well. The pointers to adjoining vertices, triangles, and */
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/* shell edges are ordered in a way that indicates their geometric relation */
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/* to each other. Furthermore, each of these pointers contains orientation */
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/* information. Each pointer to an adjoining triangle indicates which face */
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/* of that triangle is contacted. Similarly, each pointer to an adjoining */
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/* shell edge indicates which side of that shell edge is contacted, and how */
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/* the shell edge is oriented relative to the triangle. */
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/* */
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/* Shell edges are found abutting edges of triangles; either sandwiched */
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/* between two triangles, or resting against one triangle on an exterior */
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/* boundary or hole boundary. */
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/* */
|
|
/* A shell edge consists of a list of two vertices, a list of two */
|
|
/* adjoining shell edges, and a list of two adjoining triangles. One of */
|
|
/* the two adjoining triangles may not be present (though there should */
|
|
/* always be one), and neighboring shell edges might not be present. */
|
|
/* Shell edges also store a user-defined integer "boundary marker". */
|
|
/* Typically, this integer is used to indicate what sort of boundary */
|
|
/* conditions are to be applied at that location in a finite element */
|
|
/* simulation. */
|
|
/* */
|
|
/* Like triangles, shell edges maintain information about the relative */
|
|
/* orientation of neighboring objects. */
|
|
/* */
|
|
/* Points are relatively simple. A point is a list of floating point */
|
|
/* numbers, starting with the x, and y coordinates, followed by an */
|
|
/* arbitrary number of optional user-defined floating-point attributes, */
|
|
/* followed by an integer boundary marker. During the segment insertion */
|
|
/* phase, there is also a pointer from each point to a triangle that may */
|
|
/* contain it. Each pointer is not always correct, but when one is, it */
|
|
/* speeds up segment insertion. These pointers are assigned values once */
|
|
/* at the beginning of the segment insertion phase, and are not used or */
|
|
/* updated at any other time. Edge swapping during segment insertion will */
|
|
/* render some of them incorrect. Hence, don't rely upon them for */
|
|
/* anything. For the most part, points do not have any information about */
|
|
/* what triangles or shell edges they are linked to. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* Handles */
|
|
/* */
|
|
/* The oriented triangle (`triedge') and oriented shell edge (`edge') data */
|
|
/* structures defined below do not themselves store any part of the mesh. */
|
|
/* The mesh itself is made of `triangle's, `shelle's, and `point's. */
|
|
/* */
|
|
/* Oriented triangles and oriented shell edges will usually be referred to */
|
|
/* as "handles". A handle is essentially a pointer into the mesh; it */
|
|
/* allows you to "hold" one particular part of the mesh. Handles are used */
|
|
/* to specify the regions in which one is traversing and modifying the mesh.*/
|
|
/* A single `triangle' may be held by many handles, or none at all. (The */
|
|
/* latter case is not a memory leak, because the triangle is still */
|
|
/* connected to other triangles in the mesh.) */
|
|
/* */
|
|
/* A `triedge' is a handle that holds a triangle. It holds a specific side */
|
|
/* of the triangle. An `edge' is a handle that holds a shell edge. It */
|
|
/* holds either the left or right side of the edge. */
|
|
/* */
|
|
/* Navigation about the mesh is accomplished through a set of mesh */
|
|
/* manipulation primitives, further below. Many of these primitives take */
|
|
/* a handle and produce a new handle that holds the mesh near the first */
|
|
/* handle. Other primitives take two handles and glue the corresponding */
|
|
/* parts of the mesh together. The exact position of the handles is */
|
|
/* important. For instance, when two triangles are glued together by the */
|
|
/* bond() primitive, they are glued by the sides on which the handles lie. */
|
|
/* */
|
|
/* Because points have no information about which triangles they are */
|
|
/* attached to, I commonly represent a point by use of a handle whose */
|
|
/* origin is the point. A single handle can simultaneously represent a */
|
|
/* triangle, an edge, and a point. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
/* The triangle data structure. Each triangle contains three pointers to */
|
|
/* adjoining triangles, plus three pointers to vertex points, plus three */
|
|
/* pointers to shell edges (defined below; these pointers are usually */
|
|
/* `dummysh'). It may or may not also contain user-defined attributes */
|
|
/* and/or a floating-point "area constraint". It may also contain extra */
|
|
/* pointers for nodes, when the user asks for high-order elements. */
|
|
/* Because the size and structure of a `triangle' is not decided until */
|
|
/* runtime, I haven't simply defined the type `triangle' to be a struct. */
|
|
|
|
typedef REAL **triangle; /* Really: typedef triangle *triangle */
|
|
|
|
/* An oriented triangle: includes a pointer to a triangle and orientation. */
|
|
/* The orientation denotes an edge of the triangle. Hence, there are */
|
|
/* three possible orientations. By convention, each edge is always */
|
|
/* directed to point counterclockwise about the corresponding triangle. */
|
|
|
|
struct triedge {
|
|
triangle *tri;
|
|
int orient; /* Ranges from 0 to 2. */
|
|
};
|
|
|
|
/* The shell data structure. Each shell edge contains two pointers to */
|
|
/* adjoining shell edges, plus two pointers to vertex points, plus two */
|
|
/* pointers to adjoining triangles, plus one shell marker. */
|
|
|
|
typedef REAL **shelle; /* Really: typedef shelle *shelle */
|
|
|
|
/* An oriented shell edge: includes a pointer to a shell edge and an */
|
|
/* orientation. The orientation denotes a side of the edge. Hence, there */
|
|
/* are two possible orientations. By convention, the edge is always */
|
|
/* directed so that the "side" denoted is the right side of the edge. */
|
|
|
|
struct edge {
|
|
shelle *sh;
|
|
int shorient; /* Ranges from 0 to 1. */
|
|
};
|
|
|
|
/* The point data structure. Each point is actually an array of REALs. */
|
|
/* The number of REALs is unknown until runtime. An integer boundary */
|
|
/* marker, and sometimes a pointer to a triangle, is appended after the */
|
|
/* REALs. */
|
|
|
|
typedef REAL *point;
|
|
|
|
/* A queue used to store encroached segments. Each segment's vertices are */
|
|
/* stored so that one can check whether a segment is still the same. */
|
|
|
|
struct badsegment {
|
|
struct edge encsegment; /* An encroached segment. */
|
|
point segorg, segdest; /* The two vertices. */
|
|
struct badsegment *nextsegment; /* Pointer to next encroached segment. */
|
|
};
|
|
|
|
/* A queue used to store bad triangles. The key is the square of the cosine */
|
|
/* of the smallest angle of the triangle. Each triangle's vertices are */
|
|
/* stored so that one can check whether a triangle is still the same. */
|
|
|
|
struct badface {
|
|
struct triedge badfacetri; /* A bad triangle. */
|
|
REAL key; /* cos^2 of smallest (apical) angle. */
|
|
point faceorg, facedest, faceapex; /* The three vertices. */
|
|
struct badface *nextface; /* Pointer to next bad triangle. */
|
|
};
|
|
|
|
/* A node in a heap used to store events for the sweepline Delaunay */
|
|
/* algorithm. Nodes do not point directly to their parents or children in */
|
|
/* the heap. Instead, each node knows its position in the heap, and can */
|
|
/* look up its parent and children in a separate array. The `eventptr' */
|
|
/* points either to a `point' or to a triangle (in encoded format, so that */
|
|
/* an orientation is included). In the latter case, the origin of the */
|
|
/* oriented triangle is the apex of a "circle event" of the sweepline */
|
|
/* algorithm. To distinguish site events from circle events, all circle */
|
|
/* events are given an invalid (smaller than `xmin') x-coordinate `xkey'. */
|
|
|
|
struct event {
|
|
REAL xkey, ykey; /* Coordinates of the event. */
|
|
VOID *eventptr; /* Can be a point or the location of a circle event. */
|
|
int heapposition; /* Marks this event's position in the heap. */
|
|
};
|
|
|
|
/* A node in the splay tree. Each node holds an oriented ghost triangle */
|
|
/* that represents a boundary edge of the growing triangulation. When a */
|
|
/* circle event covers two boundary edges with a triangle, so that they */
|
|
/* are no longer boundary edges, those edges are not immediately deleted */
|
|
/* from the tree; rather, they are lazily deleted when they are next */
|
|
/* encountered. (Since only a random sample of boundary edges are kept */
|
|
/* in the tree, lazy deletion is faster.) `keydest' is used to verify */
|
|
/* that a triangle is still the same as when it entered the splay tree; if */
|
|
/* it has been rotated (due to a circle event), it no longer represents a */
|
|
/* boundary edge and should be deleted. */
|
|
|
|
struct splaynode {
|
|
struct triedge keyedge; /* Lprev of an edge on the front. */
|
|
point keydest; /* Used to verify that splay node is still live. */
|
|
struct splaynode *lchild, *rchild; /* Children in splay tree. */
|
|
};
|
|
|
|
/* A type used to allocate memory. firstblock is the first block of items. */
|
|
/* nowblock is the block from which items are currently being allocated. */
|
|
/* nextitem points to the next slab of free memory for an item. */
|
|
/* deaditemstack is the head of a linked list (stack) of deallocated items */
|
|
/* that can be recycled. unallocateditems is the number of items that */
|
|
/* remain to be allocated from nowblock. */
|
|
/* */
|
|
/* Traversal is the process of walking through the entire list of items, and */
|
|
/* is separate from allocation. Note that a traversal will visit items on */
|
|
/* the "deaditemstack" stack as well as live items. pathblock points to */
|
|
/* the block currently being traversed. pathitem points to the next item */
|
|
/* to be traversed. pathitemsleft is the number of items that remain to */
|
|
/* be traversed in pathblock. */
|
|
/* */
|
|
/* itemwordtype is set to POINTER or FLOATINGPOINT, and is used to suggest */
|
|
/* what sort of word the record is primarily made up of. alignbytes */
|
|
/* determines how new records should be aligned in memory. itembytes and */
|
|
/* itemwords are the length of a record in bytes (after rounding up) and */
|
|
/* words. itemsperblock is the number of items allocated at once in a */
|
|
/* single block. items is the number of currently allocated items. */
|
|
/* maxitems is the maximum number of items that have been allocated at */
|
|
/* once; it is the current number of items plus the number of records kept */
|
|
/* on deaditemstack. */
|
|
|
|
struct memorypool {
|
|
VOID **firstblock, **nowblock;
|
|
VOID *nextitem;
|
|
VOID *deaditemstack;
|
|
VOID **pathblock;
|
|
VOID *pathitem;
|
|
enum wordtype itemwordtype;
|
|
int alignbytes;
|
|
int itembytes, itemwords;
|
|
int itemsperblock;
|
|
long items, maxitems;
|
|
int unallocateditems;
|
|
int pathitemsleft;
|
|
};
|
|
|
|
/* Variables used to allocate memory for triangles, shell edges, points, */
|
|
/* viri (triangles being eaten), bad (encroached) segments, bad (skinny */
|
|
/* or too large) triangles, and splay tree nodes. */
|
|
|
|
static struct memorypool triangles;
|
|
static struct memorypool shelles;
|
|
static struct memorypool points;
|
|
static struct memorypool viri;
|
|
static struct memorypool badsegments;
|
|
static struct memorypool badtriangles;
|
|
static struct memorypool splaynodes;
|
|
|
|
/* Variables that maintain the bad triangle queues. The tails are pointers */
|
|
/* to the pointers that have to be filled in to enqueue an item. */
|
|
|
|
static struct badface *queuefront[64];
|
|
static struct badface **queuetail[64];
|
|
|
|
static REAL xmin, xmax, ymin, ymax; /* x and y bounds. */
|
|
static REAL xminextreme; /* Nonexistent x value used as a flag in sweepline. */
|
|
static int inpoints; /* Number of input points. */
|
|
static int inelements; /* Number of input triangles. */
|
|
static int insegments; /* Number of input segments. */
|
|
static int holes; /* Number of input holes. */
|
|
static int regions; /* Number of input regions. */
|
|
static long edges; /* Number of output edges. */
|
|
static int mesh_dim; /* Dimension (ought to be 2). */
|
|
static int nextras; /* Number of attributes per point. */
|
|
static int eextras; /* Number of attributes per triangle. */
|
|
static long hullsize; /* Number of edges of convex hull. */
|
|
static int triwords; /* Total words per triangle. */
|
|
static int shwords; /* Total words per shell edge. */
|
|
static int pointmarkindex; /* Index to find boundary marker of a point. */
|
|
static int point2triindex; /* Index to find a triangle adjacent to a point. */
|
|
static int highorderindex; /* Index to find extra nodes for high-order elements. */
|
|
static int elemattribindex; /* Index to find attributes of a triangle. */
|
|
static int areaboundindex; /* Index to find area bound of a triangle. */
|
|
static int checksegments; /* Are there segments in the triangulation yet? */
|
|
static int readnodefile; /* Has a .node file been read? */
|
|
static long samples; /* Number of random samples for point location. */
|
|
static unsigned long randomseed; /* Current random number seed. */
|
|
|
|
static REAL splitter; /* Used to split REAL factors for exact multiplication. */
|
|
static REAL epsilon; /* Floating-point machine epsilon. */
|
|
static REAL resulterrbound;
|
|
static REAL ccwerrboundA, ccwerrboundB, ccwerrboundC;
|
|
static REAL iccerrboundA, iccerrboundB, iccerrboundC;
|
|
|
|
static long incirclecount; /* Number of incircle tests performed. */
|
|
static long counterclockcount; /* Number of counterclockwise tests performed. */
|
|
static long hyperbolacount; /* Number of right-of-hyperbola tests performed. */
|
|
static long circumcentercount; /* Number of circumcenter calculations performed. */
|
|
static long circletopcount; /* Number of circle top calculations performed. */
|
|
|
|
/* Switches for the triangulator. */
|
|
/* poly: -p switch. refine: -r switch. */
|
|
/* quality: -q switch. */
|
|
/* minangle: minimum angle bound, specified after -q switch. */
|
|
/* goodangle: cosine squared of minangle. */
|
|
/* vararea: -a switch without number. */
|
|
/* fixedarea: -a switch with number. */
|
|
/* maxarea: maximum area bound, specified after -a switch. */
|
|
/* regionattrib: -A switch. convex: -c switch. */
|
|
/* firstnumber: inverse of -z switch. All items are numbered starting */
|
|
/* from firstnumber. */
|
|
/* edgesout: -e switch. voronoi: -v switch. */
|
|
/* neighbors: -n switch. geomview: -g switch. */
|
|
/* nobound: -B switch. nopolywritten: -P switch. */
|
|
/* nonodewritten: -N switch. noelewritten: -E switch. */
|
|
/* noiterationnum: -I switch. noholes: -O switch. */
|
|
/* noexact: -X switch. */
|
|
/* order: element order, specified after -o switch. */
|
|
/* nobisect: count of how often -Y switch is selected. */
|
|
/* steiner: maximum number of Steiner points, specified after -S switch. */
|
|
/* steinerleft: number of Steiner points not yet used. */
|
|
/* incremental: -i switch. sweepline: -F switch. */
|
|
/* dwyer: inverse of -l switch. */
|
|
/* splitseg: -s switch. */
|
|
/* docheck: -C switch. */
|
|
/* quiet: -Q switch. verbose: count of how often -V switch is selected. */
|
|
/* useshelles: -p, -r, -q, or -c switch; determines whether shell edges */
|
|
/* are used at all. */
|
|
/* */
|
|
/* Read the instructions to find out the meaning of these switches. */
|
|
|
|
static int poly, refine, quality, vararea, fixedarea, regionattrib, convex;
|
|
static int firstnumber;
|
|
static int edgesout, voronoi, neighbors, geomview;
|
|
static int nobound, nopolywritten, nonodewritten, noelewritten, noiterationnum;
|
|
static int noholes, noexact;
|
|
static int incremental, sweepline, dwyer;
|
|
static int splitseg;
|
|
static int docheck;
|
|
static int quiet, verbose;
|
|
static int useshelles;
|
|
static int order;
|
|
static int nobisect;
|
|
static int steiner, steinerleft;
|
|
static REAL minangle, goodangle;
|
|
static REAL maxarea;
|
|
|
|
/* Variables for file names. */
|
|
|
|
#ifndef TRILIBRARY
|
|
char innodefilename[FILENAMESIZE];
|
|
char inelefilename[FILENAMESIZE];
|
|
char inpolyfilename[FILENAMESIZE];
|
|
char areafilename[FILENAMESIZE];
|
|
char outnodefilename[FILENAMESIZE];
|
|
char outelefilename[FILENAMESIZE];
|
|
char outpolyfilename[FILENAMESIZE];
|
|
char edgefilename[FILENAMESIZE];
|
|
char vnodefilename[FILENAMESIZE];
|
|
char vedgefilename[FILENAMESIZE];
|
|
char neighborfilename[FILENAMESIZE];
|
|
char offfilename[FILENAMESIZE];
|
|
#endif /* not TRILIBRARY */
|
|
|
|
/* Triangular bounding box points. */
|
|
|
|
static point infpoint1, infpoint2, infpoint3;
|
|
|
|
/* Pointer to the `triangle' that occupies all of "outer space". */
|
|
|
|
static triangle *dummytri;
|
|
static triangle *dummytribase; /* Keep base address so we can free() it later. */
|
|
|
|
/* Pointer to the omnipresent shell edge. Referenced by any triangle or */
|
|
/* shell edge that isn't really connected to a shell edge at that */
|
|
/* location. */
|
|
|
|
static shelle *dummysh;
|
|
static shelle *dummyshbase; /* Keep base address so we can free() it later. */
|
|
|
|
/* Pointer to a recently visited triangle. Improves point location if */
|
|
/* proximate points are inserted sequentially. */
|
|
|
|
static struct triedge recenttri;
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* Mesh manipulation primitives. Each triangle contains three pointers to */
|
|
/* other triangles, with orientations. Each pointer points not to the */
|
|
/* first byte of a triangle, but to one of the first three bytes of a */
|
|
/* triangle. It is necessary to extract both the triangle itself and the */
|
|
/* orientation. To save memory, I keep both pieces of information in one */
|
|
/* pointer. To make this possible, I assume that all triangles are aligned */
|
|
/* to four-byte boundaries. The `decode' routine below decodes a pointer, */
|
|
/* extracting an orientation (in the range 0 to 2) and a pointer to the */
|
|
/* beginning of a triangle. The `encode' routine compresses a pointer to a */
|
|
/* triangle and an orientation into a single pointer. My assumptions that */
|
|
/* triangles are four-byte-aligned and that the `unsigned long' type is */
|
|
/* long enough to hold a pointer are two of the few kludges in this program.*/
|
|
/* */
|
|
/* Shell edges are manipulated similarly. A pointer to a shell edge */
|
|
/* carries both an address and an orientation in the range 0 to 1. */
|
|
/* */
|
|
/* The other primitives take an oriented triangle or oriented shell edge, */
|
|
/* and return an oriented triangle or oriented shell edge or point; or they */
|
|
/* change the connections in the data structure. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
/********* Mesh manipulation primitives begin here *********/
|
|
/** **/
|
|
/** **/
|
|
|
|
/* Fast lookup arrays to speed some of the mesh manipulation primitives. */
|
|
|
|
int plus1mod3[3] = {1, 2, 0};
|
|
int minus1mod3[3] = {2, 0, 1};
|
|
|
|
/********* Primitives for triangles *********/
|
|
/* */
|
|
/* */
|
|
|
|
/* decode() converts a pointer to an oriented triangle. The orientation is */
|
|
/* extracted from the two least significant bits of the pointer. */
|
|
|
|
#define decode(ptr, triedge) \
|
|
(triedge).orient = (int) ((unsigned long) (ptr) & (unsigned long) 3l); \
|
|
(triedge).tri = (triangle *) \
|
|
((unsigned long) (ptr) ^ (unsigned long) (triedge).orient)
|
|
|
|
/* encode() compresses an oriented triangle into a single pointer. It */
|
|
/* relies on the assumption that all triangles are aligned to four-byte */
|
|
/* boundaries, so the two least significant bits of (triedge).tri are zero.*/
|
|
|
|
#define encode(triedge) \
|
|
(triangle) ((unsigned long) (triedge).tri | (unsigned long) (triedge).orient)
|
|
|
|
/* The following edge manipulation primitives are all described by Guibas */
|
|
/* and Stolfi. However, they use an edge-based data structure, whereas I */
|
|
/* am using a triangle-based data structure. */
|
|
|
|
/* sym() finds the abutting triangle, on the same edge. Note that the */
|
|
/* edge direction is necessarily reversed, because triangle/edge handles */
|
|
/* are always directed counterclockwise around the triangle. */
|
|
|
|
#define sym(triedge1, triedge2) \
|
|
ptr = (triedge1).tri[(triedge1).orient]; \
|
|
decode(ptr, triedge2);
|
|
|
|
#define symself(triedge) \
|
|
ptr = (triedge).tri[(triedge).orient]; \
|
|
decode(ptr, triedge);
|
|
|
|
/* lnext() finds the next edge (counterclockwise) of a triangle. */
|
|
|
|
#define lnext(triedge1, triedge2) \
|
|
(triedge2).tri = (triedge1).tri; \
|
|
(triedge2).orient = plus1mod3[(triedge1).orient]
|
|
|
|
#define lnextself(triedge) \
|
|
(triedge).orient = plus1mod3[(triedge).orient]
|
|
|
|
/* lprev() finds the previous edge (clockwise) of a triangle. */
|
|
|
|
#define lprev(triedge1, triedge2) \
|
|
(triedge2).tri = (triedge1).tri; \
|
|
(triedge2).orient = minus1mod3[(triedge1).orient]
|
|
|
|
#define lprevself(triedge) \
|
|
(triedge).orient = minus1mod3[(triedge).orient]
|
|
|
|
/* onext() spins counterclockwise around a point; that is, it finds the next */
|
|
/* edge with the same origin in the counterclockwise direction. This edge */
|
|
/* will be part of a different triangle. */
|
|
|
|
#define onext(triedge1, triedge2) \
|
|
lprev(triedge1, triedge2); \
|
|
symself(triedge2);
|
|
|
|
#define onextself(triedge) \
|
|
lprevself(triedge); \
|
|
symself(triedge);
|
|
|
|
/* oprev() spins clockwise around a point; that is, it finds the next edge */
|
|
/* with the same origin in the clockwise direction. This edge will be */
|
|
/* part of a different triangle. */
|
|
|
|
#define oprev(triedge1, triedge2) \
|
|
sym(triedge1, triedge2); \
|
|
lnextself(triedge2);
|
|
|
|
#define oprevself(triedge) \
|
|
symself(triedge); \
|
|
lnextself(triedge);
|
|
|
|
/* dnext() spins counterclockwise around a point; that is, it finds the next */
|
|
/* edge with the same destination in the counterclockwise direction. This */
|
|
/* edge will be part of a different triangle. */
|
|
|
|
#define dnext(triedge1, triedge2) \
|
|
sym(triedge1, triedge2); \
|
|
lprevself(triedge2);
|
|
|
|
#define dnextself(triedge) \
|
|
symself(triedge); \
|
|
lprevself(triedge);
|
|
|
|
/* dprev() spins clockwise around a point; that is, it finds the next edge */
|
|
/* with the same destination in the clockwise direction. This edge will */
|
|
/* be part of a different triangle. */
|
|
|
|
#define dprev(triedge1, triedge2) \
|
|
lnext(triedge1, triedge2); \
|
|
symself(triedge2);
|
|
|
|
#define dprevself(triedge) \
|
|
lnextself(triedge); \
|
|
symself(triedge);
|
|
|
|
/* rnext() moves one edge counterclockwise about the adjacent triangle. */
|
|
/* (It's best understood by reading Guibas and Stolfi. It involves */
|
|
/* changing triangles twice.) */
|
|
|
|
#define rnext(triedge1, triedge2) \
|
|
sym(triedge1, triedge2); \
|
|
lnextself(triedge2); \
|
|
symself(triedge2);
|
|
|
|
#define rnextself(triedge) \
|
|
symself(triedge); \
|
|
lnextself(triedge); \
|
|
symself(triedge);
|
|
|
|
/* rnext() moves one edge clockwise about the adjacent triangle. */
|
|
/* (It's best understood by reading Guibas and Stolfi. It involves */
|
|
/* changing triangles twice.) */
|
|
|
|
#define rprev(triedge1, triedge2) \
|
|
sym(triedge1, triedge2); \
|
|
lprevself(triedge2); \
|
|
symself(triedge2);
|
|
|
|
#define rprevself(triedge) \
|
|
symself(triedge); \
|
|
lprevself(triedge); \
|
|
symself(triedge);
|
|
|
|
/* These primitives determine or set the origin, destination, or apex of a */
|
|
/* triangle. */
|
|
|
|
#define org(triedge, pointptr) \
|
|
pointptr = (point) (triedge).tri[plus1mod3[(triedge).orient] + 3]
|
|
|
|
#define dest(triedge, pointptr) \
|
|
pointptr = (point) (triedge).tri[minus1mod3[(triedge).orient] + 3]
|
|
|
|
#define apex(triedge, pointptr) \
|
|
pointptr = (point) (triedge).tri[(triedge).orient + 3]
|
|
|
|
#define setorg(triedge, pointptr) \
|
|
(triedge).tri[plus1mod3[(triedge).orient] + 3] = (triangle) pointptr
|
|
|
|
#define setdest(triedge, pointptr) \
|
|
(triedge).tri[minus1mod3[(triedge).orient] + 3] = (triangle) pointptr
|
|
|
|
#define setapex(triedge, pointptr) \
|
|
(triedge).tri[(triedge).orient + 3] = (triangle) pointptr
|
|
|
|
#define setvertices2null(triedge) \
|
|
(triedge).tri[3] = (triangle) NULL; \
|
|
(triedge).tri[4] = (triangle) NULL; \
|
|
(triedge).tri[5] = (triangle) NULL;
|
|
|
|
/* Bond two triangles together. */
|
|
|
|
#define bond(triedge1, triedge2) \
|
|
(triedge1).tri[(triedge1).orient] = encode(triedge2); \
|
|
(triedge2).tri[(triedge2).orient] = encode(triedge1)
|
|
|
|
/* Dissolve a bond (from one side). Note that the other triangle will still */
|
|
/* think it's connected to this triangle. Usually, however, the other */
|
|
/* triangle is being deleted entirely, or bonded to another triangle, so */
|
|
/* it doesn't matter. */
|
|
|
|
#define dissolve(triedge) \
|
|
(triedge).tri[(triedge).orient] = (triangle) dummytri
|
|
|
|
/* Copy a triangle/edge handle. */
|
|
|
|
#define triedgecopy(triedge1, triedge2) \
|
|
(triedge2).tri = (triedge1).tri; \
|
|
(triedge2).orient = (triedge1).orient
|
|
|
|
/* Test for equality of triangle/edge handles. */
|
|
|
|
#define triedgeequal(triedge1, triedge2) \
|
|
(((triedge1).tri == (triedge2).tri) && \
|
|
((triedge1).orient == (triedge2).orient))
|
|
|
|
/* Primitives to infect or cure a triangle with the virus. These rely on */
|
|
/* the assumption that all shell edges are aligned to four-byte boundaries.*/
|
|
|
|
#define infect(triedge) \
|
|
(triedge).tri[6] = (triangle) \
|
|
((unsigned long) (triedge).tri[6] | (unsigned long) 2l)
|
|
|
|
#define uninfect(triedge) \
|
|
(triedge).tri[6] = (triangle) \
|
|
((unsigned long) (triedge).tri[6] & ~ (unsigned long) 2l)
|
|
|
|
/* Test a triangle for viral infection. */
|
|
|
|
#define infected(triedge) \
|
|
(((unsigned long) (triedge).tri[6] & (unsigned long) 2l) != 0)
|
|
|
|
/* Check or set a triangle's attributes. */
|
|
|
|
#define elemattribute(triedge, attnum) \
|
|
((REAL *) (triedge).tri)[elemattribindex + (attnum)]
|
|
|
|
#define setelemattribute(triedge, attnum, value) \
|
|
((REAL *) (triedge).tri)[elemattribindex + (attnum)] = (REAL)value
|
|
|
|
/* Check or set a triangle's maximum area bound. */
|
|
|
|
#define areabound(triedge) ((REAL *) (triedge).tri)[areaboundindex]
|
|
|
|
#define setareabound(triedge, value) \
|
|
((REAL *) (triedge).tri)[areaboundindex] = (REAL)value
|
|
|
|
/********* Primitives for shell edges *********/
|
|
/* */
|
|
/* */
|
|
|
|
/* sdecode() converts a pointer to an oriented shell edge. The orientation */
|
|
/* is extracted from the least significant bit of the pointer. The two */
|
|
/* least significant bits (one for orientation, one for viral infection) */
|
|
/* are masked out to produce the real pointer. */
|
|
|
|
#define sdecode(sptr, edge) \
|
|
(edge).shorient = (int) ((unsigned long) (sptr) & (unsigned long) 1l); \
|
|
(edge).sh = (shelle *) \
|
|
((unsigned long) (sptr) & ~ (unsigned long) 3l)
|
|
|
|
/* sencode() compresses an oriented shell edge into a single pointer. It */
|
|
/* relies on the assumption that all shell edges are aligned to two-byte */
|
|
/* boundaries, so the least significant bit of (edge).sh is zero. */
|
|
|
|
#define sencode(edge) \
|
|
(shelle) ((unsigned long) (edge).sh | (unsigned long) (edge).shorient)
|
|
|
|
/* ssym() toggles the orientation of a shell edge. */
|
|
|
|
#define ssym(edge1, edge2) \
|
|
(edge2).sh = (edge1).sh; \
|
|
(edge2).shorient = 1 - (edge1).shorient
|
|
|
|
#define ssymself(edge) \
|
|
(edge).shorient = 1 - (edge).shorient
|
|
|
|
/* spivot() finds the other shell edge (from the same segment) that shares */
|
|
/* the same origin. */
|
|
|
|
#define spivot(edge1, edge2) \
|
|
sptr = (edge1).sh[(edge1).shorient]; \
|
|
sdecode(sptr, edge2)
|
|
|
|
#define spivotself(edge) \
|
|
sptr = (edge).sh[(edge).shorient]; \
|
|
sdecode(sptr, edge)
|
|
|
|
/* snext() finds the next shell edge (from the same segment) in sequence; */
|
|
/* one whose origin is the input shell edge's destination. */
|
|
|
|
#define snext(edge1, edge2) \
|
|
sptr = (edge1).sh[1 - (edge1).shorient]; \
|
|
sdecode(sptr, edge2)
|
|
|
|
#define snextself(edge) \
|
|
sptr = (edge).sh[1 - (edge).shorient]; \
|
|
sdecode(sptr, edge)
|
|
|
|
/* These primitives determine or set the origin or destination of a shell */
|
|
/* edge. */
|
|
|
|
#define sorg(edge, pointptr) \
|
|
pointptr = (point) (edge).sh[2 + (edge).shorient]
|
|
|
|
#define sdest(edge, pointptr) \
|
|
pointptr = (point) (edge).sh[3 - (edge).shorient]
|
|
|
|
#define setsorg(edge, pointptr) \
|
|
(edge).sh[2 + (edge).shorient] = (shelle) pointptr
|
|
|
|
#define setsdest(edge, pointptr) \
|
|
(edge).sh[3 - (edge).shorient] = (shelle) pointptr
|
|
|
|
/* These primitives read or set a shell marker. Shell markers are used to */
|
|
/* hold user boundary information. */
|
|
|
|
#define mark(edge) (* (int *) ((edge).sh + 6))
|
|
|
|
#define setmark(edge, value) \
|
|
* (int *) ((edge).sh + 6) = value
|
|
|
|
/* Bond two shell edges together. */
|
|
|
|
#define sbond(edge1, edge2) \
|
|
(edge1).sh[(edge1).shorient] = sencode(edge2); \
|
|
(edge2).sh[(edge2).shorient] = sencode(edge1)
|
|
|
|
/* Dissolve a shell edge bond (from one side). Note that the other shell */
|
|
/* edge will still think it's connected to this shell edge. */
|
|
|
|
#define sdissolve(edge) \
|
|
(edge).sh[(edge).shorient] = (shelle) dummysh
|
|
|
|
/* Copy a shell edge. */
|
|
|
|
#define shellecopy(edge1, edge2) \
|
|
(edge2).sh = (edge1).sh; \
|
|
(edge2).shorient = (edge1).shorient
|
|
|
|
/* Test for equality of shell edges. */
|
|
|
|
#define shelleequal(edge1, edge2) \
|
|
(((edge1).sh == (edge2).sh) && \
|
|
((edge1).shorient == (edge2).shorient))
|
|
|
|
/********* Primitives for interacting triangles and shell edges *********/
|
|
/* */
|
|
/* */
|
|
|
|
/* tspivot() finds a shell edge abutting a triangle. */
|
|
|
|
#define tspivot(triedge, edge) \
|
|
sptr = (shelle) (triedge).tri[6 + (triedge).orient]; \
|
|
sdecode(sptr, edge)
|
|
|
|
/* stpivot() finds a triangle abutting a shell edge. It requires that the */
|
|
/* variable `ptr' of type `triangle' be defined. */
|
|
|
|
#define stpivot(edge, triedge) \
|
|
ptr = (triangle) (edge).sh[4 + (edge).shorient]; \
|
|
decode(ptr, triedge)
|
|
|
|
/* Bond a triangle to a shell edge. */
|
|
|
|
#define tsbond(triedge, edge) \
|
|
(triedge).tri[6 + (triedge).orient] = (triangle) sencode(edge); \
|
|
(edge).sh[4 + (edge).shorient] = (shelle) encode(triedge)
|
|
|
|
/* Dissolve a bond (from the triangle side). */
|
|
|
|
#define tsdissolve(triedge) \
|
|
(triedge).tri[6 + (triedge).orient] = (triangle) dummysh
|
|
|
|
/* Dissolve a bond (from the shell edge side). */
|
|
|
|
#define stdissolve(edge) \
|
|
(edge).sh[4 + (edge).shorient] = (shelle) dummytri
|
|
|
|
/********* Primitives for points *********/
|
|
/* */
|
|
/* */
|
|
|
|
#define pointmark(pt) ((int *) (pt))[pointmarkindex]
|
|
|
|
#define setpointmark(pt, value) \
|
|
((int *) (pt))[pointmarkindex] = value
|
|
|
|
#define point2tri(pt) ((triangle *) (pt))[point2triindex]
|
|
|
|
#define setpoint2tri(pt, value) \
|
|
((triangle *) (pt))[point2triindex] = value
|
|
|
|
/** **/
|
|
/** **/
|
|
/********* Mesh manipulation primitives end here *********/
|
|
|
|
/********* User interaction routines begin here *********/
|
|
/** **/
|
|
/** **/
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* syntax() Print list of command line switches. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
#ifndef TRILIBRARY
|
|
|
|
void syntax()
|
|
{
|
|
#ifdef CDT_ONLY
|
|
#ifdef REDUCED
|
|
printf("triangle [-pAcevngBPNEIOXzo_lQVh] input_file\n");
|
|
#else /* not REDUCED */
|
|
printf("triangle [-pAcevngBPNEIOXzo_iFlCQVh] input_file\n");
|
|
#endif /* not REDUCED */
|
|
#else /* not CDT_ONLY */
|
|
#ifdef REDUCED
|
|
printf("triangle [-prq__a__AcevngBPNEIOXzo_YS__lQVh] input_file\n");
|
|
#else /* not REDUCED */
|
|
printf("triangle [-prq__a__AcevngBPNEIOXzo_YS__iFlsCQVh] input_file\n");
|
|
#endif /* not REDUCED */
|
|
#endif /* not CDT_ONLY */
|
|
|
|
printf(" -p Triangulates a Planar Straight Line Graph (.poly file).\n");
|
|
#ifndef CDT_ONLY
|
|
printf(" -r Refines a previously generated mesh.\n");
|
|
printf(
|
|
" -q Quality mesh generation. A minimum angle may be specified.\n");
|
|
printf(" -a Applies a maximum triangle area constraint.\n");
|
|
#endif /* not CDT_ONLY */
|
|
printf(
|
|
" -A Applies attributes to identify elements in certain regions.\n");
|
|
printf(" -c Encloses the convex hull with segments.\n");
|
|
printf(" -e Generates an edge list.\n");
|
|
printf(" -v Generates a Voronoi diagram.\n");
|
|
printf(" -n Generates a list of triangle neighbors.\n");
|
|
printf(" -g Generates an .off file for Geomview.\n");
|
|
printf(" -B Suppresses output of boundary information.\n");
|
|
printf(" -P Suppresses output of .poly file.\n");
|
|
printf(" -N Suppresses output of .node file.\n");
|
|
printf(" -E Suppresses output of .ele file.\n");
|
|
printf(" -I Suppresses mesh iteration numbers.\n");
|
|
printf(" -O Ignores holes in .poly file.\n");
|
|
printf(" -X Suppresses use of exact arithmetic.\n");
|
|
printf(" -z Numbers all items starting from zero (rather than one).\n");
|
|
printf(" -o2 Generates second-order subparametric elements.\n");
|
|
#ifndef CDT_ONLY
|
|
printf(" -Y Suppresses boundary segment splitting.\n");
|
|
printf(" -S Specifies maximum number of added Steiner points.\n");
|
|
#endif /* not CDT_ONLY */
|
|
#ifndef REDUCED
|
|
printf(" -i Uses incremental method, rather than divide-and-conquer.\n");
|
|
printf(" -F Uses Fortune's sweepline algorithm, rather than d-and-c.\n");
|
|
#endif /* not REDUCED */
|
|
printf(" -l Uses vertical cuts only, rather than alternating cuts.\n");
|
|
#ifndef REDUCED
|
|
#ifndef CDT_ONLY
|
|
printf(
|
|
" -s Force segments into mesh by splitting (instead of using CDT).\n");
|
|
#endif /* not CDT_ONLY */
|
|
printf(" -C Check consistency of final mesh.\n");
|
|
#endif /* not REDUCED */
|
|
printf(" -Q Quiet: No terminal output except errors.\n");
|
|
printf(" -V Verbose: Detailed information on what I'm doing.\n");
|
|
printf(" -h Help: Detailed instructions for Triangle.\n");
|
|
exit(0);
|
|
}
|
|
|
|
#endif /* not TRILIBRARY */
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* info() Print out complete instructions. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
#ifndef TRILIBRARY
|
|
|
|
void info()
|
|
{
|
|
printf("Triangle\n");
|
|
printf(
|
|
"A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator.\n");
|
|
printf("Version 1.3\n\n");
|
|
printf(
|
|
"Copyright 1996 Jonathan Richard Shewchuk (bugs/comments to jrs@cs.cmu.edu)\n"
|
|
);
|
|
printf("School of Computer Science / Carnegie Mellon University\n");
|
|
printf("5000 Forbes Avenue / Pittsburgh, Pennsylvania 15213-3891\n");
|
|
printf(
|
|
"Created as part of the Archimedes project (tools for parallel FEM).\n");
|
|
printf(
|
|
"Supported in part by NSF Grant CMS-9318163 and an NSERC 1967 Scholarship.\n");
|
|
printf("There is no warranty whatsoever. Use at your own risk.\n");
|
|
#ifdef SINGLE
|
|
printf("This executable is compiled for single precision arithmetic.\n\n\n");
|
|
#else /* not SINGLE */
|
|
printf("This executable is compiled for double precision arithmetic.\n\n\n");
|
|
#endif /* not SINGLE */
|
|
printf(
|
|
"Triangle generates exact Delaunay triangulations, constrained Delaunay\n");
|
|
printf(
|
|
"triangulations, and quality conforming Delaunay triangulations. The latter\n"
|
|
);
|
|
printf(
|
|
"can be generated with no small angles, and are thus suitable for finite\n");
|
|
printf(
|
|
"element analysis. If no command line switches are specified, your .node\n");
|
|
printf(
|
|
"input file will be read, and the Delaunay triangulation will be returned in\n"
|
|
);
|
|
printf(".node and .ele output files. The command syntax is:\n\n");
|
|
#ifdef CDT_ONLY
|
|
#ifdef REDUCED
|
|
printf("triangle [-pAcevngBPNEIOXzo_lQVh] input_file\n\n");
|
|
#else /* not REDUCED */
|
|
printf("triangle [-pAcevngBPNEIOXzo_iFlCQVh] input_file\n\n");
|
|
#endif /* not REDUCED */
|
|
#else /* not CDT_ONLY */
|
|
#ifdef REDUCED
|
|
printf("triangle [-prq__a__AcevngBPNEIOXzo_YS__lQVh] input_file\n\n");
|
|
#else /* not REDUCED */
|
|
printf("triangle [-prq__a__AcevngBPNEIOXzo_YS__iFlsCQVh] input_file\n\n");
|
|
#endif /* not REDUCED */
|
|
#endif /* not CDT_ONLY */
|
|
printf(
|
|
"Underscores indicate that numbers may optionally follow certain switches;\n");
|
|
printf(
|
|
"do not leave any space between a switch and its numeric parameter.\n");
|
|
printf(
|
|
"input_file must be a file with extension .node, or extension .poly if the\n");
|
|
printf(
|
|
"-p switch is used. If -r is used, you must supply .node and .ele files,\n");
|
|
printf(
|
|
"and possibly a .poly file and .area file as well. The formats of these\n");
|
|
printf("files are described below.\n\n");
|
|
printf("Command Line Switches:\n\n");
|
|
printf(
|
|
" -p Reads a Planar Straight Line Graph (.poly file), which can specify\n"
|
|
);
|
|
printf(
|
|
" points, segments, holes, and regional attributes and area\n");
|
|
printf(
|
|
" constraints. Will generate a constrained Delaunay triangulation\n");
|
|
printf(
|
|
" fitting the input; or, if -s, -q, or -a is used, a conforming\n");
|
|
printf(
|
|
" Delaunay triangulation. If -p is not used, Triangle reads a .node\n"
|
|
);
|
|
printf(" file by default.\n");
|
|
printf(
|
|
" -r Refines a previously generated mesh. The mesh is read from a .node\n"
|
|
);
|
|
printf(
|
|
" file and an .ele file. If -p is also used, a .poly file is read\n");
|
|
printf(
|
|
" and used to constrain edges in the mesh. Further details on\n");
|
|
printf(" refinement are given below.\n");
|
|
printf(
|
|
" -q Quality mesh generation by Jim Ruppert's Delaunay refinement\n");
|
|
printf(
|
|
" algorithm. Adds points to the mesh to ensure that no angles\n");
|
|
printf(
|
|
" smaller than 20 degrees occur. An alternative minimum angle may be\n"
|
|
);
|
|
printf(
|
|
" specified after the `q'. If the minimum angle is 20.7 degrees or\n");
|
|
printf(
|
|
" smaller, the triangulation algorithm is theoretically guaranteed to\n"
|
|
);
|
|
printf(
|
|
" terminate (assuming infinite precision arithmetic - Triangle may\n");
|
|
printf(
|
|
" fail to terminate if you run out of precision). In practice, the\n");
|
|
printf(
|
|
" algorithm often succeeds for minimum angles up to 33.8 degrees.\n");
|
|
printf(
|
|
" For highly refined meshes, however, it may be necessary to reduce\n");
|
|
printf(
|
|
" the minimum angle to well below 20 to avoid problems associated\n");
|
|
printf(
|
|
" with insufficient floating-point precision. The specified angle\n");
|
|
printf(" may include a decimal point.\n");
|
|
printf(
|
|
" -a Imposes a maximum triangle area. If a number follows the `a', no\n");
|
|
printf(
|
|
" triangle will be generated whose area is larger than that number.\n");
|
|
printf(
|
|
" If no number is specified, an .area file (if -r is used) or .poly\n");
|
|
printf(
|
|
" file (if -r is not used) specifies a number of maximum area\n");
|
|
printf(
|
|
" constraints. An .area file contains a separate area constraint for\n"
|
|
);
|
|
printf(
|
|
" each triangle, and is useful for refining a finite element mesh\n");
|
|
printf(
|
|
" based on a posteriori error estimates. A .poly file can optionally\n"
|
|
);
|
|
printf(
|
|
" contain an area constraint for each segment-bounded region, thereby\n"
|
|
);
|
|
printf(
|
|
" enforcing triangle densities in a first triangulation. You can\n");
|
|
printf(
|
|
" impose both a fixed area constraint and a varying area constraint\n");
|
|
printf(
|
|
" by invoking the -a switch twice, once with and once without a\n");
|
|
printf(
|
|
" number following. Each area specified may include a decimal point.\n"
|
|
);
|
|
printf(
|
|
" -A Assigns an additional attribute to each triangle that identifies\n");
|
|
printf(
|
|
" what segment-bounded region each triangle belongs to. Attributes\n");
|
|
printf(
|
|
" are assigned to regions by the .poly file. If a region is not\n");
|
|
printf(
|
|
" explicitly marked by the .poly file, triangles in that region are\n");
|
|
printf(
|
|
" assigned an attribute of zero. The -A switch has an effect only\n");
|
|
printf(" when the -p switch is used and the -r switch is not.\n");
|
|
printf(
|
|
" -c Creates segments on the convex hull of the triangulation. If you\n");
|
|
printf(
|
|
" are triangulating a point set, this switch causes a .poly file to\n");
|
|
printf(
|
|
" be written, containing all edges in the convex hull. (By default,\n"
|
|
);
|
|
printf(
|
|
" a .poly file is written only if a .poly file is read.) If you are\n"
|
|
);
|
|
printf(
|
|
" triangulating a PSLG, this switch specifies that the interior of\n");
|
|
printf(
|
|
" the convex hull of the PSLG should be triangulated. If you do not\n"
|
|
);
|
|
printf(
|
|
" use this switch when triangulating a PSLG, it is assumed that you\n");
|
|
printf(
|
|
" have identified the region to be triangulated by surrounding it\n");
|
|
printf(
|
|
" with segments of the input PSLG. Beware: if you are not careful,\n"
|
|
);
|
|
printf(
|
|
" this switch can cause the introduction of an extremely thin angle\n");
|
|
printf(
|
|
" between a PSLG segment and a convex hull segment, which can cause\n");
|
|
printf(
|
|
" overrefinement or failure if Triangle runs out of precision. If\n");
|
|
printf(
|
|
" you are refining a mesh, the -c switch works differently; it\n");
|
|
printf(
|
|
" generates the set of boundary edges of the mesh, rather than the\n");
|
|
printf(" convex hull.\n");
|
|
printf(
|
|
" -e Outputs (to an .edge file) a list of edges of the triangulation.\n");
|
|
printf(
|
|
" -v Outputs the Voronoi diagram associated with the triangulation.\n");
|
|
printf(" Does not attempt to detect degeneracies.\n");
|
|
printf(
|
|
" -n Outputs (to a .neigh file) a list of triangles neighboring each\n");
|
|
printf(" triangle.\n");
|
|
printf(
|
|
" -g Outputs the mesh to an Object File Format (.off) file, suitable for\n"
|
|
);
|
|
printf(" viewing with the Geometry Center's Geomview package.\n");
|
|
printf(
|
|
" -B No boundary markers in the output .node, .poly, and .edge output\n");
|
|
printf(
|
|
" files. See the detailed discussion of boundary markers below.\n");
|
|
printf(
|
|
" -P No output .poly file. Saves disk space, but you lose the ability\n");
|
|
printf(
|
|
" to impose segment constraints on later refinements of the mesh.\n");
|
|
printf(" -N No output .node file.\n");
|
|
printf(" -E No output .ele file.\n");
|
|
printf(
|
|
" -I No iteration numbers. Suppresses the output of .node and .poly\n");
|
|
printf(
|
|
" files, so your input files won't be overwritten. (If your input is\n"
|
|
);
|
|
printf(
|
|
" a .poly file only, a .node file will be written.) Cannot be used\n");
|
|
printf(
|
|
" with the -r switch, because that would overwrite your input .ele\n");
|
|
printf(
|
|
" file. Shouldn't be used with the -s, -q, or -a switch if you are\n");
|
|
printf(
|
|
" using a .node file for input, because no .node file will be\n");
|
|
printf(" written, so there will be no record of any added points.\n");
|
|
printf(" -O No holes. Ignores the holes in the .poly file.\n");
|
|
printf(
|
|
" -X No exact arithmetic. Normally, Triangle uses exact floating-point\n"
|
|
);
|
|
printf(
|
|
" arithmetic for certain tests if it thinks the inexact tests are not\n"
|
|
);
|
|
printf(
|
|
" accurate enough. Exact arithmetic ensures the robustness of the\n");
|
|
printf(
|
|
" triangulation algorithms, despite floating-point roundoff error.\n");
|
|
printf(
|
|
" Disabling exact arithmetic with the -X switch will cause a small\n");
|
|
printf(
|
|
" improvement in speed and create the possibility (albeit small) that\n"
|
|
);
|
|
printf(
|
|
" Triangle will fail to produce a valid mesh. Not recommended.\n");
|
|
printf(
|
|
" -z Numbers all items starting from zero (rather than one). Note that\n"
|
|
);
|
|
printf(
|
|
" this switch is normally overrided by the value used to number the\n");
|
|
printf(
|
|
" first point of the input .node or .poly file. However, this switch\n"
|
|
);
|
|
printf(" is useful when calling Triangle from another program.\n");
|
|
printf(
|
|
" -o2 Generates second-order subparametric elements with six nodes each.\n"
|
|
);
|
|
printf(
|
|
" -Y No new points on the boundary. This switch is useful when the mesh\n"
|
|
);
|
|
printf(
|
|
" boundary must be preserved so that it conforms to some adjacent\n");
|
|
printf(
|
|
" mesh. Be forewarned that you will probably sacrifice some of the\n");
|
|
printf(
|
|
" quality of the mesh; Triangle will try, but the resulting mesh may\n"
|
|
);
|
|
printf(
|
|
" contain triangles of poor aspect ratio. Works well if all the\n");
|
|
printf(
|
|
" boundary points are closely spaced. Specify this switch twice\n");
|
|
printf(
|
|
" (`-YY') to prevent all segment splitting, including internal\n");
|
|
printf(" boundaries.\n");
|
|
printf(
|
|
" -S Specifies the maximum number of Steiner points (points that are not\n"
|
|
);
|
|
printf(
|
|
" in the input, but are added to meet the constraints of minimum\n");
|
|
printf(
|
|
" angle and maximum area). The default is to allow an unlimited\n");
|
|
printf(
|
|
" number. If you specify this switch with no number after it,\n");
|
|
printf(
|
|
" the limit is set to zero. Triangle always adds points at segment\n");
|
|
printf(
|
|
" intersections, even if it needs to use more points than the limit\n");
|
|
printf(
|
|
" you set. When Triangle inserts segments by splitting (-s), it\n");
|
|
printf(
|
|
" always adds enough points to ensure that all the segments appear in\n"
|
|
);
|
|
printf(
|
|
" the triangulation, again ignoring the limit. Be forewarned that\n");
|
|
printf(
|
|
" the -S switch may result in a conforming triangulation that is not\n"
|
|
);
|
|
printf(
|
|
" truly Delaunay, because Triangle may be forced to stop adding\n");
|
|
printf(
|
|
" points when the mesh is in a state where a segment is non-Delaunay\n"
|
|
);
|
|
printf(
|
|
" and needs to be split. If so, Triangle will print a warning.\n");
|
|
printf(
|
|
" -i Uses an incremental rather than divide-and-conquer algorithm to\n");
|
|
printf(
|
|
" form a Delaunay triangulation. Try it if the divide-and-conquer\n");
|
|
printf(" algorithm fails.\n");
|
|
printf(
|
|
" -F Uses Steven Fortune's sweepline algorithm to form a Delaunay\n");
|
|
printf(
|
|
" triangulation. Warning: does not use exact arithmetic for all\n");
|
|
printf(" calculations. An exact result is not guaranteed.\n");
|
|
printf(
|
|
" -l Uses only vertical cuts in the divide-and-conquer algorithm. By\n");
|
|
printf(
|
|
" default, Triangle uses alternating vertical and horizontal cuts,\n");
|
|
printf(
|
|
" which usually improve the speed except with point sets that are\n");
|
|
printf(
|
|
" small or short and wide. This switch is primarily of theoretical\n");
|
|
printf(" interest.\n");
|
|
printf(
|
|
" -s Specifies that segments should be forced into the triangulation by\n"
|
|
);
|
|
printf(
|
|
" recursively splitting them at their midpoints, rather than by\n");
|
|
printf(
|
|
" generating a constrained Delaunay triangulation. Segment splitting\n"
|
|
);
|
|
printf(
|
|
" is true to Ruppert's original algorithm, but can create needlessly\n"
|
|
);
|
|
printf(" small triangles near external small features.\n");
|
|
printf(
|
|
" -C Check the consistency of the final mesh. Uses exact arithmetic for\n"
|
|
);
|
|
printf(
|
|
" checking, even if the -X switch is used. Useful if you suspect\n");
|
|
printf(" Triangle is buggy.\n");
|
|
printf(
|
|
" -Q Quiet: Suppresses all explanation of what Triangle is doing, unless\n"
|
|
);
|
|
printf(" an error occurs.\n");
|
|
printf(
|
|
" -V Verbose: Gives detailed information about what Triangle is doing.\n");
|
|
printf(
|
|
" Add more `V's for increasing amount of detail. `-V' gives\n");
|
|
printf(
|
|
" information on algorithmic progress and more detailed statistics.\n");
|
|
printf(
|
|
" `-VV' gives point-by-point details, and will print so much that\n");
|
|
printf(
|
|
" Triangle will run much more slowly. `-VVV' gives information only\n"
|
|
);
|
|
printf(" a debugger could love.\n");
|
|
printf(" -h Help: Displays these instructions.\n");
|
|
printf("\n");
|
|
printf("Definitions:\n");
|
|
printf("\n");
|
|
printf(
|
|
" A Delaunay triangulation of a point set is a triangulation whose vertices\n"
|
|
);
|
|
printf(
|
|
" are the point set, having the property that no point in the point set\n");
|
|
printf(
|
|
" falls in the interior of the circumcircle (circle that passes through all\n"
|
|
);
|
|
printf(" three vertices) of any triangle in the triangulation.\n\n");
|
|
printf(
|
|
" A Voronoi diagram of a point set is a subdivision of the plane into\n");
|
|
printf(
|
|
" polygonal regions (some of which may be infinite), where each region is\n");
|
|
printf(
|
|
" the set of points in the plane that are closer to some input point than\n");
|
|
printf(
|
|
" to any other input point. (The Voronoi diagram is the geometric dual of\n"
|
|
);
|
|
printf(" the Delaunay triangulation.)\n\n");
|
|
printf(
|
|
" A Planar Straight Line Graph (PSLG) is a collection of points and\n");
|
|
printf(
|
|
" segments. Segments are simply edges, whose endpoints are points in the\n");
|
|
printf(
|
|
" PSLG. The file format for PSLGs (.poly files) is described below.\n");
|
|
printf("\n");
|
|
printf(
|
|
" A constrained Delaunay triangulation of a PSLG is similar to a Delaunay\n");
|
|
printf(
|
|
" triangulation, but each PSLG segment is present as a single edge in the\n");
|
|
printf(
|
|
" triangulation. (A constrained Delaunay triangulation is not truly a\n");
|
|
printf(" Delaunay triangulation.)\n\n");
|
|
printf(
|
|
" A conforming Delaunay triangulation of a PSLG is a true Delaunay\n");
|
|
printf(
|
|
" triangulation in which each PSLG segment may have been subdivided into\n");
|
|
printf(
|
|
" several edges by the insertion of additional points. These inserted\n");
|
|
printf(
|
|
" points are necessary to allow the segments to exist in the mesh while\n");
|
|
printf(" maintaining the Delaunay property.\n\n");
|
|
printf("File Formats:\n\n");
|
|
printf(
|
|
" All files may contain comments prefixed by the character '#'. Points,\n");
|
|
printf(
|
|
" triangles, edges, holes, and maximum area constraints must be numbered\n");
|
|
printf(
|
|
" consecutively, starting from either 1 or 0. Whichever you choose, all\n");
|
|
printf(
|
|
" input files must be consistent; if the nodes are numbered from 1, so must\n"
|
|
);
|
|
printf(
|
|
" be all other objects. Triangle automatically detects your choice while\n");
|
|
printf(
|
|
" reading the .node (or .poly) file. (When calling Triangle from another\n");
|
|
printf(
|
|
" program, use the -z switch if you wish to number objects from zero.)\n");
|
|
printf(" Examples of these file formats are given below.\n\n");
|
|
printf(" .node files:\n");
|
|
printf(
|
|
" First line: <# of points> <dimension (must be 2)> <# of attributes>\n");
|
|
printf(
|
|
" <# of boundary markers (0 or 1)>\n"
|
|
);
|
|
printf(
|
|
" Remaining lines: <point #> <x> <y> [attributes] [boundary marker]\n");
|
|
printf("\n");
|
|
printf(
|
|
" The attributes, which are typically floating-point values of physical\n");
|
|
printf(
|
|
" quantities (such as mass or conductivity) associated with the nodes of\n"
|
|
);
|
|
printf(
|
|
" a finite element mesh, are copied unchanged to the output mesh. If -s,\n"
|
|
);
|
|
printf(
|
|
" -q, or -a is selected, each new Steiner point added to the mesh will\n");
|
|
printf(" have attributes assigned to it by linear interpolation.\n\n");
|
|
printf(
|
|
" If the fourth entry of the first line is `1', the last column of the\n");
|
|
printf(
|
|
" remainder of the file is assumed to contain boundary markers. Boundary\n"
|
|
);
|
|
printf(
|
|
" markers are used to identify boundary points and points resting on PSLG\n"
|
|
);
|
|
printf(
|
|
" segments; a complete description appears in a section below. The .node\n"
|
|
);
|
|
printf(
|
|
" file produced by Triangle will contain boundary markers in the last\n");
|
|
printf(" column unless they are suppressed by the -B switch.\n\n");
|
|
printf(" .ele files:\n");
|
|
printf(
|
|
" First line: <# of triangles> <points per triangle> <# of attributes>\n");
|
|
printf(
|
|
" Remaining lines: <triangle #> <point> <point> <point> ... [attributes]\n"
|
|
);
|
|
printf("\n");
|
|
printf(
|
|
" Points are indices into the corresponding .node file. The first three\n"
|
|
);
|
|
printf(
|
|
" points are the corners, and are listed in counterclockwise order around\n"
|
|
);
|
|
printf(
|
|
" each triangle. (The remaining points, if any, depend on the type of\n");
|
|
printf(
|
|
" finite element used.) The attributes are just like those of .node\n");
|
|
printf(
|
|
" files. Because there is no simple mapping from input to output\n");
|
|
printf(
|
|
" triangles, an attempt is made to interpolate attributes, which may\n");
|
|
printf(
|
|
" result in a good deal of diffusion of attributes among nearby triangles\n"
|
|
);
|
|
printf(
|
|
" as the triangulation is refined. Diffusion does not occur across\n");
|
|
printf(
|
|
" segments, so attributes used to identify segment-bounded regions remain\n"
|
|
);
|
|
printf(
|
|
" intact. In output .ele files, all triangles have three points each\n");
|
|
printf(
|
|
" unless the -o2 switch is used, in which case they have six, and the\n");
|
|
printf(
|
|
" fourth, fifth, and sixth points lie on the midpoints of the edges\n");
|
|
printf(" opposite the first, second, and third corners.\n\n");
|
|
printf(" .poly files:\n");
|
|
printf(
|
|
" First line: <# of points> <dimension (must be 2)> <# of attributes>\n");
|
|
printf(
|
|
" <# of boundary markers (0 or 1)>\n"
|
|
);
|
|
printf(
|
|
" Following lines: <point #> <x> <y> [attributes] [boundary marker]\n");
|
|
printf(" One line: <# of segments> <# of boundary markers (0 or 1)>\n");
|
|
printf(
|
|
" Following lines: <segment #> <endpoint> <endpoint> [boundary marker]\n");
|
|
printf(" One line: <# of holes>\n");
|
|
printf(" Following lines: <hole #> <x> <y>\n");
|
|
printf(
|
|
" Optional line: <# of regional attributes and/or area constraints>\n");
|
|
printf(
|
|
" Optional following lines: <constraint #> <x> <y> <attrib> <max area>\n");
|
|
printf("\n");
|
|
printf(
|
|
" A .poly file represents a PSLG, as well as some additional information.\n"
|
|
);
|
|
printf(
|
|
" The first section lists all the points, and is identical to the format\n"
|
|
);
|
|
printf(
|
|
" of .node files. <# of points> may be set to zero to indicate that the\n"
|
|
);
|
|
printf(
|
|
" points are listed in a separate .node file; .poly files produced by\n");
|
|
printf(
|
|
" Triangle always have this format. This has the advantage that a point\n"
|
|
);
|
|
printf(
|
|
" set may easily be triangulated with or without segments. (The same\n");
|
|
printf(
|
|
" effect can be achieved, albeit using more disk space, by making a copy\n"
|
|
);
|
|
printf(
|
|
" of the .poly file with the extension .node; all sections of the file\n");
|
|
printf(" but the first are ignored.)\n\n");
|
|
printf(
|
|
" The second section lists the segments. Segments are edges whose\n");
|
|
printf(
|
|
" presence in the triangulation is enforced. Each segment is specified\n");
|
|
printf(
|
|
" by listing the indices of its two endpoints. This means that you must\n"
|
|
);
|
|
printf(
|
|
" include its endpoints in the point list. If -s, -q, and -a are not\n");
|
|
printf(
|
|
" selected, Triangle will produce a constrained Delaunay triangulation,\n");
|
|
printf(
|
|
" in which each segment appears as a single edge in the triangulation.\n");
|
|
printf(
|
|
" If -q or -a is selected, Triangle will produce a conforming Delaunay\n");
|
|
printf(
|
|
" triangulation, in which segments may be subdivided into smaller edges.\n"
|
|
);
|
|
printf(" Each segment, like each point, may have a boundary marker.\n\n");
|
|
printf(
|
|
" The third section lists holes (and concavities, if -c is selected) in\n");
|
|
printf(
|
|
" the triangulation. Holes are specified by identifying a point inside\n");
|
|
printf(
|
|
" each hole. After the triangulation is formed, Triangle creates holes\n");
|
|
printf(
|
|
" by eating triangles, spreading out from each hole point until its\n");
|
|
printf(
|
|
" progress is blocked by PSLG segments; you must be careful to enclose\n");
|
|
printf(
|
|
" each hole in segments, or your whole triangulation may be eaten away.\n");
|
|
printf(
|
|
" If the two triangles abutting a segment are eaten, the segment itself\n");
|
|
printf(
|
|
" is also eaten. Do not place a hole directly on a segment; if you do,\n");
|
|
printf(" Triangle will choose one side of the segment arbitrarily.\n\n");
|
|
printf(
|
|
" The optional fourth section lists regional attributes (to be assigned\n");
|
|
printf(
|
|
" to all triangles in a region) and regional constraints on the maximum\n");
|
|
printf(
|
|
" triangle area. Triangle will read this section only if the -A switch\n");
|
|
printf(
|
|
" is used or the -a switch is used without a number following it, and the\n"
|
|
);
|
|
printf(
|
|
" -r switch is not used. Regional attributes and area constraints are\n");
|
|
printf(
|
|
" propagated in the same manner as holes; you specify a point for each\n");
|
|
printf(
|
|
" attribute and/or constraint, and the attribute and/or constraint will\n");
|
|
printf(
|
|
" affect the whole region (bounded by segments) containing the point. If\n"
|
|
);
|
|
printf(
|
|
" two values are written on a line after the x and y coordinate, the\n");
|
|
printf(
|
|
" former is assumed to be a regional attribute (but will only be applied\n"
|
|
);
|
|
printf(
|
|
" if the -A switch is selected), and the latter is assumed to be a\n");
|
|
printf(
|
|
" regional area constraint (but will only be applied if the -a switch is\n"
|
|
);
|
|
printf(
|
|
" selected). You may also specify just one value after the coordinates,\n"
|
|
);
|
|
printf(
|
|
" which can serve as both an attribute and an area constraint, depending\n"
|
|
);
|
|
printf(
|
|
" on the choice of switches. If you are using the -A and -a switches\n");
|
|
printf(
|
|
" simultaneously and wish to assign an attribute to some region without\n");
|
|
printf(" imposing an area constraint, use a negative maximum area.\n\n");
|
|
printf(
|
|
" When a triangulation is created from a .poly file, you must either\n");
|
|
printf(
|
|
" enclose the entire region to be triangulated in PSLG segments, or\n");
|
|
printf(
|
|
" use the -c switch, which encloses the convex hull of the input point\n");
|
|
printf(
|
|
" set. If you do not use the -c switch, Triangle will eat all triangles\n"
|
|
);
|
|
printf(
|
|
" on the outer boundary that are not protected by segments; if you are\n");
|
|
printf(
|
|
" not careful, your whole triangulation may be eaten away. If you do\n");
|
|
printf(
|
|
" use the -c switch, you can still produce concavities by appropriate\n");
|
|
printf(" placement of holes just inside the convex hull.\n\n");
|
|
printf(
|
|
" An ideal PSLG has no intersecting segments, nor any points that lie\n");
|
|
printf(
|
|
" upon segments (except, of course, the endpoints of each segment.) You\n"
|
|
);
|
|
printf(
|
|
" aren't required to make your .poly files ideal, but you should be aware\n"
|
|
);
|
|
printf(
|
|
" of what can go wrong. Segment intersections are relatively safe -\n");
|
|
printf(
|
|
" Triangle will calculate the intersection points for you and add them to\n"
|
|
);
|
|
printf(
|
|
" the triangulation - as long as your machine's floating-point precision\n"
|
|
);
|
|
printf(
|
|
" doesn't become a problem. You are tempting the fates if you have three\n"
|
|
);
|
|
printf(
|
|
" segments that cross at the same location, and expect Triangle to figure\n"
|
|
);
|
|
printf(
|
|
" out where the intersection point is. Thanks to floating-point roundoff\n"
|
|
);
|
|
printf(
|
|
" error, Triangle will probably decide that the three segments intersect\n"
|
|
);
|
|
printf(
|
|
" at three different points, and you will find a minuscule triangle in\n");
|
|
printf(
|
|
" your output - unless Triangle tries to refine the tiny triangle, uses\n");
|
|
printf(
|
|
" up the last bit of machine precision, and fails to terminate at all.\n");
|
|
printf(
|
|
" You're better off putting the intersection point in the input files,\n");
|
|
printf(
|
|
" and manually breaking up each segment into two. Similarly, if you\n");
|
|
printf(
|
|
" place a point at the middle of a segment, and hope that Triangle will\n");
|
|
printf(
|
|
" break up the segment at that point, you might get lucky. On the other\n"
|
|
);
|
|
printf(
|
|
" hand, Triangle might decide that the point doesn't lie precisely on the\n"
|
|
);
|
|
printf(
|
|
" line, and you'll have a needle-sharp triangle in your output - or a lot\n"
|
|
);
|
|
printf(" of tiny triangles if you're generating a quality mesh.\n\n");
|
|
printf(
|
|
" When Triangle reads a .poly file, it also writes a .poly file, which\n");
|
|
printf(
|
|
" includes all edges that are part of input segments. If the -c switch\n");
|
|
printf(
|
|
" is used, the output .poly file will also include all of the edges on\n");
|
|
printf(
|
|
" the convex hull. Hence, the output .poly file is useful for finding\n");
|
|
printf(
|
|
" edges associated with input segments and setting boundary conditions in\n"
|
|
);
|
|
printf(
|
|
" finite element simulations. More importantly, you will need it if you\n"
|
|
);
|
|
printf(
|
|
" plan to refine the output mesh, and don't want segments to be missing\n");
|
|
printf(" in later triangulations.\n\n");
|
|
printf(" .area files:\n");
|
|
printf(" First line: <# of triangles>\n");
|
|
printf(" Following lines: <triangle #> <maximum area>\n\n");
|
|
printf(
|
|
" An .area file associates with each triangle a maximum area that is used\n"
|
|
);
|
|
printf(
|
|
" for mesh refinement. As with other file formats, every triangle must\n");
|
|
printf(
|
|
" be represented, and they must be numbered consecutively. A triangle\n");
|
|
printf(
|
|
" may be left unconstrained by assigning it a negative maximum area.\n");
|
|
printf("\n");
|
|
printf(" .edge files:\n");
|
|
printf(" First line: <# of edges> <# of boundary markers (0 or 1)>\n");
|
|
printf(
|
|
" Following lines: <edge #> <endpoint> <endpoint> [boundary marker]\n");
|
|
printf("\n");
|
|
printf(
|
|
" Endpoints are indices into the corresponding .node file. Triangle can\n"
|
|
);
|
|
printf(
|
|
" produce .edge files (use the -e switch), but cannot read them. The\n");
|
|
printf(
|
|
" optional column of boundary markers is suppressed by the -B switch.\n");
|
|
printf("\n");
|
|
printf(
|
|
" In Voronoi diagrams, one also finds a special kind of edge that is an\n");
|
|
printf(
|
|
" infinite ray with only one endpoint. For these edges, a different\n");
|
|
printf(" format is used:\n\n");
|
|
printf(" <edge #> <endpoint> -1 <direction x> <direction y>\n\n");
|
|
printf(
|
|
" The `direction' is a floating-point vector that indicates the direction\n"
|
|
);
|
|
printf(" of the infinite ray.\n\n");
|
|
printf(" .neigh files:\n");
|
|
printf(
|
|
" First line: <# of triangles> <# of neighbors per triangle (always 3)>\n"
|
|
);
|
|
printf(
|
|
" Following lines: <triangle #> <neighbor> <neighbor> <neighbor>\n");
|
|
printf("\n");
|
|
printf(
|
|
" Neighbors are indices into the corresponding .ele file. An index of -1\n"
|
|
);
|
|
printf(
|
|
" indicates a mesh boundary, and therefore no neighbor. Triangle can\n");
|
|
printf(
|
|
" produce .neigh files (use the -n switch), but cannot read them.\n");
|
|
printf("\n");
|
|
printf(
|
|
" The first neighbor of triangle i is opposite the first corner of\n");
|
|
printf(" triangle i, and so on.\n\n");
|
|
printf("Boundary Markers:\n\n");
|
|
printf(
|
|
" Boundary markers are tags used mainly to identify which output points and\n"
|
|
);
|
|
printf(
|
|
" edges are associated with which PSLG segment, and to identify which\n");
|
|
printf(
|
|
" points and edges occur on a boundary of the triangulation. A common use\n"
|
|
);
|
|
printf(
|
|
" is to determine where boundary conditions should be applied to a finite\n");
|
|
printf(
|
|
" element mesh. You can prevent boundary markers from being written into\n");
|
|
printf(" files produced by Triangle by using the -B switch.\n\n");
|
|
printf(
|
|
" The boundary marker associated with each segment in an output .poly file\n"
|
|
);
|
|
printf(" or edge in an output .edge file is chosen as follows:\n");
|
|
printf(
|
|
" - If an output edge is part or all of a PSLG segment with a nonzero\n");
|
|
printf(
|
|
" boundary marker, then the edge is assigned the same marker.\n");
|
|
printf(
|
|
" - Otherwise, if the edge occurs on a boundary of the triangulation\n");
|
|
printf(
|
|
" (including boundaries of holes), then the edge is assigned the marker\n"
|
|
);
|
|
printf(" one (1).\n");
|
|
printf(" - Otherwise, the edge is assigned the marker zero (0).\n");
|
|
printf(
|
|
" The boundary marker associated with each point in an output .node file is\n"
|
|
);
|
|
printf(" chosen as follows:\n");
|
|
printf(
|
|
" - If a point is assigned a nonzero boundary marker in the input file,\n");
|
|
printf(
|
|
" then it is assigned the same marker in the output .node file.\n");
|
|
printf(
|
|
" - Otherwise, if the point lies on a PSLG segment (including the\n");
|
|
printf(
|
|
" segment's endpoints) with a nonzero boundary marker, then the point\n");
|
|
printf(
|
|
" is assigned the same marker. If the point lies on several such\n");
|
|
printf(" segments, one of the markers is chosen arbitrarily.\n");
|
|
printf(
|
|
" - Otherwise, if the point occurs on a boundary of the triangulation,\n");
|
|
printf(" then the point is assigned the marker one (1).\n");
|
|
printf(" - Otherwise, the point is assigned the marker zero (0).\n");
|
|
printf("\n");
|
|
printf(
|
|
" If you want Triangle to determine for you which points and edges are on\n");
|
|
printf(
|
|
" the boundary, assign them the boundary marker zero (or use no markers at\n"
|
|
);
|
|
printf(
|
|
" all) in your input files. Alternatively, you can mark some of them and\n");
|
|
printf(" leave others marked zero, allowing Triangle to label them.\n\n");
|
|
printf("Triangulation Iteration Numbers:\n\n");
|
|
printf(
|
|
" Because Triangle can read and refine its own triangulations, input\n");
|
|
printf(
|
|
" and output files have iteration numbers. For instance, Triangle might\n");
|
|
printf(
|
|
" read the files mesh.3.node, mesh.3.ele, and mesh.3.poly, refine the\n");
|
|
printf(
|
|
" triangulation, and output the files mesh.4.node, mesh.4.ele, and\n");
|
|
printf(" mesh.4.poly. Files with no iteration number are treated as if\n");
|
|
printf(
|
|
" their iteration number is zero; hence, Triangle might read the file\n");
|
|
printf(
|
|
" points.node, triangulate it, and produce the files points.1.node and\n");
|
|
printf(" points.1.ele.\n\n");
|
|
printf(
|
|
" Iteration numbers allow you to create a sequence of successively finer\n");
|
|
printf(
|
|
" meshes suitable for multigrid methods. They also allow you to produce a\n"
|
|
);
|
|
printf(
|
|
" sequence of meshes using error estimate-driven mesh refinement.\n");
|
|
printf("\n");
|
|
printf(
|
|
" If you're not using refinement or quality meshing, and you don't like\n");
|
|
printf(
|
|
" iteration numbers, use the -I switch to disable them. This switch will\n");
|
|
printf(
|
|
" also disable output of .node and .poly files to prevent your input files\n"
|
|
);
|
|
printf(
|
|
" from being overwritten. (If the input is a .poly file that contains its\n"
|
|
);
|
|
printf(" own points, a .node file will be written.)\n\n");
|
|
printf("Examples of How to Use Triangle:\n\n");
|
|
printf(
|
|
" `triangle dots' will read points from dots.node, and write their Delaunay\n"
|
|
);
|
|
printf(
|
|
" triangulation to dots.1.node and dots.1.ele. (dots.1.node will be\n");
|
|
printf(
|
|
" identical to dots.node.) `triangle -I dots' writes the triangulation to\n"
|
|
);
|
|
printf(
|
|
" dots.ele instead. (No additional .node file is needed, so none is\n");
|
|
printf(" written.)\n\n");
|
|
printf(
|
|
" `triangle -pe object.1' will read a PSLG from object.1.poly (and possibly\n"
|
|
);
|
|
printf(
|
|
" object.1.node, if the points are omitted from object.1.poly) and write\n");
|
|
printf(" their constrained Delaunay triangulation to object.2.node and\n");
|
|
printf(
|
|
" object.2.ele. The segments will be copied to object.2.poly, and all\n");
|
|
printf(" edges will be written to object.2.edge.\n\n");
|
|
printf(
|
|
" `triangle -pq31.5a.1 object' will read a PSLG from object.poly (and\n");
|
|
printf(
|
|
" possibly object.node), generate a mesh whose angles are all greater than\n"
|
|
);
|
|
printf(
|
|
" 31.5 degrees and whose triangles all have area smaller than 0.1, and\n");
|
|
printf(
|
|
" write the mesh to object.1.node and object.1.ele. Each segment may have\n"
|
|
);
|
|
printf(
|
|
" been broken up into multiple edges; the resulting constrained edges are\n");
|
|
printf(" written to object.1.poly.\n\n");
|
|
printf(
|
|
" Here is a sample file `box.poly' describing a square with a square hole:\n"
|
|
);
|
|
printf("\n");
|
|
printf(
|
|
" # A box with eight points in 2D, no attributes, one boundary marker.\n");
|
|
printf(" 8 2 0 1\n");
|
|
printf(" # Outer box has these vertices:\n");
|
|
printf(" 1 0 0 0\n");
|
|
printf(" 2 0 3 0\n");
|
|
printf(" 3 3 0 0\n");
|
|
printf(" 4 3 3 33 # A special marker for this point.\n");
|
|
printf(" # Inner square has these vertices:\n");
|
|
printf(" 5 1 1 0\n");
|
|
printf(" 6 1 2 0\n");
|
|
printf(" 7 2 1 0\n");
|
|
printf(" 8 2 2 0\n");
|
|
printf(" # Five segments with boundary markers.\n");
|
|
printf(" 5 1\n");
|
|
printf(" 1 1 2 5 # Left side of outer box.\n");
|
|
printf(" 2 5 7 0 # Segments 2 through 5 enclose the hole.\n");
|
|
printf(" 3 7 8 0\n");
|
|
printf(" 4 8 6 10\n");
|
|
printf(" 5 6 5 0\n");
|
|
printf(" # One hole in the middle of the inner square.\n");
|
|
printf(" 1\n");
|
|
printf(" 1 1.5 1.5\n\n");
|
|
printf(
|
|
" Note that some segments are missing from the outer square, so one must\n");
|
|
printf(
|
|
" use the `-c' switch. After `triangle -pqc box.poly', here is the output\n"
|
|
);
|
|
printf(
|
|
" file `box.1.node', with twelve points. The last four points were added\n");
|
|
printf(
|
|
" to meet the angle constraint. Points 1, 2, and 9 have markers from\n");
|
|
printf(
|
|
" segment 1. Points 6 and 8 have markers from segment 4. All the other\n");
|
|
printf(
|
|
" points but 4 have been marked to indicate that they lie on a boundary.\n");
|
|
printf("\n");
|
|
printf(" 12 2 0 1\n");
|
|
printf(" 1 0 0 5\n");
|
|
printf(" 2 0 3 5\n");
|
|
printf(" 3 3 0 1\n");
|
|
printf(" 4 3 3 33\n");
|
|
printf(" 5 1 1 1\n");
|
|
printf(" 6 1 2 10\n");
|
|
printf(" 7 2 1 1\n");
|
|
printf(" 8 2 2 10\n");
|
|
printf(" 9 0 1.5 5\n");
|
|
printf(" 10 1.5 0 1\n");
|
|
printf(" 11 3 1.5 1\n");
|
|
printf(" 12 1.5 3 1\n");
|
|
printf(" # Generated by triangle -pqc box.poly\n\n");
|
|
printf(" Here is the output file `box.1.ele', with twelve triangles.\n\n");
|
|
printf(" 12 3 0\n");
|
|
printf(" 1 5 6 9\n");
|
|
printf(" 2 10 3 7\n");
|
|
printf(" 3 6 8 12\n");
|
|
printf(" 4 9 1 5\n");
|
|
printf(" 5 6 2 9\n");
|
|
printf(" 6 7 3 11\n");
|
|
printf(" 7 11 4 8\n");
|
|
printf(" 8 7 5 10\n");
|
|
printf(" 9 12 2 6\n");
|
|
printf(" 10 8 7 11\n");
|
|
printf(" 11 5 1 10\n");
|
|
printf(" 12 8 4 12\n");
|
|
printf(" # Generated by triangle -pqc box.poly\n\n");
|
|
printf(
|
|
" Here is the output file `box.1.poly'. Note that segments have been added\n"
|
|
);
|
|
printf(
|
|
" to represent the convex hull, and some segments have been split by newly\n"
|
|
);
|
|
printf(
|
|
" added points. Note also that <# of points> is set to zero to indicate\n");
|
|
printf(" that the points should be read from the .node file.\n\n");
|
|
printf(" 0 2 0 1\n");
|
|
printf(" 12 1\n");
|
|
printf(" 1 1 9 5\n");
|
|
printf(" 2 5 7 1\n");
|
|
printf(" 3 8 7 1\n");
|
|
printf(" 4 6 8 10\n");
|
|
printf(" 5 5 6 1\n");
|
|
printf(" 6 3 10 1\n");
|
|
printf(" 7 4 11 1\n");
|
|
printf(" 8 2 12 1\n");
|
|
printf(" 9 9 2 5\n");
|
|
printf(" 10 10 1 1\n");
|
|
printf(" 11 11 3 1\n");
|
|
printf(" 12 12 4 1\n");
|
|
printf(" 1\n");
|
|
printf(" 1 1.5 1.5\n");
|
|
printf(" # Generated by triangle -pqc box.poly\n\n");
|
|
printf("Refinement and Area Constraints:\n\n");
|
|
printf(
|
|
" The -r switch causes a mesh (.node and .ele files) to be read and\n");
|
|
printf(
|
|
" refined. If the -p switch is also used, a .poly file is read and used to\n"
|
|
);
|
|
printf(
|
|
" specify edges that are constrained and cannot be eliminated (although\n");
|
|
printf(
|
|
" they can be divided into smaller edges) by the refinement process.\n");
|
|
printf("\n");
|
|
printf(
|
|
" When you refine a mesh, you generally want to impose tighter quality\n");
|
|
printf(
|
|
" constraints. One way to accomplish this is to use -q with a larger\n");
|
|
printf(
|
|
" angle, or -a followed by a smaller area than you used to generate the\n");
|
|
printf(
|
|
" mesh you are refining. Another way to do this is to create an .area\n");
|
|
printf(
|
|
" file, which specifies a maximum area for each triangle, and use the -a\n");
|
|
printf(
|
|
" switch (without a number following). Each triangle's area constraint is\n"
|
|
);
|
|
printf(
|
|
" applied to that triangle. Area constraints tend to diffuse as the mesh\n");
|
|
printf(
|
|
" is refined, so if there are large variations in area constraint between\n");
|
|
printf(" adjacent triangles, you may not get the results you want.\n\n");
|
|
printf(
|
|
" If you are refining a mesh composed of linear (three-node) elements, the\n"
|
|
);
|
|
printf(
|
|
" output mesh will contain all the nodes present in the input mesh, in the\n"
|
|
);
|
|
printf(
|
|
" same order, with new nodes added at the end of the .node file. However,\n"
|
|
);
|
|
printf(
|
|
" there is no guarantee that each output element is contained in a single\n");
|
|
printf(
|
|
" input element. Often, output elements will overlap two input elements,\n");
|
|
printf(
|
|
" and input edges are not present in the output mesh. Hence, a sequence of\n"
|
|
);
|
|
printf(
|
|
" refined meshes will form a hierarchy of nodes, but not a hierarchy of\n");
|
|
printf(
|
|
" elements. If you a refining a mesh of higher-order elements, the\n");
|
|
printf(
|
|
" hierarchical property applies only to the nodes at the corners of an\n");
|
|
printf(" element; other nodes may not be present in the refined mesh.\n\n");
|
|
printf(
|
|
" It is important to understand that maximum area constraints in .poly\n");
|
|
printf(
|
|
" files are handled differently from those in .area files. A maximum area\n"
|
|
);
|
|
printf(
|
|
" in a .poly file applies to the whole (segment-bounded) region in which a\n"
|
|
);
|
|
printf(
|
|
" point falls, whereas a maximum area in an .area file applies to only one\n"
|
|
);
|
|
printf(
|
|
" triangle. Area constraints in .poly files are used only when a mesh is\n");
|
|
printf(
|
|
" first generated, whereas area constraints in .area files are used only to\n"
|
|
);
|
|
printf(
|
|
" refine an existing mesh, and are typically based on a posteriori error\n");
|
|
printf(
|
|
" estimates resulting from a finite element simulation on that mesh.\n");
|
|
printf("\n");
|
|
printf(
|
|
" `triangle -rq25 object.1' will read object.1.node and object.1.ele, then\n"
|
|
);
|
|
printf(
|
|
" refine the triangulation to enforce a 25 degree minimum angle, and then\n");
|
|
printf(
|
|
" write the refined triangulation to object.2.node and object.2.ele.\n");
|
|
printf("\n");
|
|
printf(
|
|
" `triangle -rpaa6.2 z.3' will read z.3.node, z.3.ele, z.3.poly, and\n");
|
|
printf(
|
|
" z.3.area. After reconstructing the mesh and its segments, Triangle will\n"
|
|
);
|
|
printf(
|
|
" refine the mesh so that no triangle has area greater than 6.2, and\n");
|
|
printf(
|
|
" furthermore the triangles satisfy the maximum area constraints in\n");
|
|
printf(
|
|
" z.3.area. The output is written to z.4.node, z.4.ele, and z.4.poly.\n");
|
|
printf("\n");
|
|
printf(
|
|
" The sequence `triangle -qa1 x', `triangle -rqa.3 x.1', `triangle -rqa.1\n");
|
|
printf(
|
|
" x.2' creates a sequence of successively finer meshes x.1, x.2, and x.3,\n");
|
|
printf(" suitable for multigrid.\n\n");
|
|
printf("Convex Hulls and Mesh Boundaries:\n\n");
|
|
printf(
|
|
" If the input is a point set (rather than a PSLG), Triangle produces its\n");
|
|
printf(
|
|
" convex hull as a by-product in the output .poly file if you use the -c\n");
|
|
printf(
|
|
" switch. There are faster algorithms for finding a two-dimensional convex\n"
|
|
);
|
|
printf(
|
|
" hull than triangulation, of course, but this one comes for free. If the\n"
|
|
);
|
|
printf(
|
|
" input is an unconstrained mesh (you are using the -r switch but not the\n");
|
|
printf(
|
|
" -p switch), Triangle produces a list of its boundary edges (including\n");
|
|
printf(" hole boundaries) as a by-product if you use the -c switch.\n\n");
|
|
printf("Voronoi Diagrams:\n\n");
|
|
printf(
|
|
" The -v switch produces a Voronoi diagram, in files suffixed .v.node and\n");
|
|
printf(
|
|
" .v.edge. For example, `triangle -v points' will read points.node,\n");
|
|
printf(
|
|
" produce its Delaunay triangulation in points.1.node and points.1.ele,\n");
|
|
printf(
|
|
" and produce its Voronoi diagram in points.1.v.node and points.1.v.edge.\n");
|
|
printf(
|
|
" The .v.node file contains a list of all Voronoi vertices, and the .v.edge\n"
|
|
);
|
|
printf(
|
|
" file contains a list of all Voronoi edges, some of which may be infinite\n"
|
|
);
|
|
printf(
|
|
" rays. (The choice of filenames makes it easy to run the set of Voronoi\n");
|
|
printf(" vertices through Triangle, if so desired.)\n\n");
|
|
printf(
|
|
" This implementation does not use exact arithmetic to compute the Voronoi\n"
|
|
);
|
|
printf(
|
|
" vertices, and does not check whether neighboring vertices are identical.\n"
|
|
);
|
|
printf(
|
|
" Be forewarned that if the Delaunay triangulation is degenerate or\n");
|
|
printf(
|
|
" near-degenerate, the Voronoi diagram may have duplicate points, crossing\n"
|
|
);
|
|
printf(
|
|
" edges, or infinite rays whose direction vector is zero. Also, if you\n");
|
|
printf(
|
|
" generate a constrained (as opposed to conforming) Delaunay triangulation,\n"
|
|
);
|
|
printf(
|
|
" or if the triangulation has holes, the corresponding Voronoi diagram is\n");
|
|
printf(" likely to have crossing edges and unlikely to make sense.\n\n");
|
|
printf("Mesh Topology:\n\n");
|
|
printf(
|
|
" You may wish to know which triangles are adjacent to a certain Delaunay\n");
|
|
printf(
|
|
" edge in an .edge file, which Voronoi regions are adjacent to a certain\n");
|
|
printf(
|
|
" Voronoi edge in a .v.edge file, or which Voronoi regions are adjacent to\n"
|
|
);
|
|
printf(
|
|
" each other. All of this information can be found by cross-referencing\n");
|
|
printf(
|
|
" output files with the recollection that the Delaunay triangulation and\n");
|
|
printf(" the Voronoi diagrams are planar duals.\n\n");
|
|
printf(
|
|
" Specifically, edge i of an .edge file is the dual of Voronoi edge i of\n");
|
|
printf(
|
|
" the corresponding .v.edge file, and is rotated 90 degrees counterclock-\n");
|
|
printf(
|
|
" wise from the Voronoi edge. Triangle j of an .ele file is the dual of\n");
|
|
printf(
|
|
" vertex j of the corresponding .v.node file; and Voronoi region k is the\n");
|
|
printf(" dual of point k of the corresponding .node file.\n\n");
|
|
printf(
|
|
" Hence, to find the triangles adjacent to a Delaunay edge, look at the\n");
|
|
printf(
|
|
" vertices of the corresponding Voronoi edge; their dual triangles are on\n");
|
|
printf(
|
|
" the left and right of the Delaunay edge, respectively. To find the\n");
|
|
printf(
|
|
" Voronoi regions adjacent to a Voronoi edge, look at the endpoints of the\n"
|
|
);
|
|
printf(
|
|
" corresponding Delaunay edge; their dual regions are on the right and left\n"
|
|
);
|
|
printf(
|
|
" of the Voronoi edge, respectively. To find which Voronoi regions are\n");
|
|
printf(" adjacent to each other, just read the list of Delaunay edges.\n");
|
|
printf("\n");
|
|
printf("Statistics:\n");
|
|
printf("\n");
|
|
printf(
|
|
" After generating a mesh, Triangle prints a count of the number of points,\n"
|
|
);
|
|
printf(
|
|
" triangles, edges, boundary edges, and segments in the output mesh. If\n");
|
|
printf(
|
|
" you've forgotten the statistics for an existing mesh, the -rNEP switches\n"
|
|
);
|
|
printf(
|
|
" (or -rpNEP if you've got a .poly file for the existing mesh) will\n");
|
|
printf(" regenerate these statistics without writing any output.\n\n");
|
|
printf(
|
|
" The -V switch produces extended statistics, including a rough estimate\n");
|
|
printf(
|
|
" of memory use and a histogram of triangle aspect ratios and angles in the\n"
|
|
);
|
|
printf(" mesh.\n\n");
|
|
printf("Exact Arithmetic:\n\n");
|
|
printf(
|
|
" Triangle uses adaptive exact arithmetic to perform what computational\n");
|
|
printf(
|
|
" geometers call the `orientation' and `incircle' tests. If the floating-\n"
|
|
);
|
|
printf(
|
|
" point arithmetic of your machine conforms to the IEEE 754 standard (as\n");
|
|
printf(
|
|
" most workstations do), and does not use extended precision internal\n");
|
|
printf(
|
|
" registers, then your output is guaranteed to be an absolutely true\n");
|
|
printf(" Delaunay or conforming Delaunay triangulation, roundoff error\n");
|
|
printf(
|
|
" notwithstanding. The word `adaptive' implies that these arithmetic\n");
|
|
printf(
|
|
" routines compute the result only to the precision necessary to guarantee\n"
|
|
);
|
|
printf(
|
|
" correctness, so they are usually nearly as fast as their approximate\n");
|
|
printf(
|
|
" counterparts. The exact tests can be disabled with the -X switch. On\n");
|
|
printf(
|
|
" most inputs, this switch will reduce the computation time by about eight\n"
|
|
);
|
|
printf(
|
|
" percent - it's not worth the risk. There are rare difficult inputs\n");
|
|
printf(
|
|
" (having many collinear and cocircular points), however, for which the\n");
|
|
printf(
|
|
" difference could be a factor of two. These are precisely the inputs most\n"
|
|
);
|
|
printf(" likely to cause errors if you use the -X switch.\n\n");
|
|
printf(
|
|
" Unfortunately, these routines don't solve every numerical problem. Exact\n"
|
|
);
|
|
printf(
|
|
" arithmetic is not used to compute the positions of points, because the\n");
|
|
printf(
|
|
" bit complexity of point coordinates would grow without bound. Hence,\n");
|
|
printf(
|
|
" segment intersections aren't computed exactly; in very unusual cases,\n");
|
|
printf(
|
|
" roundoff error in computing an intersection point might actually lead to\n"
|
|
);
|
|
printf(
|
|
" an inverted triangle and an invalid triangulation. (This is one reason\n");
|
|
printf(
|
|
" to compute your own intersection points in your .poly files.) Similarly,\n"
|
|
);
|
|
printf(
|
|
" exact arithmetic is not used to compute the vertices of the Voronoi\n");
|
|
printf(" diagram.\n\n");
|
|
printf(
|
|
" Underflow and overflow can also cause difficulties; the exact arithmetic\n"
|
|
);
|
|
printf(
|
|
" routines do not ameliorate out-of-bounds exponents, which can arise\n");
|
|
printf(
|
|
" during the orientation and incircle tests. As a rule of thumb, you\n");
|
|
printf(
|
|
" should ensure that your input values are within a range such that their\n");
|
|
printf(
|
|
" third powers can be taken without underflow or overflow. Underflow can\n");
|
|
printf(
|
|
" silently prevent the tests from being performed exactly, while overflow\n");
|
|
printf(" will typically cause a floating exception.\n\n");
|
|
printf("Calling Triangle from Another Program:\n\n");
|
|
printf(" Read the file triangle.h for details.\n\n");
|
|
printf("Troubleshooting:\n\n");
|
|
printf(" Please read this section before mailing me bugs.\n\n");
|
|
printf(" `My output mesh has no triangles!'\n\n");
|
|
printf(
|
|
" If you're using a PSLG, you've probably failed to specify a proper set\n"
|
|
);
|
|
printf(
|
|
" of bounding segments, or forgotten to use the -c switch. Or you may\n");
|
|
printf(
|
|
" have placed a hole badly. To test these possibilities, try again with\n"
|
|
);
|
|
printf(
|
|
" the -c and -O switches. Alternatively, all your input points may be\n");
|
|
printf(
|
|
" collinear, in which case you can hardly expect to triangulate them.\n");
|
|
printf("\n");
|
|
printf(" `Triangle doesn't terminate, or just crashes.'\n");
|
|
printf("\n");
|
|
printf(
|
|
" Bad things can happen when triangles get so small that the distance\n");
|
|
printf(
|
|
" between their vertices isn't much larger than the precision of your\n");
|
|
printf(
|
|
" machine's arithmetic. If you've compiled Triangle for single-precision\n"
|
|
);
|
|
printf(
|
|
" arithmetic, you might do better by recompiling it for double-precision.\n"
|
|
);
|
|
printf(
|
|
" Then again, you might just have to settle for more lenient constraints\n"
|
|
);
|
|
printf(
|
|
" on the minimum angle and the maximum area than you had planned.\n");
|
|
printf("\n");
|
|
printf(
|
|
" You can minimize precision problems by ensuring that the origin lies\n");
|
|
printf(
|
|
" inside your point set, or even inside the densest part of your\n");
|
|
printf(
|
|
" mesh. On the other hand, if you're triangulating an object whose x\n");
|
|
printf(
|
|
" coordinates all fall between 6247133 and 6247134, you're not leaving\n");
|
|
printf(" much floating-point precision for Triangle to work with.\n\n");
|
|
printf(
|
|
" Precision problems can occur covertly if the input PSLG contains two\n");
|
|
printf(
|
|
" segments that meet (or intersect) at a very small angle, or if such an\n"
|
|
);
|
|
printf(
|
|
" angle is introduced by the -c switch, which may occur if a point lies\n");
|
|
printf(
|
|
" ever-so-slightly inside the convex hull, and is connected by a PSLG\n");
|
|
printf(
|
|
" segment to a point on the convex hull. If you don't realize that a\n");
|
|
printf(
|
|
" small angle is being formed, you might never discover why Triangle is\n");
|
|
printf(
|
|
" crashing. To check for this possibility, use the -S switch (with an\n");
|
|
printf(
|
|
" appropriate limit on the number of Steiner points, found by trial-and-\n"
|
|
);
|
|
printf(
|
|
" error) to stop Triangle early, and view the output .poly file with\n");
|
|
printf(
|
|
" Show Me (described below). Look carefully for small angles between\n");
|
|
printf(
|
|
" segments; zoom in closely, as such segments might look like a single\n");
|
|
printf(" segment from a distance.\n\n");
|
|
printf(
|
|
" If some of the input values are too large, Triangle may suffer a\n");
|
|
printf(
|
|
" floating exception due to overflow when attempting to perform an\n");
|
|
printf(
|
|
" orientation or incircle test. (Read the section on exact arithmetic\n");
|
|
printf(
|
|
" above.) Again, I recommend compiling Triangle for double (rather\n");
|
|
printf(" than single) precision arithmetic.\n\n");
|
|
printf(
|
|
" `The numbering of the output points doesn't match the input points.'\n");
|
|
printf("\n");
|
|
printf(
|
|
" You may have eaten some of your input points with a hole, or by placing\n"
|
|
);
|
|
printf(" them outside the area enclosed by segments.\n\n");
|
|
printf(
|
|
" `Triangle executes without incident, but when I look at the resulting\n");
|
|
printf(
|
|
" mesh, it has overlapping triangles or other geometric inconsistencies.'\n");
|
|
printf("\n");
|
|
printf(
|
|
" If you select the -X switch, Triangle's divide-and-conquer Delaunay\n");
|
|
printf(
|
|
" triangulation algorithm occasionally makes mistakes due to floating-\n");
|
|
printf(
|
|
" point roundoff error. Although these errors are rare, don't use the -X\n"
|
|
);
|
|
printf(" switch. If you still have problems, please report the bug.\n");
|
|
printf("\n");
|
|
printf(
|
|
" Strange things can happen if you've taken liberties with your PSLG. Do\n");
|
|
printf(
|
|
" you have a point lying in the middle of a segment? Triangle sometimes\n");
|
|
printf(
|
|
" copes poorly with that sort of thing. Do you want to lay out a collinear\n"
|
|
);
|
|
printf(
|
|
" row of evenly spaced, segment-connected points? Have you simply defined\n"
|
|
);
|
|
printf(
|
|
" one long segment connecting the leftmost point to the rightmost point,\n");
|
|
printf(
|
|
" and a bunch of points lying along it? This method occasionally works,\n");
|
|
printf(
|
|
" especially with horizontal and vertical lines, but often it doesn't, and\n"
|
|
);
|
|
printf(
|
|
" you'll have to connect each adjacent pair of points with a separate\n");
|
|
printf(" segment. If you don't like it, tough.\n\n");
|
|
printf(
|
|
" Furthermore, if you have segments that intersect other than at their\n");
|
|
printf(
|
|
" endpoints, try not to let the intersections fall extremely close to PSLG\n"
|
|
);
|
|
printf(" points or each other.\n\n");
|
|
printf(
|
|
" If you have problems refining a triangulation not produced by Triangle:\n");
|
|
printf(
|
|
" Are you sure the triangulation is geometrically valid? Is it formatted\n");
|
|
printf(
|
|
" correctly for Triangle? Are the triangles all listed so the first three\n"
|
|
);
|
|
printf(" points are their corners in counterclockwise order?\n\n");
|
|
printf("Show Me:\n\n");
|
|
printf(
|
|
" Triangle comes with a separate program named `Show Me', whose primary\n");
|
|
printf(
|
|
" purpose is to draw meshes on your screen or in PostScript. Its secondary\n"
|
|
);
|
|
printf(
|
|
" purpose is to check the validity of your input files, and do so more\n");
|
|
printf(
|
|
" thoroughly than Triangle does. Show Me requires that you have the X\n");
|
|
printf(
|
|
" Windows system. If you didn't receive Show Me with Triangle, complain to\n"
|
|
);
|
|
printf(" whomever you obtained Triangle from, then send me mail.\n\n");
|
|
printf("Triangle on the Web:\n\n");
|
|
printf(
|
|
" To see an illustrated, updated version of these instructions, check out\n");
|
|
printf("\n");
|
|
printf(" http://www.cs.cmu.edu/~quake/triangle.html\n");
|
|
printf("\n");
|
|
printf("A Brief Plea:\n");
|
|
printf("\n");
|
|
printf(
|
|
" If you use Triangle, and especially if you use it to accomplish real\n");
|
|
printf(
|
|
" work, I would like very much to hear from you. A short letter or email\n");
|
|
printf(
|
|
" (to jrs@cs.cmu.edu) describing how you use Triangle will mean a lot to\n");
|
|
printf(
|
|
" me. The more people I know are using this program, the more easily I can\n"
|
|
);
|
|
printf(
|
|
" justify spending time on improvements and on the three-dimensional\n");
|
|
printf(
|
|
" successor to Triangle, which in turn will benefit you. Also, I can put\n");
|
|
printf(
|
|
" you on a list to receive email whenever a new version of Triangle is\n");
|
|
printf(" available.\n\n");
|
|
printf(
|
|
" If you use a mesh generated by Triangle in a publication, please include\n"
|
|
);
|
|
printf(" an acknowledgment as well.\n\n");
|
|
printf("Research credit:\n\n");
|
|
printf(
|
|
" Of course, I can take credit for only a fraction of the ideas that made\n");
|
|
printf(
|
|
" this mesh generator possible. Triangle owes its existence to the efforts\n"
|
|
);
|
|
printf(
|
|
" of many fine computational geometers and other researchers, including\n");
|
|
printf(
|
|
" Marshall Bern, L. Paul Chew, Boris Delaunay, Rex A. Dwyer, David\n");
|
|
printf(
|
|
" Eppstein, Steven Fortune, Leonidas J. Guibas, Donald E. Knuth, C. L.\n");
|
|
printf(
|
|
" Lawson, Der-Tsai Lee, Ernst P. Mucke, Douglas M. Priest, Jim Ruppert,\n");
|
|
printf(
|
|
" Isaac Saias, Bruce J. Schachter, Micha Sharir, Jorge Stolfi, Christopher\n"
|
|
);
|
|
printf(
|
|
" J. Van Wyk, David F. Watson, and Binhai Zhu. See the comments at the\n");
|
|
printf(" beginning of the source code for references.\n\n");
|
|
exit(0);
|
|
}
|
|
|
|
#endif /* not TRILIBRARY */
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* internalerror() Ask the user to send me the defective product. Exit. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
void internalerror()
|
|
{
|
|
printf(" Please report this bug to jrs@cs.cmu.edu\n");
|
|
printf(" Include the message above, your input data set, and the exact\n");
|
|
printf(" command line you used to run Triangle.\n");
|
|
exit(1);
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* parsecommandline() Read the command line, identify switches, and set */
|
|
/* up options and file names. */
|
|
/* */
|
|
/* The effects of this routine are felt entirely through global variables. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
void parsecommandline(argc, argv)
|
|
int argc;
|
|
char **argv;
|
|
{
|
|
#ifdef TRILIBRARY
|
|
#define STARTINDEX 0
|
|
#else /* not TRILIBRARY */
|
|
#define STARTINDEX 1
|
|
int increment;
|
|
int meshnumber;
|
|
#endif /* not TRILIBRARY */
|
|
int i, j;
|
|
#ifndef CDT_ONLY
|
|
int k;
|
|
char workstring[FILENAMESIZE];
|
|
#endif
|
|
|
|
poly = refine = quality = vararea = fixedarea = regionattrib = convex = 0;
|
|
firstnumber = 1;
|
|
edgesout = voronoi = neighbors = geomview = 0;
|
|
nobound = nopolywritten = nonodewritten = noelewritten = noiterationnum = 0;
|
|
noholes = noexact = 0;
|
|
incremental = sweepline = 0;
|
|
dwyer = 1;
|
|
splitseg = 0;
|
|
docheck = 0;
|
|
nobisect = 0;
|
|
steiner = -1;
|
|
order = 1;
|
|
minangle = 0.0;
|
|
maxarea = -1.0;
|
|
quiet = verbose = 0;
|
|
#ifndef TRILIBRARY
|
|
innodefilename[0] = '\0';
|
|
#endif /* not TRILIBRARY */
|
|
|
|
for (i = STARTINDEX; i < argc; i++) {
|
|
#ifndef TRILIBRARY
|
|
if (argv[i][0] == '-') {
|
|
#endif /* not TRILIBRARY */
|
|
for (j = STARTINDEX; argv[i][j] != '\0'; j++) {
|
|
if (argv[i][j] == 'p') {
|
|
poly = 1;
|
|
}
|
|
#ifndef CDT_ONLY
|
|
if (argv[i][j] == 'r') {
|
|
refine = 1;
|
|
}
|
|
if (argv[i][j] == 'q') {
|
|
quality = 1;
|
|
if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
|
|
(argv[i][j + 1] == '.')) {
|
|
k = 0;
|
|
while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
|
|
(argv[i][j + 1] == '.')) {
|
|
j++;
|
|
workstring[k] = argv[i][j];
|
|
k++;
|
|
}
|
|
workstring[k] = '\0';
|
|
minangle = (REAL) strtod(workstring, (char **) NULL);
|
|
} else {
|
|
minangle = 20.0;
|
|
}
|
|
}
|
|
if (argv[i][j] == 'a') {
|
|
quality = 1;
|
|
if (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
|
|
(argv[i][j + 1] == '.')) {
|
|
fixedarea = 1;
|
|
k = 0;
|
|
while (((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) ||
|
|
(argv[i][j + 1] == '.')) {
|
|
j++;
|
|
workstring[k] = argv[i][j];
|
|
k++;
|
|
}
|
|
workstring[k] = '\0';
|
|
maxarea = (REAL) strtod(workstring, (char **) NULL);
|
|
if (maxarea <= 0.0) {
|
|
printf("Error: Maximum area must be greater than zero.\n");
|
|
exit(1);
|
|
}
|
|
} else {
|
|
vararea = 1;
|
|
}
|
|
}
|
|
#endif /* not CDT_ONLY */
|
|
if (argv[i][j] == 'A') {
|
|
regionattrib = 1;
|
|
}
|
|
if (argv[i][j] == 'c') {
|
|
convex = 1;
|
|
}
|
|
if (argv[i][j] == 'z') {
|
|
firstnumber = 0;
|
|
}
|
|
if (argv[i][j] == 'e') {
|
|
edgesout = 1;
|
|
}
|
|
if (argv[i][j] == 'v') {
|
|
voronoi = 1;
|
|
}
|
|
if (argv[i][j] == 'n') {
|
|
neighbors = 1;
|
|
}
|
|
if (argv[i][j] == 'g') {
|
|
geomview = 1;
|
|
}
|
|
if (argv[i][j] == 'B') {
|
|
nobound = 1;
|
|
}
|
|
if (argv[i][j] == 'P') {
|
|
nopolywritten = 1;
|
|
}
|
|
if (argv[i][j] == 'N') {
|
|
nonodewritten = 1;
|
|
}
|
|
if (argv[i][j] == 'E') {
|
|
noelewritten = 1;
|
|
}
|
|
#ifndef TRILIBRARY
|
|
if (argv[i][j] == 'I') {
|
|
noiterationnum = 1;
|
|
}
|
|
#endif /* not TRILIBRARY */
|
|
if (argv[i][j] == 'O') {
|
|
noholes = 1;
|
|
}
|
|
if (argv[i][j] == 'X') {
|
|
noexact = 1;
|
|
}
|
|
if (argv[i][j] == 'o') {
|
|
if (argv[i][j + 1] == '2') {
|
|
j++;
|
|
order = 2;
|
|
}
|
|
}
|
|
#ifndef CDT_ONLY
|
|
if (argv[i][j] == 'Y') {
|
|
nobisect++;
|
|
}
|
|
if (argv[i][j] == 'S') {
|
|
steiner = 0;
|
|
while ((argv[i][j + 1] >= '0') && (argv[i][j + 1] <= '9')) {
|
|
j++;
|
|
steiner = steiner * 10 + (int) (argv[i][j] - '0');
|
|
}
|
|
}
|
|
#endif /* not CDT_ONLY */
|
|
#ifndef REDUCED
|
|
if (argv[i][j] == 'i') {
|
|
incremental = 1;
|
|
}
|
|
if (argv[i][j] == 'F') {
|
|
sweepline = 1;
|
|
}
|
|
#endif /* not REDUCED */
|
|
if (argv[i][j] == 'l') {
|
|
dwyer = 0;
|
|
}
|
|
#ifndef REDUCED
|
|
#ifndef CDT_ONLY
|
|
if (argv[i][j] == 's') {
|
|
splitseg = 1;
|
|
}
|
|
#endif /* not CDT_ONLY */
|
|
if (argv[i][j] == 'C') {
|
|
docheck = 1;
|
|
}
|
|
#endif /* not REDUCED */
|
|
if (argv[i][j] == 'Q') {
|
|
quiet = 1;
|
|
}
|
|
if (argv[i][j] == 'V') {
|
|
verbose++;
|
|
}
|
|
#ifndef TRILIBRARY
|
|
if ((argv[i][j] == 'h') || (argv[i][j] == 'H') ||
|
|
(argv[i][j] == '?')) {
|
|
info();
|
|
}
|
|
#endif /* not TRILIBRARY */
|
|
}
|
|
#ifndef TRILIBRARY
|
|
} else {
|
|
strncpy(innodefilename, argv[i], FILENAMESIZE - 1);
|
|
innodefilename[FILENAMESIZE - 1] = '\0';
|
|
}
|
|
#endif /* not TRILIBRARY */
|
|
}
|
|
#ifndef TRILIBRARY
|
|
if (innodefilename[0] == '\0') {
|
|
syntax();
|
|
}
|
|
if (!strcmp(&innodefilename[strlen(innodefilename) - 5], ".node")) {
|
|
innodefilename[strlen(innodefilename) - 5] = '\0';
|
|
}
|
|
if (!strcmp(&innodefilename[strlen(innodefilename) - 5], ".poly")) {
|
|
innodefilename[strlen(innodefilename) - 5] = '\0';
|
|
poly = 1;
|
|
}
|
|
#ifndef CDT_ONLY
|
|
if (!strcmp(&innodefilename[strlen(innodefilename) - 4], ".ele")) {
|
|
innodefilename[strlen(innodefilename) - 4] = '\0';
|
|
refine = 1;
|
|
}
|
|
if (!strcmp(&innodefilename[strlen(innodefilename) - 5], ".area")) {
|
|
innodefilename[strlen(innodefilename) - 5] = '\0';
|
|
refine = 1;
|
|
quality = 1;
|
|
vararea = 1;
|
|
}
|
|
#endif /* not CDT_ONLY */
|
|
#endif /* not TRILIBRARY */
|
|
steinerleft = steiner;
|
|
useshelles = poly || refine || quality || convex;
|
|
goodangle = (REAL)cos(minangle * PI / 180.0);
|
|
goodangle *= goodangle;
|
|
if (refine && noiterationnum) {
|
|
printf(
|
|
"Error: You cannot use the -I switch when refining a triangulation.\n");
|
|
exit(1);
|
|
}
|
|
/* Be careful not to allocate space for element area constraints that */
|
|
/* will never be assigned any value (other than the default -1.0). */
|
|
if (!refine && !poly) {
|
|
vararea = 0;
|
|
}
|
|
/* Be careful not to add an extra attribute to each element unless the */
|
|
/* input supports it (PSLG in, but not refining a preexisting mesh). */
|
|
if (refine || !poly) {
|
|
regionattrib = 0;
|
|
}
|
|
|
|
#ifndef TRILIBRARY
|
|
strcpy(inpolyfilename, innodefilename);
|
|
strcpy(inelefilename, innodefilename);
|
|
strcpy(areafilename, innodefilename);
|
|
increment = 0;
|
|
strcpy(workstring, innodefilename);
|
|
j = 1;
|
|
while (workstring[j] != '\0') {
|
|
if ((workstring[j] == '.') && (workstring[j + 1] != '\0')) {
|
|
increment = j + 1;
|
|
}
|
|
j++;
|
|
}
|
|
meshnumber = 0;
|
|
if (increment > 0) {
|
|
j = increment;
|
|
do {
|
|
if ((workstring[j] >= '0') && (workstring[j] <= '9')) {
|
|
meshnumber = meshnumber * 10 + (int) (workstring[j] - '0');
|
|
} else {
|
|
increment = 0;
|
|
}
|
|
j++;
|
|
} while (workstring[j] != '\0');
|
|
}
|
|
if (noiterationnum) {
|
|
strcpy(outnodefilename, innodefilename);
|
|
strcpy(outelefilename, innodefilename);
|
|
strcpy(edgefilename, innodefilename);
|
|
strcpy(vnodefilename, innodefilename);
|
|
strcpy(vedgefilename, innodefilename);
|
|
strcpy(neighborfilename, innodefilename);
|
|
strcpy(offfilename, innodefilename);
|
|
strcat(outnodefilename, ".node");
|
|
strcat(outelefilename, ".ele");
|
|
strcat(edgefilename, ".edge");
|
|
strcat(vnodefilename, ".v.node");
|
|
strcat(vedgefilename, ".v.edge");
|
|
strcat(neighborfilename, ".neigh");
|
|
strcat(offfilename, ".off");
|
|
} else if (increment == 0) {
|
|
strcpy(outnodefilename, innodefilename);
|
|
strcpy(outpolyfilename, innodefilename);
|
|
strcpy(outelefilename, innodefilename);
|
|
strcpy(edgefilename, innodefilename);
|
|
strcpy(vnodefilename, innodefilename);
|
|
strcpy(vedgefilename, innodefilename);
|
|
strcpy(neighborfilename, innodefilename);
|
|
strcpy(offfilename, innodefilename);
|
|
strcat(outnodefilename, ".1.node");
|
|
strcat(outpolyfilename, ".1.poly");
|
|
strcat(outelefilename, ".1.ele");
|
|
strcat(edgefilename, ".1.edge");
|
|
strcat(vnodefilename, ".1.v.node");
|
|
strcat(vedgefilename, ".1.v.edge");
|
|
strcat(neighborfilename, ".1.neigh");
|
|
strcat(offfilename, ".1.off");
|
|
} else {
|
|
workstring[increment] = '%';
|
|
workstring[increment + 1] = 'd';
|
|
workstring[increment + 2] = '\0';
|
|
sprintf(outnodefilename, workstring, meshnumber + 1);
|
|
strcpy(outpolyfilename, outnodefilename);
|
|
strcpy(outelefilename, outnodefilename);
|
|
strcpy(edgefilename, outnodefilename);
|
|
strcpy(vnodefilename, outnodefilename);
|
|
strcpy(vedgefilename, outnodefilename);
|
|
strcpy(neighborfilename, outnodefilename);
|
|
strcpy(offfilename, outnodefilename);
|
|
strcat(outnodefilename, ".node");
|
|
strcat(outpolyfilename, ".poly");
|
|
strcat(outelefilename, ".ele");
|
|
strcat(edgefilename, ".edge");
|
|
strcat(vnodefilename, ".v.node");
|
|
strcat(vedgefilename, ".v.edge");
|
|
strcat(neighborfilename, ".neigh");
|
|
strcat(offfilename, ".off");
|
|
}
|
|
strcat(innodefilename, ".node");
|
|
strcat(inpolyfilename, ".poly");
|
|
strcat(inelefilename, ".ele");
|
|
strcat(areafilename, ".area");
|
|
#endif /* not TRILIBRARY */
|
|
}
|
|
|
|
/** **/
|
|
/** **/
|
|
/********* User interaction routines begin here *********/
|
|
|
|
/********* Debugging routines begin here *********/
|
|
/** **/
|
|
/** **/
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* printtriangle() Print out the details of a triangle/edge handle. */
|
|
/* */
|
|
/* I originally wrote this procedure to simplify debugging; it can be */
|
|
/* called directly from the debugger, and presents information about a */
|
|
/* triangle/edge handle in digestible form. It's also used when the */
|
|
/* highest level of verbosity (`-VVV') is specified. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
void printtriangle(t)
|
|
struct triedge *t;
|
|
{
|
|
struct triedge printtri;
|
|
struct edge printsh;
|
|
point printpoint;
|
|
|
|
printf("triangle x%lx with orientation %d:\n", (unsigned long) t->tri,
|
|
t->orient);
|
|
decode(t->tri[0], printtri);
|
|
if (printtri.tri == dummytri) {
|
|
printf(" [0] = Outer space\n");
|
|
} else {
|
|
printf(" [0] = x%lx %d\n", (unsigned long) printtri.tri,
|
|
printtri.orient);
|
|
}
|
|
decode(t->tri[1], printtri);
|
|
if (printtri.tri == dummytri) {
|
|
printf(" [1] = Outer space\n");
|
|
} else {
|
|
printf(" [1] = x%lx %d\n", (unsigned long) printtri.tri,
|
|
printtri.orient);
|
|
}
|
|
decode(t->tri[2], printtri);
|
|
if (printtri.tri == dummytri) {
|
|
printf(" [2] = Outer space\n");
|
|
} else {
|
|
printf(" [2] = x%lx %d\n", (unsigned long) printtri.tri,
|
|
printtri.orient);
|
|
}
|
|
org(*t, printpoint);
|
|
if (printpoint == (point) NULL)
|
|
printf(" Origin[%d] = NULL\n", (t->orient + 1) % 3 + 3);
|
|
else
|
|
printf(" Origin[%d] = x%lx (%.12g, %.12g)\n",
|
|
(t->orient + 1) % 3 + 3, (unsigned long) printpoint,
|
|
printpoint[0], printpoint[1]);
|
|
dest(*t, printpoint);
|
|
if (printpoint == (point) NULL)
|
|
printf(" Dest [%d] = NULL\n", (t->orient + 2) % 3 + 3);
|
|
else
|
|
printf(" Dest [%d] = x%lx (%.12g, %.12g)\n",
|
|
(t->orient + 2) % 3 + 3, (unsigned long) printpoint,
|
|
printpoint[0], printpoint[1]);
|
|
apex(*t, printpoint);
|
|
if (printpoint == (point) NULL)
|
|
printf(" Apex [%d] = NULL\n", t->orient + 3);
|
|
else
|
|
printf(" Apex [%d] = x%lx (%.12g, %.12g)\n",
|
|
t->orient + 3, (unsigned long) printpoint,
|
|
printpoint[0], printpoint[1]);
|
|
if (useshelles) {
|
|
sdecode(t->tri[6], printsh);
|
|
if (printsh.sh != dummysh) {
|
|
printf(" [6] = x%lx %d\n", (unsigned long) printsh.sh,
|
|
printsh.shorient);
|
|
}
|
|
sdecode(t->tri[7], printsh);
|
|
if (printsh.sh != dummysh) {
|
|
printf(" [7] = x%lx %d\n", (unsigned long) printsh.sh,
|
|
printsh.shorient);
|
|
}
|
|
sdecode(t->tri[8], printsh);
|
|
if (printsh.sh != dummysh) {
|
|
printf(" [8] = x%lx %d\n", (unsigned long) printsh.sh,
|
|
printsh.shorient);
|
|
}
|
|
}
|
|
if (vararea) {
|
|
printf(" Area constraint: %.4g\n", areabound(*t));
|
|
}
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* printshelle() Print out the details of a shell edge handle. */
|
|
/* */
|
|
/* I originally wrote this procedure to simplify debugging; it can be */
|
|
/* called directly from the debugger, and presents information about a */
|
|
/* shell edge handle in digestible form. It's also used when the highest */
|
|
/* level of verbosity (`-VVV') is specified. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
void printshelle(s)
|
|
struct edge *s;
|
|
{
|
|
struct edge printsh;
|
|
struct triedge printtri;
|
|
point printpoint;
|
|
|
|
printf("shell edge x%lx with orientation %d and mark %d:\n",
|
|
(unsigned long) s->sh, s->shorient, mark(*s));
|
|
sdecode(s->sh[0], printsh);
|
|
if (printsh.sh == dummysh) {
|
|
printf(" [0] = No shell\n");
|
|
} else {
|
|
printf(" [0] = x%lx %d\n", (unsigned long) printsh.sh,
|
|
printsh.shorient);
|
|
}
|
|
sdecode(s->sh[1], printsh);
|
|
if (printsh.sh == dummysh) {
|
|
printf(" [1] = No shell\n");
|
|
} else {
|
|
printf(" [1] = x%lx %d\n", (unsigned long) printsh.sh,
|
|
printsh.shorient);
|
|
}
|
|
sorg(*s, printpoint);
|
|
if (printpoint == (point) NULL)
|
|
printf(" Origin[%d] = NULL\n", 2 + s->shorient);
|
|
else
|
|
printf(" Origin[%d] = x%lx (%.12g, %.12g)\n",
|
|
2 + s->shorient, (unsigned long) printpoint,
|
|
printpoint[0], printpoint[1]);
|
|
sdest(*s, printpoint);
|
|
if (printpoint == (point) NULL)
|
|
printf(" Dest [%d] = NULL\n", 3 - s->shorient);
|
|
else
|
|
printf(" Dest [%d] = x%lx (%.12g, %.12g)\n",
|
|
3 - s->shorient, (unsigned long) printpoint,
|
|
printpoint[0], printpoint[1]);
|
|
decode(s->sh[4], printtri);
|
|
if (printtri.tri == dummytri) {
|
|
printf(" [4] = Outer space\n");
|
|
} else {
|
|
printf(" [4] = x%lx %d\n", (unsigned long) printtri.tri,
|
|
printtri.orient);
|
|
}
|
|
decode(s->sh[5], printtri);
|
|
if (printtri.tri == dummytri) {
|
|
printf(" [5] = Outer space\n");
|
|
} else {
|
|
printf(" [5] = x%lx %d\n", (unsigned long) printtri.tri,
|
|
printtri.orient);
|
|
}
|
|
}
|
|
|
|
/** **/
|
|
/** **/
|
|
/********* Debugging routines end here *********/
|
|
|
|
/********* Memory management routines begin here *********/
|
|
/** **/
|
|
/** **/
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* poolinit() Initialize a pool of memory for allocation of items. */
|
|
/* */
|
|
/* This routine initializes the machinery for allocating items. A `pool' */
|
|
/* is created whose records have size at least `bytecount'. Items will be */
|
|
/* allocated in `itemcount'-item blocks. Each item is assumed to be a */
|
|
/* collection of words, and either pointers or floating-point values are */
|
|
/* assumed to be the "primary" word type. (The "primary" word type is used */
|
|
/* to determine alignment of items.) If `alignment' isn't zero, all items */
|
|
/* will be `alignment'-byte aligned in memory. `alignment' must be either */
|
|
/* a multiple or a factor of the primary word size; powers of two are safe. */
|
|
/* `alignment' is normally used to create a few unused bits at the bottom */
|
|
/* of each item's pointer, in which information may be stored. */
|
|
/* */
|
|
/* Don't change this routine unless you understand it. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
void poolinit(pool, bytecount, itemcount, wtype, alignment)
|
|
struct memorypool *pool;
|
|
int bytecount;
|
|
int itemcount;
|
|
enum wordtype wtype;
|
|
int alignment;
|
|
{
|
|
int wordsize;
|
|
|
|
/* Initialize values in the pool. */
|
|
pool->itemwordtype = wtype;
|
|
wordsize = (pool->itemwordtype == POINTER) ? sizeof(VOID *) : sizeof(REAL);
|
|
/* Find the proper alignment, which must be at least as large as: */
|
|
/* - The parameter `alignment'. */
|
|
/* - The primary word type, to avoid unaligned accesses. */
|
|
/* - sizeof(VOID *), so the stack of dead items can be maintained */
|
|
/* without unaligned accesses. */
|
|
if (alignment > wordsize) {
|
|
pool->alignbytes = alignment;
|
|
} else {
|
|
pool->alignbytes = wordsize;
|
|
}
|
|
if (sizeof(VOID *) > pool->alignbytes) {
|
|
pool->alignbytes = sizeof(VOID *);
|
|
}
|
|
pool->itemwords = ((bytecount + pool->alignbytes - 1) / pool->alignbytes)
|
|
* (pool->alignbytes / wordsize);
|
|
pool->itembytes = pool->itemwords * wordsize;
|
|
pool->itemsperblock = itemcount;
|
|
|
|
/* Allocate a block of items. Space for `itemsperblock' items and one */
|
|
/* pointer (to point to the next block) are allocated, as well as space */
|
|
/* to ensure alignment of the items. */
|
|
pool->firstblock = (VOID **) malloc(pool->itemsperblock * pool->itembytes
|
|
+ sizeof(VOID *) + pool->alignbytes);
|
|
if (pool->firstblock == (VOID **) NULL) {
|
|
printf("Error: Out of memory.\n");
|
|
exit(1);
|
|
}
|
|
/* Set the next block pointer to NULL. */
|
|
*(pool->firstblock) = (VOID *) NULL;
|
|
poolrestart(pool);
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* poolrestart() Deallocate all items in a pool. */
|
|
/* */
|
|
/* The pool is returned to its starting state, except that no memory is */
|
|
/* freed to the operating system. Rather, the previously allocated blocks */
|
|
/* are ready to be reused. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
void poolrestart(pool)
|
|
struct memorypool *pool;
|
|
{
|
|
unsigned long alignptr;
|
|
|
|
pool->items = 0;
|
|
pool->maxitems = 0;
|
|
|
|
/* Set the currently active block. */
|
|
pool->nowblock = pool->firstblock;
|
|
/* Find the first item in the pool. Increment by the size of (VOID *). */
|
|
alignptr = (unsigned long) (pool->nowblock + 1);
|
|
/* Align the item on an `alignbytes'-byte boundary. */
|
|
pool->nextitem = (VOID *)
|
|
(alignptr + (unsigned long) pool->alignbytes
|
|
- (alignptr % (unsigned long) pool->alignbytes));
|
|
/* There are lots of unallocated items left in this block. */
|
|
pool->unallocateditems = pool->itemsperblock;
|
|
/* The stack of deallocated items is empty. */
|
|
pool->deaditemstack = (VOID *) NULL;
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* pooldeinit() Free to the operating system all memory taken by a pool. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
void pooldeinit(pool)
|
|
struct memorypool *pool;
|
|
{
|
|
while (pool->firstblock != (VOID **) NULL) {
|
|
pool->nowblock = (VOID **) *(pool->firstblock);
|
|
free(pool->firstblock);
|
|
pool->firstblock = pool->nowblock;
|
|
}
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* poolalloc() Allocate space for an item. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
VOID *poolalloc(pool)
|
|
struct memorypool *pool;
|
|
{
|
|
VOID *newitem;
|
|
VOID **newblock;
|
|
unsigned long alignptr;
|
|
|
|
/* First check the linked list of dead items. If the list is not */
|
|
/* empty, allocate an item from the list rather than a fresh one. */
|
|
if (pool->deaditemstack != (VOID *) NULL) {
|
|
newitem = pool->deaditemstack; /* Take first item in list. */
|
|
pool->deaditemstack = * (VOID **) pool->deaditemstack;
|
|
} else {
|
|
/* Check if there are any free items left in the current block. */
|
|
if (pool->unallocateditems == 0) {
|
|
/* Check if another block must be allocated. */
|
|
if (*(pool->nowblock) == (VOID *) NULL) {
|
|
/* Allocate a new block of items, pointed to by the previous block. */
|
|
newblock = (VOID **) malloc(pool->itemsperblock * pool->itembytes
|
|
+ sizeof(VOID *) + pool->alignbytes);
|
|
if (newblock == (VOID **) NULL) {
|
|
printf("Error: Out of memory.\n");
|
|
exit(1);
|
|
}
|
|
*(pool->nowblock) = (VOID *) newblock;
|
|
/* The next block pointer is NULL. */
|
|
*newblock = (VOID *) NULL;
|
|
}
|
|
/* Move to the new block. */
|
|
pool->nowblock = (VOID **) *(pool->nowblock);
|
|
/* Find the first item in the block. */
|
|
/* Increment by the size of (VOID *). */
|
|
alignptr = (unsigned long) (pool->nowblock + 1);
|
|
/* Align the item on an `alignbytes'-byte boundary. */
|
|
pool->nextitem = (VOID *)
|
|
(alignptr + (unsigned long) pool->alignbytes
|
|
- (alignptr % (unsigned long) pool->alignbytes));
|
|
/* There are lots of unallocated items left in this block. */
|
|
pool->unallocateditems = pool->itemsperblock;
|
|
}
|
|
/* Allocate a new item. */
|
|
newitem = pool->nextitem;
|
|
/* Advance `nextitem' pointer to next free item in block. */
|
|
if (pool->itemwordtype == POINTER) {
|
|
pool->nextitem = (VOID *) ((VOID **) pool->nextitem + pool->itemwords);
|
|
} else {
|
|
pool->nextitem = (VOID *) ((REAL *) pool->nextitem + pool->itemwords);
|
|
}
|
|
pool->unallocateditems--;
|
|
pool->maxitems++;
|
|
}
|
|
pool->items++;
|
|
return newitem;
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* pooldealloc() Deallocate space for an item. */
|
|
/* */
|
|
/* The deallocated space is stored in a queue for later reuse. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
void pooldealloc(pool, dyingitem)
|
|
struct memorypool *pool;
|
|
VOID *dyingitem;
|
|
{
|
|
/* Push freshly killed item onto stack. */
|
|
*((VOID **) dyingitem) = pool->deaditemstack;
|
|
pool->deaditemstack = dyingitem;
|
|
pool->items--;
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* traversalinit() Prepare to traverse the entire list of items. */
|
|
/* */
|
|
/* This routine is used in conjunction with traverse(). */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
void traversalinit(pool)
|
|
struct memorypool *pool;
|
|
{
|
|
unsigned long alignptr;
|
|
|
|
/* Begin the traversal in the first block. */
|
|
pool->pathblock = pool->firstblock;
|
|
/* Find the first item in the block. Increment by the size of (VOID *). */
|
|
alignptr = (unsigned long) (pool->pathblock + 1);
|
|
/* Align with item on an `alignbytes'-byte boundary. */
|
|
pool->pathitem = (VOID *)
|
|
(alignptr + (unsigned long) pool->alignbytes
|
|
- (alignptr % (unsigned long) pool->alignbytes));
|
|
/* Set the number of items left in the current block. */
|
|
pool->pathitemsleft = pool->itemsperblock;
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* traverse() Find the next item in the list. */
|
|
/* */
|
|
/* This routine is used in conjunction with traversalinit(). Be forewarned */
|
|
/* that this routine successively returns all items in the list, including */
|
|
/* deallocated ones on the deaditemqueue. It's up to you to figure out */
|
|
/* which ones are actually dead. Why? I don't want to allocate extra */
|
|
/* space just to demarcate dead items. It can usually be done more */
|
|
/* space-efficiently by a routine that knows something about the structure */
|
|
/* of the item. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
VOID *traverse(pool)
|
|
struct memorypool *pool;
|
|
{
|
|
VOID *newitem;
|
|
unsigned long alignptr;
|
|
|
|
/* Stop upon exhausting the list of items. */
|
|
if (pool->pathitem == pool->nextitem) {
|
|
return (VOID *) NULL;
|
|
}
|
|
/* Check whether any untraversed items remain in the current block. */
|
|
if (pool->pathitemsleft == 0) {
|
|
/* Find the next block. */
|
|
pool->pathblock = (VOID **) *(pool->pathblock);
|
|
/* Find the first item in the block. Increment by the size of (VOID *). */
|
|
alignptr = (unsigned long) (pool->pathblock + 1);
|
|
/* Align with item on an `alignbytes'-byte boundary. */
|
|
pool->pathitem = (VOID *)
|
|
(alignptr + (unsigned long) pool->alignbytes
|
|
- (alignptr % (unsigned long) pool->alignbytes));
|
|
/* Set the number of items left in the current block. */
|
|
pool->pathitemsleft = pool->itemsperblock;
|
|
}
|
|
newitem = pool->pathitem;
|
|
/* Find the next item in the block. */
|
|
if (pool->itemwordtype == POINTER) {
|
|
pool->pathitem = (VOID *) ((VOID **) pool->pathitem + pool->itemwords);
|
|
} else {
|
|
pool->pathitem = (VOID *) ((REAL *) pool->pathitem + pool->itemwords);
|
|
}
|
|
pool->pathitemsleft--;
|
|
return newitem;
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* dummyinit() Initialize the triangle that fills "outer space" and the */
|
|
/* omnipresent shell edge. */
|
|
/* */
|
|
/* The triangle that fills "outer space", called `dummytri', is pointed to */
|
|
/* by every triangle and shell edge on a boundary (be it outer or inner) of */
|
|
/* the triangulation. Also, `dummytri' points to one of the triangles on */
|
|
/* the convex hull (until the holes and concavities are carved), making it */
|
|
/* possible to find a starting triangle for point location. */
|
|
/* */
|
|
/* The omnipresent shell edge, `dummysh', is pointed to by every triangle */
|
|
/* or shell edge that doesn't have a full complement of real shell edges */
|
|
/* to point to. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
void dummyinit(trianglewords, shellewords)
|
|
int trianglewords;
|
|
int shellewords;
|
|
{
|
|
unsigned long alignptr;
|
|
|
|
/* `triwords' and `shwords' are used by the mesh manipulation primitives */
|
|
/* to extract orientations of triangles and shell edges from pointers. */
|
|
triwords = trianglewords; /* Initialize `triwords' once and for all. */
|
|
shwords = shellewords; /* Initialize `shwords' once and for all. */
|
|
|
|
/* Set up `dummytri', the `triangle' that occupies "outer space". */
|
|
dummytribase = (triangle *) malloc(triwords * sizeof(triangle)
|
|
+ triangles.alignbytes);
|
|
if (dummytribase == (triangle *) NULL) {
|
|
printf("Error: Out of memory.\n");
|
|
exit(1);
|
|
}
|
|
/* Align `dummytri' on a `triangles.alignbytes'-byte boundary. */
|
|
alignptr = (unsigned long) dummytribase;
|
|
dummytri = (triangle *)
|
|
(alignptr + (unsigned long) triangles.alignbytes
|
|
- (alignptr % (unsigned long) triangles.alignbytes));
|
|
/* Initialize the three adjoining triangles to be "outer space". These */
|
|
/* will eventually be changed by various bonding operations, but their */
|
|
/* values don't really matter, as long as they can legally be */
|
|
/* dereferenced. */
|
|
dummytri[0] = (triangle) dummytri;
|
|
dummytri[1] = (triangle) dummytri;
|
|
dummytri[2] = (triangle) dummytri;
|
|
/* Three NULL vertex points. */
|
|
dummytri[3] = (triangle) NULL;
|
|
dummytri[4] = (triangle) NULL;
|
|
dummytri[5] = (triangle) NULL;
|
|
|
|
if (useshelles) {
|
|
/* Set up `dummysh', the omnipresent "shell edge" pointed to by any */
|
|
/* triangle side or shell edge end that isn't attached to a real shell */
|
|
/* edge. */
|
|
dummyshbase = (shelle *) malloc(shwords * sizeof(shelle)
|
|
+ shelles.alignbytes);
|
|
if (dummyshbase == (shelle *) NULL) {
|
|
printf("Error: Out of memory.\n");
|
|
exit(1);
|
|
}
|
|
/* Align `dummysh' on a `shelles.alignbytes'-byte boundary. */
|
|
alignptr = (unsigned long) dummyshbase;
|
|
dummysh = (shelle *)
|
|
(alignptr + (unsigned long) shelles.alignbytes
|
|
- (alignptr % (unsigned long) shelles.alignbytes));
|
|
/* Initialize the two adjoining shell edges to be the omnipresent shell */
|
|
/* edge. These will eventually be changed by various bonding */
|
|
/* operations, but their values don't really matter, as long as they */
|
|
/* can legally be dereferenced. */
|
|
dummysh[0] = (shelle) dummysh;
|
|
dummysh[1] = (shelle) dummysh;
|
|
/* Two NULL vertex points. */
|
|
dummysh[2] = (shelle) NULL;
|
|
dummysh[3] = (shelle) NULL;
|
|
/* Initialize the two adjoining triangles to be "outer space". */
|
|
dummysh[4] = (shelle) dummytri;
|
|
dummysh[5] = (shelle) dummytri;
|
|
/* Set the boundary marker to zero. */
|
|
* (int *) (dummysh + 6) = 0;
|
|
|
|
/* Initialize the three adjoining shell edges of `dummytri' to be */
|
|
/* the omnipresent shell edge. */
|
|
dummytri[6] = (triangle) dummysh;
|
|
dummytri[7] = (triangle) dummysh;
|
|
dummytri[8] = (triangle) dummysh;
|
|
}
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* initializepointpool() Calculate the size of the point data structure */
|
|
/* and initialize its memory pool. */
|
|
/* */
|
|
/* This routine also computes the `pointmarkindex' and `point2triindex' */
|
|
/* indices used to find values within each point. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
void initializepointpool()
|
|
{
|
|
int pointsize;
|
|
|
|
/* The index within each point at which the boundary marker is found. */
|
|
/* Ensure the point marker is aligned to a sizeof(int)-byte address. */
|
|
pointmarkindex = ((mesh_dim + nextras) * sizeof(REAL) + sizeof(int) - 1)
|
|
/ sizeof(int);
|
|
pointsize = (pointmarkindex + 1) * sizeof(int);
|
|
if (poly) {
|
|
/* The index within each point at which a triangle pointer is found. */
|
|
/* Ensure the pointer is aligned to a sizeof(triangle)-byte address. */
|
|
point2triindex = (pointsize + sizeof(triangle) - 1) / sizeof(triangle);
|
|
pointsize = (point2triindex + 1) * sizeof(triangle);
|
|
}
|
|
/* Initialize the pool of points. */
|
|
poolinit(&points, pointsize, POINTPERBLOCK,
|
|
(sizeof(REAL) >= sizeof(triangle)) ? FLOATINGPOINT : POINTER, 0);
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* initializetrisegpools() Calculate the sizes of the triangle and shell */
|
|
/* edge data structures and initialize their */
|
|
/* memory pools. */
|
|
/* */
|
|
/* This routine also computes the `highorderindex', `elemattribindex', and */
|
|
/* `areaboundindex' indices used to find values within each triangle. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
void initializetrisegpools()
|
|
{
|
|
int trisize;
|
|
|
|
/* The index within each triangle at which the extra nodes (above three) */
|
|
/* associated with high order elements are found. There are three */
|
|
/* pointers to other triangles, three pointers to corners, and possibly */
|
|
/* three pointers to shell edges before the extra nodes. */
|
|
highorderindex = 6 + (useshelles * 3);
|
|
/* The number of bytes occupied by a triangle. */
|
|
trisize = ((order + 1) * (order + 2) / 2 + (highorderindex - 3)) *
|
|
sizeof(triangle);
|
|
/* The index within each triangle at which its attributes are found, */
|
|
/* where the index is measured in REALs. */
|
|
elemattribindex = (trisize + sizeof(REAL) - 1) / sizeof(REAL);
|
|
/* The index within each triangle at which the maximum area constraint */
|
|
/* is found, where the index is measured in REALs. Note that if the */
|
|
/* `regionattrib' flag is set, an additional attribute will be added. */
|
|
areaboundindex = elemattribindex + eextras + regionattrib;
|
|
/* If triangle attributes or an area bound are needed, increase the number */
|
|
/* of bytes occupied by a triangle. */
|
|
if (vararea) {
|
|
trisize = (areaboundindex + 1) * sizeof(REAL);
|
|
} else if (eextras + regionattrib > 0) {
|
|
trisize = areaboundindex * sizeof(REAL);
|
|
}
|
|
/* If a Voronoi diagram or triangle neighbor graph is requested, make */
|
|
/* sure there's room to store an integer index in each triangle. This */
|
|
/* integer index can occupy the same space as the shell edges or */
|
|
/* attributes or area constraint or extra nodes. */
|
|
if ((voronoi || neighbors) &&
|
|
(trisize < 6 * sizeof(triangle) + sizeof(int))) {
|
|
trisize = 6 * sizeof(triangle) + sizeof(int);
|
|
}
|
|
/* Having determined the memory size of a triangle, initialize the pool. */
|
|
poolinit(&triangles, trisize, TRIPERBLOCK, POINTER, 4);
|
|
|
|
if (useshelles) {
|
|
/* Initialize the pool of shell edges. */
|
|
poolinit(&shelles, 6 * sizeof(triangle) + sizeof(int), SHELLEPERBLOCK,
|
|
POINTER, 4);
|
|
|
|
/* Initialize the "outer space" triangle and omnipresent shell edge. */
|
|
dummyinit(triangles.itemwords, shelles.itemwords);
|
|
} else {
|
|
/* Initialize the "outer space" triangle. */
|
|
dummyinit(triangles.itemwords, 0);
|
|
}
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* triangledealloc() Deallocate space for a triangle, marking it dead. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
void triangledealloc(dyingtriangle)
|
|
triangle *dyingtriangle;
|
|
{
|
|
/* Set triangle's vertices to NULL. This makes it possible to */
|
|
/* detect dead triangles when traversing the list of all triangles. */
|
|
dyingtriangle[3] = (triangle) NULL;
|
|
dyingtriangle[4] = (triangle) NULL;
|
|
dyingtriangle[5] = (triangle) NULL;
|
|
pooldealloc(&triangles, (VOID *) dyingtriangle);
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* triangletraverse() Traverse the triangles, skipping dead ones. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
triangle *triangletraverse()
|
|
{
|
|
triangle *newtriangle;
|
|
|
|
do {
|
|
newtriangle = (triangle *) traverse(&triangles);
|
|
if (newtriangle == (triangle *) NULL) {
|
|
return (triangle *) NULL;
|
|
}
|
|
} while (newtriangle[3] == (triangle) NULL); /* Skip dead ones. */
|
|
return newtriangle;
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* shelledealloc() Deallocate space for a shell edge, marking it dead. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
void shelledealloc(dyingshelle)
|
|
shelle *dyingshelle;
|
|
{
|
|
/* Set shell edge's vertices to NULL. This makes it possible to */
|
|
/* detect dead shells when traversing the list of all shells. */
|
|
dyingshelle[2] = (shelle) NULL;
|
|
dyingshelle[3] = (shelle) NULL;
|
|
pooldealloc(&shelles, (VOID *) dyingshelle);
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* shelletraverse() Traverse the shell edges, skipping dead ones. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
shelle *shelletraverse()
|
|
{
|
|
shelle *newshelle;
|
|
|
|
do {
|
|
newshelle = (shelle *) traverse(&shelles);
|
|
if (newshelle == (shelle *) NULL) {
|
|
return (shelle *) NULL;
|
|
}
|
|
} while (newshelle[2] == (shelle) NULL); /* Skip dead ones. */
|
|
return newshelle;
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* pointdealloc() Deallocate space for a point, marking it dead. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
void pointdealloc(dyingpoint)
|
|
point dyingpoint;
|
|
{
|
|
/* Mark the point as dead. This makes it possible to detect dead points */
|
|
/* when traversing the list of all points. */
|
|
setpointmark(dyingpoint, DEADPOINT);
|
|
pooldealloc(&points, (VOID *) dyingpoint);
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* pointtraverse() Traverse the points, skipping dead ones. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
point pointtraverse()
|
|
{
|
|
point newpoint;
|
|
|
|
do {
|
|
newpoint = (point) traverse(&points);
|
|
if (newpoint == (point) NULL) {
|
|
return (point) NULL;
|
|
}
|
|
} while (pointmark(newpoint) == DEADPOINT); /* Skip dead ones. */
|
|
return newpoint;
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* badsegmentdealloc() Deallocate space for a bad segment, marking it */
|
|
/* dead. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
#ifndef CDT_ONLY
|
|
|
|
void badsegmentdealloc(dyingseg)
|
|
struct edge *dyingseg;
|
|
{
|
|
/* Set segment's orientation to -1. This makes it possible to */
|
|
/* detect dead segments when traversing the list of all segments. */
|
|
dyingseg->shorient = -1;
|
|
pooldealloc(&badsegments, (VOID *) dyingseg);
|
|
}
|
|
|
|
#endif /* not CDT_ONLY */
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* badsegmenttraverse() Traverse the bad segments, skipping dead ones. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
#ifndef CDT_ONLY
|
|
|
|
struct edge *badsegmenttraverse()
|
|
{
|
|
struct edge *newseg;
|
|
|
|
do {
|
|
newseg = (struct edge *) traverse(&badsegments);
|
|
if (newseg == (struct edge *) NULL) {
|
|
return (struct edge *) NULL;
|
|
}
|
|
} while (newseg->shorient == -1); /* Skip dead ones. */
|
|
return newseg;
|
|
}
|
|
|
|
#endif /* not CDT_ONLY */
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* getpoint() Get a specific point, by number, from the list. */
|
|
/* */
|
|
/* The first point is number 'firstnumber'. */
|
|
/* */
|
|
/* Note that this takes O(n) time (with a small constant, if POINTPERBLOCK */
|
|
/* is large). I don't care to take the trouble to make it work in constant */
|
|
/* time. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
point getpoint(number)
|
|
int number;
|
|
{
|
|
VOID **getblock;
|
|
point foundpoint;
|
|
unsigned long alignptr;
|
|
int current;
|
|
|
|
getblock = points.firstblock;
|
|
current = firstnumber;
|
|
/* Find the right block. */
|
|
while (current + points.itemsperblock <= number) {
|
|
getblock = (VOID **) *getblock;
|
|
current += points.itemsperblock;
|
|
}
|
|
/* Now find the right point. */
|
|
alignptr = (unsigned long) (getblock + 1);
|
|
foundpoint = (point) (alignptr + (unsigned long) points.alignbytes
|
|
- (alignptr % (unsigned long) points.alignbytes));
|
|
while (current < number) {
|
|
foundpoint += points.itemwords;
|
|
current++;
|
|
}
|
|
return foundpoint;
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* triangledeinit() Free all remaining allocated memory. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
void triangledeinit()
|
|
{
|
|
pooldeinit(&triangles);
|
|
free(dummytribase);
|
|
if (useshelles) {
|
|
pooldeinit(&shelles);
|
|
free(dummyshbase);
|
|
}
|
|
pooldeinit(&points);
|
|
#ifndef CDT_ONLY
|
|
if (quality) {
|
|
pooldeinit(&badsegments);
|
|
if ((minangle > 0.0) || vararea || fixedarea) {
|
|
pooldeinit(&badtriangles);
|
|
}
|
|
}
|
|
#endif /* not CDT_ONLY */
|
|
}
|
|
|
|
/** **/
|
|
/** **/
|
|
/********* Memory management routines end here *********/
|
|
|
|
/********* Constructors begin here *********/
|
|
/** **/
|
|
/** **/
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* maketriangle() Create a new triangle with orientation zero. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
void maketriangle(newtriedge)
|
|
struct triedge *newtriedge;
|
|
{
|
|
int i;
|
|
|
|
newtriedge->tri = (triangle *) poolalloc(&triangles);
|
|
/* Initialize the three adjoining triangles to be "outer space". */
|
|
newtriedge->tri[0] = (triangle) dummytri;
|
|
newtriedge->tri[1] = (triangle) dummytri;
|
|
newtriedge->tri[2] = (triangle) dummytri;
|
|
/* Three NULL vertex points. */
|
|
newtriedge->tri[3] = (triangle) NULL;
|
|
newtriedge->tri[4] = (triangle) NULL;
|
|
newtriedge->tri[5] = (triangle) NULL;
|
|
/* Initialize the three adjoining shell edges to be the omnipresent */
|
|
/* shell edge. */
|
|
if (useshelles) {
|
|
newtriedge->tri[6] = (triangle) dummysh;
|
|
newtriedge->tri[7] = (triangle) dummysh;
|
|
newtriedge->tri[8] = (triangle) dummysh;
|
|
}
|
|
for (i = 0; i < eextras; i++) {
|
|
setelemattribute(*newtriedge, i, 0.0);
|
|
}
|
|
if (vararea) {
|
|
setareabound(*newtriedge, -1.0);
|
|
}
|
|
|
|
newtriedge->orient = 0;
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* makeshelle() Create a new shell edge with orientation zero. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
void makeshelle(newedge)
|
|
struct edge *newedge;
|
|
{
|
|
newedge->sh = (shelle *) poolalloc(&shelles);
|
|
/* Initialize the two adjoining shell edges to be the omnipresent */
|
|
/* shell edge. */
|
|
newedge->sh[0] = (shelle) dummysh;
|
|
newedge->sh[1] = (shelle) dummysh;
|
|
/* Two NULL vertex points. */
|
|
newedge->sh[2] = (shelle) NULL;
|
|
newedge->sh[3] = (shelle) NULL;
|
|
/* Initialize the two adjoining triangles to be "outer space". */
|
|
newedge->sh[4] = (shelle) dummytri;
|
|
newedge->sh[5] = (shelle) dummytri;
|
|
/* Set the boundary marker to zero. */
|
|
setmark(*newedge, 0);
|
|
|
|
newedge->shorient = 0;
|
|
}
|
|
|
|
/** **/
|
|
/** **/
|
|
/********* Constructors end here *********/
|
|
|
|
/********* Determinant evaluation routines begin here *********/
|
|
/** **/
|
|
/** **/
|
|
|
|
/* The adaptive exact arithmetic geometric predicates implemented herein are */
|
|
/* described in detail in my Technical Report CMU-CS-96-140. The complete */
|
|
/* reference is given in the header. */
|
|
|
|
/* Which of the following two methods of finding the absolute values is */
|
|
/* fastest is compiler-dependent. A few compilers can inline and optimize */
|
|
/* the fabs() call; but most will incur the overhead of a function call, */
|
|
/* which is disastrously slow. A faster way on IEEE machines might be to */
|
|
/* mask the appropriate bit, but that's difficult to do in C. */
|
|
|
|
#define Absolute(a) ((a) >= 0.0 ? (a) : -(a))
|
|
/* #define Absolute(a) fabs(a) */
|
|
|
|
/* Many of the operations are broken up into two pieces, a main part that */
|
|
/* performs an approximate operation, and a "tail" that computes the */
|
|
/* roundoff error of that operation. */
|
|
/* */
|
|
/* The operations Fast_Two_Sum(), Fast_Two_Diff(), Two_Sum(), Two_Diff(), */
|
|
/* Split(), and Two_Product() are all implemented as described in the */
|
|
/* reference. Each of these macros requires certain variables to be */
|
|
/* defined in the calling routine. The variables `bvirt', `c', `abig', */
|
|
/* `_i', `_j', `_k', `_l', `_m', and `_n' are declared `INEXACT' because */
|
|
/* they store the result of an operation that may incur roundoff error. */
|
|
/* The input parameter `x' (or the highest numbered `x_' parameter) must */
|
|
/* also be declared `INEXACT'. */
|
|
|
|
#define Fast_Two_Sum_Tail(a, b, x, y) \
|
|
bvirt = x - a; \
|
|
y = b - bvirt
|
|
|
|
#define Fast_Two_Sum(a, b, x, y) \
|
|
x = (REAL) (a + b); \
|
|
Fast_Two_Sum_Tail(a, b, x, y)
|
|
|
|
#define Two_Sum_Tail(a, b, x, y) \
|
|
bvirt = (REAL) (x - a); \
|
|
avirt = x - bvirt; \
|
|
bround = b - bvirt; \
|
|
around = a - avirt; \
|
|
y = around + bround
|
|
|
|
#define Two_Sum(a, b, x, y) \
|
|
x = (REAL) (a + b); \
|
|
Two_Sum_Tail(a, b, x, y)
|
|
|
|
#define Two_Diff_Tail(a, b, x, y) \
|
|
bvirt = (REAL) (a - x); \
|
|
avirt = x + bvirt; \
|
|
bround = bvirt - b; \
|
|
around = a - avirt; \
|
|
y = around + bround
|
|
|
|
#define Two_Diff(a, b, x, y) \
|
|
x = (REAL) (a - b); \
|
|
Two_Diff_Tail(a, b, x, y)
|
|
|
|
#define Split(a, ahi, alo) \
|
|
c = (REAL) (splitter * a); \
|
|
abig = (REAL) (c - a); \
|
|
ahi = (REAL)(c - abig); \
|
|
alo = (REAL)(a - ahi)
|
|
|
|
#define Two_Product_Tail(a, b, x, y) \
|
|
Split(a, ahi, alo); \
|
|
Split(b, bhi, blo); \
|
|
err1 = x - (ahi * bhi); \
|
|
err2 = err1 - (alo * bhi); \
|
|
err3 = err2 - (ahi * blo); \
|
|
y = (alo * blo) - err3
|
|
|
|
#define Two_Product(a, b, x, y) \
|
|
x = (REAL) (a * b); \
|
|
Two_Product_Tail(a, b, x, y)
|
|
|
|
/* Two_Product_Presplit() is Two_Product() where one of the inputs has */
|
|
/* already been split. Avoids redundant splitting. */
|
|
|
|
#define Two_Product_Presplit(a, b, bhi, blo, x, y) \
|
|
x = (REAL) (a * b); \
|
|
Split(a, ahi, alo); \
|
|
err1 = x - (ahi * bhi); \
|
|
err2 = err1 - (alo * bhi); \
|
|
err3 = err2 - (ahi * blo); \
|
|
y = (alo * blo) - err3
|
|
|
|
/* Square() can be done more quickly than Two_Product(). */
|
|
|
|
#define Square_Tail(a, x, y) \
|
|
Split(a, ahi, alo); \
|
|
err1 = x - (ahi * ahi); \
|
|
err3 = err1 - ((ahi + ahi) * alo); \
|
|
y = (alo * alo) - err3
|
|
|
|
#define Square(a, x, y) \
|
|
x = (REAL) (a * a); \
|
|
Square_Tail(a, x, y)
|
|
|
|
/* Macros for summing expansions of various fixed lengths. These are all */
|
|
/* unrolled versions of Expansion_Sum(). */
|
|
|
|
#define Two_One_Sum(a1, a0, b, x2, x1, x0) \
|
|
Two_Sum(a0, b , _i, x0); \
|
|
Two_Sum(a1, _i, x2, x1)
|
|
|
|
#define Two_One_Diff(a1, a0, b, x2, x1, x0) \
|
|
Two_Diff(a0, b , _i, x0); \
|
|
Two_Sum( a1, _i, x2, x1)
|
|
|
|
#define Two_Two_Sum(a1, a0, b1, b0, x3, x2, x1, x0) \
|
|
Two_One_Sum(a1, a0, b0, _j, _0, x0); \
|
|
Two_One_Sum(_j, _0, b1, x3, x2, x1)
|
|
|
|
#define Two_Two_Diff(a1, a0, b1, b0, x3, x2, x1, x0) \
|
|
Two_One_Diff(a1, a0, b0, _j, _0, x0); \
|
|
Two_One_Diff(_j, _0, b1, x3, x2, x1)
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* exactinit() Initialize the variables used for exact arithmetic. */
|
|
/* */
|
|
/* `epsilon' is the largest power of two such that 1.0 + epsilon = 1.0 in */
|
|
/* floating-point arithmetic. `epsilon' bounds the relative roundoff */
|
|
/* error. It is used for floating-point error analysis. */
|
|
/* */
|
|
/* `splitter' is used to split floating-point numbers into two half- */
|
|
/* length significands for exact multiplication. */
|
|
/* */
|
|
/* I imagine that a highly optimizing compiler might be too smart for its */
|
|
/* own good, and somehow cause this routine to fail, if it pretends that */
|
|
/* floating-point arithmetic is too much like real arithmetic. */
|
|
/* */
|
|
/* Don't change this routine unless you fully understand it. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
void exactinit()
|
|
{
|
|
REAL half;
|
|
REAL check, lastcheck;
|
|
int every_other;
|
|
|
|
every_other = 1;
|
|
half = 0.5;
|
|
epsilon = 1.0;
|
|
splitter = 1.0;
|
|
check = 1.0;
|
|
/* Repeatedly divide `epsilon' by two until it is too small to add to */
|
|
/* one without causing roundoff. (Also check if the sum is equal to */
|
|
/* the previous sum, for machines that round up instead of using exact */
|
|
/* rounding. Not that these routines will work on such machines anyway. */
|
|
do {
|
|
lastcheck = check;
|
|
epsilon *= half;
|
|
if (every_other) {
|
|
splitter *= 2.0;
|
|
}
|
|
every_other = !every_other;
|
|
check = (REAL)(1.0 + epsilon);
|
|
} while ((check != 1.0) && (check != lastcheck));
|
|
splitter += 1.0;
|
|
if (verbose > 1) {
|
|
printf("Floating point roundoff is of magnitude %.17g\n", epsilon);
|
|
printf("Floating point splitter is %.17g\n", splitter);
|
|
}
|
|
/* Error bounds for orientation and incircle tests. */
|
|
resulterrbound = (REAL)((3.0 + 8.0 * epsilon) * epsilon);
|
|
ccwerrboundA = (REAL)((3.0 + 16.0 * epsilon) * epsilon);
|
|
ccwerrboundB = (REAL)((2.0 + 12.0 * epsilon) * epsilon);
|
|
ccwerrboundC = (REAL)((9.0 + 64.0 * epsilon) * epsilon * epsilon);
|
|
iccerrboundA = (REAL)((10.0 + 96.0 * epsilon) * epsilon);
|
|
iccerrboundB = (REAL)((4.0 + 48.0 * epsilon) * epsilon);
|
|
iccerrboundC = (REAL)((44.0 + 576.0 * epsilon) * epsilon * epsilon);
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* fast_expansion_sum_zeroelim() Sum two expansions, eliminating zero */
|
|
/* components from the output expansion. */
|
|
/* */
|
|
/* Sets h = e + f. See my Robust Predicates paper for details. */
|
|
/* */
|
|
/* If round-to-even is used (as with IEEE 754), maintains the strongly */
|
|
/* nonoverlapping property. (That is, if e is strongly nonoverlapping, h */
|
|
/* will be also.) Does NOT maintain the nonoverlapping or nonadjacent */
|
|
/* properties. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
int fast_expansion_sum_zeroelim(elen, e, flen, f, h) /* h cannot be e or f. */
|
|
int elen;
|
|
REAL *e;
|
|
int flen;
|
|
REAL *f;
|
|
REAL *h;
|
|
{
|
|
REAL Q;
|
|
INEXACT REAL Qnew;
|
|
INEXACT REAL hh;
|
|
INEXACT REAL bvirt;
|
|
REAL avirt, bround, around;
|
|
int eindex, findex, hindex;
|
|
REAL enow, fnow;
|
|
|
|
enow = e[0];
|
|
fnow = f[0];
|
|
eindex = findex = 0;
|
|
if ((fnow > enow) == (fnow > -enow)) {
|
|
Q = enow;
|
|
enow = e[++eindex];
|
|
} else {
|
|
Q = fnow;
|
|
fnow = f[++findex];
|
|
}
|
|
hindex = 0;
|
|
if ((eindex < elen) && (findex < flen)) {
|
|
if ((fnow > enow) == (fnow > -enow)) {
|
|
Fast_Two_Sum(enow, Q, Qnew, hh);
|
|
enow = e[++eindex];
|
|
} else {
|
|
Fast_Two_Sum(fnow, Q, Qnew, hh);
|
|
fnow = f[++findex];
|
|
}
|
|
Q = Qnew;
|
|
if (hh != 0.0) {
|
|
h[hindex++] = hh;
|
|
}
|
|
while ((eindex < elen) && (findex < flen)) {
|
|
if ((fnow > enow) == (fnow > -enow)) {
|
|
Two_Sum(Q, enow, Qnew, hh);
|
|
enow = e[++eindex];
|
|
} else {
|
|
Two_Sum(Q, fnow, Qnew, hh);
|
|
fnow = f[++findex];
|
|
}
|
|
Q = Qnew;
|
|
if (hh != 0.0) {
|
|
h[hindex++] = hh;
|
|
}
|
|
}
|
|
}
|
|
while (eindex < elen) {
|
|
Two_Sum(Q, enow, Qnew, hh);
|
|
enow = e[++eindex];
|
|
Q = Qnew;
|
|
if (hh != 0.0) {
|
|
h[hindex++] = hh;
|
|
}
|
|
}
|
|
while (findex < flen) {
|
|
Two_Sum(Q, fnow, Qnew, hh);
|
|
fnow = f[++findex];
|
|
Q = Qnew;
|
|
if (hh != 0.0) {
|
|
h[hindex++] = hh;
|
|
}
|
|
}
|
|
if ((Q != 0.0) || (hindex == 0)) {
|
|
h[hindex++] = Q;
|
|
}
|
|
return hindex;
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* scale_expansion_zeroelim() Multiply an expansion by a scalar, */
|
|
/* eliminating zero components from the */
|
|
/* output expansion. */
|
|
/* */
|
|
/* Sets h = be. See my Robust Predicates paper for details. */
|
|
/* */
|
|
/* Maintains the nonoverlapping property. If round-to-even is used (as */
|
|
/* with IEEE 754), maintains the strongly nonoverlapping and nonadjacent */
|
|
/* properties as well. (That is, if e has one of these properties, so */
|
|
/* will h.) */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
int scale_expansion_zeroelim(elen, e, b, h) /* e and h cannot be the same. */
|
|
int elen;
|
|
REAL *e;
|
|
REAL b;
|
|
REAL *h;
|
|
{
|
|
INEXACT REAL Q, sum;
|
|
REAL hh;
|
|
INEXACT REAL product1;
|
|
REAL product0;
|
|
int eindex, hindex;
|
|
REAL enow;
|
|
INEXACT REAL bvirt;
|
|
REAL avirt, bround, around;
|
|
INEXACT REAL c;
|
|
INEXACT REAL abig;
|
|
REAL ahi, alo, bhi, blo;
|
|
REAL err1, err2, err3;
|
|
|
|
Split(b, bhi, blo);
|
|
Two_Product_Presplit(e[0], b, bhi, blo, Q, hh);
|
|
hindex = 0;
|
|
if (hh != 0) {
|
|
h[hindex++] = hh;
|
|
}
|
|
for (eindex = 1; eindex < elen; eindex++) {
|
|
enow = e[eindex];
|
|
Two_Product_Presplit(enow, b, bhi, blo, product1, product0);
|
|
Two_Sum(Q, product0, sum, hh);
|
|
if (hh != 0) {
|
|
h[hindex++] = hh;
|
|
}
|
|
Fast_Two_Sum(product1, sum, Q, hh);
|
|
if (hh != 0) {
|
|
h[hindex++] = hh;
|
|
}
|
|
}
|
|
if ((Q != 0.0) || (hindex == 0)) {
|
|
h[hindex++] = Q;
|
|
}
|
|
return hindex;
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* estimate() Produce a one-word estimate of an expansion's value. */
|
|
/* */
|
|
/* See my Robust Predicates paper for details. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
REAL estimate(elen, e)
|
|
int elen;
|
|
REAL *e;
|
|
{
|
|
REAL Q;
|
|
int eindex;
|
|
|
|
Q = e[0];
|
|
for (eindex = 1; eindex < elen; eindex++) {
|
|
Q += e[eindex];
|
|
}
|
|
return Q;
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* counterclockwise() Return a positive value if the points pa, pb, and */
|
|
/* pc occur in counterclockwise order; a negative */
|
|
/* value if they occur in clockwise order; and zero */
|
|
/* if they are collinear. The result is also a rough */
|
|
/* approximation of twice the signed area of the */
|
|
/* triangle defined by the three points. */
|
|
/* */
|
|
/* Uses exact arithmetic if necessary to ensure a correct answer. The */
|
|
/* result returned is the determinant of a matrix. This determinant is */
|
|
/* computed adaptively, in the sense that exact arithmetic is used only to */
|
|
/* the degree it is needed to ensure that the returned value has the */
|
|
/* correct sign. Hence, this function is usually quite fast, but will run */
|
|
/* more slowly when the input points are collinear or nearly so. */
|
|
/* */
|
|
/* See my Robust Predicates paper for details. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
REAL counterclockwiseadapt(pa, pb, pc, detsum)
|
|
point pa;
|
|
point pb;
|
|
point pc;
|
|
REAL detsum;
|
|
{
|
|
INEXACT REAL acx, acy, bcx, bcy;
|
|
REAL acxtail, acytail, bcxtail, bcytail;
|
|
INEXACT REAL detleft, detright;
|
|
REAL detlefttail, detrighttail;
|
|
REAL det, errbound;
|
|
REAL B[4], C1[8], C2[12], D[16];
|
|
INEXACT REAL B3;
|
|
int C1length, C2length, Dlength;
|
|
REAL u[4];
|
|
INEXACT REAL u3;
|
|
INEXACT REAL s1, t1;
|
|
REAL s0, t0;
|
|
|
|
INEXACT REAL bvirt;
|
|
REAL avirt, bround, around;
|
|
INEXACT REAL c;
|
|
INEXACT REAL abig;
|
|
REAL ahi, alo, bhi, blo;
|
|
REAL err1, err2, err3;
|
|
INEXACT REAL _i, _j;
|
|
REAL _0;
|
|
|
|
acx = (REAL) (pa[0] - pc[0]);
|
|
bcx = (REAL) (pb[0] - pc[0]);
|
|
acy = (REAL) (pa[1] - pc[1]);
|
|
bcy = (REAL) (pb[1] - pc[1]);
|
|
|
|
Two_Product(acx, bcy, detleft, detlefttail);
|
|
Two_Product(acy, bcx, detright, detrighttail);
|
|
|
|
Two_Two_Diff(detleft, detlefttail, detright, detrighttail,
|
|
B3, B[2], B[1], B[0]);
|
|
B[3] = B3;
|
|
|
|
det = estimate(4, B);
|
|
errbound = (REAL)(ccwerrboundB * detsum);
|
|
if ((det >= errbound) || (-det >= errbound)) {
|
|
return det;
|
|
}
|
|
|
|
Two_Diff_Tail(pa[0], pc[0], acx, acxtail);
|
|
Two_Diff_Tail(pb[0], pc[0], bcx, bcxtail);
|
|
Two_Diff_Tail(pa[1], pc[1], acy, acytail);
|
|
Two_Diff_Tail(pb[1], pc[1], bcy, bcytail);
|
|
|
|
if ((acxtail == 0.0) && (acytail == 0.0)
|
|
&& (bcxtail == 0.0) && (bcytail == 0.0)) {
|
|
return det;
|
|
}
|
|
|
|
errbound = (REAL)(ccwerrboundC * detsum + resulterrbound * Absolute(det));
|
|
det += (acx * bcytail + bcy * acxtail)
|
|
- (acy * bcxtail + bcx * acytail);
|
|
if ((det >= errbound) || (-det >= errbound)) {
|
|
return det;
|
|
}
|
|
|
|
Two_Product(acxtail, bcy, s1, s0);
|
|
Two_Product(acytail, bcx, t1, t0);
|
|
Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
|
|
u[3] = u3;
|
|
C1length = fast_expansion_sum_zeroelim(4, B, 4, u, C1);
|
|
|
|
Two_Product(acx, bcytail, s1, s0);
|
|
Two_Product(acy, bcxtail, t1, t0);
|
|
Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
|
|
u[3] = u3;
|
|
C2length = fast_expansion_sum_zeroelim(C1length, C1, 4, u, C2);
|
|
|
|
Two_Product(acxtail, bcytail, s1, s0);
|
|
Two_Product(acytail, bcxtail, t1, t0);
|
|
Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
|
|
u[3] = u3;
|
|
Dlength = fast_expansion_sum_zeroelim(C2length, C2, 4, u, D);
|
|
|
|
return(D[Dlength - 1]);
|
|
}
|
|
|
|
REAL counterclockwise(pa, pb, pc)
|
|
point pa;
|
|
point pb;
|
|
point pc;
|
|
{
|
|
REAL detleft, detright, det;
|
|
REAL detsum, errbound;
|
|
|
|
counterclockcount++;
|
|
|
|
detleft = (pa[0] - pc[0]) * (pb[1] - pc[1]);
|
|
detright = (pa[1] - pc[1]) * (pb[0] - pc[0]);
|
|
det = detleft - detright;
|
|
|
|
if (noexact) {
|
|
return det;
|
|
}
|
|
|
|
if (detleft > 0.0) {
|
|
if (detright <= 0.0) {
|
|
return det;
|
|
} else {
|
|
detsum = detleft + detright;
|
|
}
|
|
} else if (detleft < 0.0) {
|
|
if (detright >= 0.0) {
|
|
return det;
|
|
} else {
|
|
detsum = -detleft - detright;
|
|
}
|
|
} else {
|
|
return det;
|
|
}
|
|
|
|
errbound = ccwerrboundA * detsum;
|
|
if ((det >= errbound) || (-det >= errbound)) {
|
|
return det;
|
|
}
|
|
|
|
return counterclockwiseadapt(pa, pb, pc, detsum);
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* incircle() Return a positive value if the point pd lies inside the */
|
|
/* circle passing through pa, pb, and pc; a negative value if */
|
|
/* it lies outside; and zero if the four points are cocircular.*/
|
|
/* The points pa, pb, and pc must be in counterclockwise */
|
|
/* order, or the sign of the result will be reversed. */
|
|
/* */
|
|
/* Uses exact arithmetic if necessary to ensure a correct answer. The */
|
|
/* result returned is the determinant of a matrix. This determinant is */
|
|
/* computed adaptively, in the sense that exact arithmetic is used only to */
|
|
/* the degree it is needed to ensure that the returned value has the */
|
|
/* correct sign. Hence, this function is usually quite fast, but will run */
|
|
/* more slowly when the input points are cocircular or nearly so. */
|
|
/* */
|
|
/* See my Robust Predicates paper for details. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
REAL incircleadapt(pa, pb, pc, pd, permanent)
|
|
point pa;
|
|
point pb;
|
|
point pc;
|
|
point pd;
|
|
REAL permanent;
|
|
{
|
|
INEXACT REAL adx, bdx, cdx, ady, bdy, cdy;
|
|
REAL det, errbound;
|
|
|
|
INEXACT REAL bdxcdy1, cdxbdy1, cdxady1, adxcdy1, adxbdy1, bdxady1;
|
|
REAL bdxcdy0, cdxbdy0, cdxady0, adxcdy0, adxbdy0, bdxady0;
|
|
REAL bc[4], ca[4], ab[4];
|
|
INEXACT REAL bc3, ca3, ab3;
|
|
REAL axbc[8], axxbc[16], aybc[8], ayybc[16], adet[32];
|
|
int axbclen, axxbclen, aybclen, ayybclen, alen;
|
|
REAL bxca[8], bxxca[16], byca[8], byyca[16], bdet[32];
|
|
int bxcalen, bxxcalen, bycalen, byycalen, blen;
|
|
REAL cxab[8], cxxab[16], cyab[8], cyyab[16], cdet[32];
|
|
int cxablen, cxxablen, cyablen, cyyablen, clen;
|
|
REAL abdet[64];
|
|
int ablen;
|
|
REAL fin1[1152], fin2[1152];
|
|
REAL *finnow, *finother, *finswap;
|
|
int finlength;
|
|
|
|
REAL adxtail, bdxtail, cdxtail, adytail, bdytail, cdytail;
|
|
INEXACT REAL adxadx1, adyady1, bdxbdx1, bdybdy1, cdxcdx1, cdycdy1;
|
|
REAL adxadx0, adyady0, bdxbdx0, bdybdy0, cdxcdx0, cdycdy0;
|
|
REAL aa[4], bb[4], cc[4];
|
|
INEXACT REAL aa3, bb3, cc3;
|
|
INEXACT REAL ti1, tj1;
|
|
REAL ti0, tj0;
|
|
REAL u[4], v[4];
|
|
INEXACT REAL u3, v3;
|
|
REAL temp8[8], temp16a[16], temp16b[16], temp16c[16];
|
|
REAL temp32a[32], temp32b[32], temp48[48], temp64[64];
|
|
int temp8len, temp16alen, temp16blen, temp16clen;
|
|
int temp32alen, temp32blen, temp48len, temp64len;
|
|
REAL axtbb[8], axtcc[8], aytbb[8], aytcc[8];
|
|
int axtbblen, axtcclen, aytbblen, aytcclen;
|
|
REAL bxtaa[8], bxtcc[8], bytaa[8], bytcc[8];
|
|
int bxtaalen, bxtcclen, bytaalen, bytcclen;
|
|
REAL cxtaa[8], cxtbb[8], cytaa[8], cytbb[8];
|
|
int cxtaalen, cxtbblen, cytaalen, cytbblen;
|
|
REAL axtbc[8], aytbc[8], bxtca[8], bytca[8], cxtab[8], cytab[8];
|
|
int axtbclen, aytbclen, bxtcalen, bytcalen, cxtablen, cytablen;
|
|
REAL axtbct[16], aytbct[16], bxtcat[16], bytcat[16], cxtabt[16], cytabt[16];
|
|
int axtbctlen, aytbctlen, bxtcatlen, bytcatlen, cxtabtlen, cytabtlen;
|
|
REAL axtbctt[8], aytbctt[8], bxtcatt[8];
|
|
REAL bytcatt[8], cxtabtt[8], cytabtt[8];
|
|
int axtbcttlen, aytbcttlen, bxtcattlen, bytcattlen, cxtabttlen, cytabttlen;
|
|
REAL abt[8], bct[8], cat[8];
|
|
int abtlen, bctlen, catlen;
|
|
REAL abtt[4], bctt[4], catt[4];
|
|
int abttlen, bcttlen, cattlen;
|
|
INEXACT REAL abtt3, bctt3, catt3;
|
|
REAL negate;
|
|
|
|
INEXACT REAL bvirt;
|
|
REAL avirt, bround, around;
|
|
INEXACT REAL c;
|
|
INEXACT REAL abig;
|
|
REAL ahi, alo, bhi, blo;
|
|
REAL err1, err2, err3;
|
|
INEXACT REAL _i, _j;
|
|
REAL _0;
|
|
|
|
adx = (REAL) (pa[0] - pd[0]);
|
|
bdx = (REAL) (pb[0] - pd[0]);
|
|
cdx = (REAL) (pc[0] - pd[0]);
|
|
ady = (REAL) (pa[1] - pd[1]);
|
|
bdy = (REAL) (pb[1] - pd[1]);
|
|
cdy = (REAL) (pc[1] - pd[1]);
|
|
|
|
Two_Product(bdx, cdy, bdxcdy1, bdxcdy0);
|
|
Two_Product(cdx, bdy, cdxbdy1, cdxbdy0);
|
|
Two_Two_Diff(bdxcdy1, bdxcdy0, cdxbdy1, cdxbdy0, bc3, bc[2], bc[1], bc[0]);
|
|
bc[3] = bc3;
|
|
axbclen = scale_expansion_zeroelim(4, bc, adx, axbc);
|
|
axxbclen = scale_expansion_zeroelim(axbclen, axbc, adx, axxbc);
|
|
aybclen = scale_expansion_zeroelim(4, bc, ady, aybc);
|
|
ayybclen = scale_expansion_zeroelim(aybclen, aybc, ady, ayybc);
|
|
alen = fast_expansion_sum_zeroelim(axxbclen, axxbc, ayybclen, ayybc, adet);
|
|
|
|
Two_Product(cdx, ady, cdxady1, cdxady0);
|
|
Two_Product(adx, cdy, adxcdy1, adxcdy0);
|
|
Two_Two_Diff(cdxady1, cdxady0, adxcdy1, adxcdy0, ca3, ca[2], ca[1], ca[0]);
|
|
ca[3] = ca3;
|
|
bxcalen = scale_expansion_zeroelim(4, ca, bdx, bxca);
|
|
bxxcalen = scale_expansion_zeroelim(bxcalen, bxca, bdx, bxxca);
|
|
bycalen = scale_expansion_zeroelim(4, ca, bdy, byca);
|
|
byycalen = scale_expansion_zeroelim(bycalen, byca, bdy, byyca);
|
|
blen = fast_expansion_sum_zeroelim(bxxcalen, bxxca, byycalen, byyca, bdet);
|
|
|
|
Two_Product(adx, bdy, adxbdy1, adxbdy0);
|
|
Two_Product(bdx, ady, bdxady1, bdxady0);
|
|
Two_Two_Diff(adxbdy1, adxbdy0, bdxady1, bdxady0, ab3, ab[2], ab[1], ab[0]);
|
|
ab[3] = ab3;
|
|
cxablen = scale_expansion_zeroelim(4, ab, cdx, cxab);
|
|
cxxablen = scale_expansion_zeroelim(cxablen, cxab, cdx, cxxab);
|
|
cyablen = scale_expansion_zeroelim(4, ab, cdy, cyab);
|
|
cyyablen = scale_expansion_zeroelim(cyablen, cyab, cdy, cyyab);
|
|
clen = fast_expansion_sum_zeroelim(cxxablen, cxxab, cyyablen, cyyab, cdet);
|
|
|
|
ablen = fast_expansion_sum_zeroelim(alen, adet, blen, bdet, abdet);
|
|
finlength = fast_expansion_sum_zeroelim(ablen, abdet, clen, cdet, fin1);
|
|
|
|
det = estimate(finlength, fin1);
|
|
errbound = (REAL)(iccerrboundB * permanent);
|
|
if ((det >= errbound) || (-det >= errbound)) {
|
|
return det;
|
|
}
|
|
|
|
Two_Diff_Tail(pa[0], pd[0], adx, adxtail);
|
|
Two_Diff_Tail(pa[1], pd[1], ady, adytail);
|
|
Two_Diff_Tail(pb[0], pd[0], bdx, bdxtail);
|
|
Two_Diff_Tail(pb[1], pd[1], bdy, bdytail);
|
|
Two_Diff_Tail(pc[0], pd[0], cdx, cdxtail);
|
|
Two_Diff_Tail(pc[1], pd[1], cdy, cdytail);
|
|
if ((adxtail == 0.0) && (bdxtail == 0.0) && (cdxtail == 0.0)
|
|
&& (adytail == 0.0) && (bdytail == 0.0) && (cdytail == 0.0)) {
|
|
return det;
|
|
}
|
|
|
|
errbound = (REAL)(iccerrboundC * permanent + resulterrbound * Absolute(det));
|
|
det += (REAL)(((adx * adx + ady * ady) * ((bdx * cdytail + cdy * bdxtail)
|
|
- (bdy * cdxtail + cdx * bdytail))
|
|
+ 2.0 * (adx * adxtail + ady * adytail) * (bdx * cdy - bdy * cdx))
|
|
+ ((bdx * bdx + bdy * bdy) * ((cdx * adytail + ady * cdxtail)
|
|
- (cdy * adxtail + adx * cdytail))
|
|
+ 2.0 * (bdx * bdxtail + bdy * bdytail) * (cdx * ady - cdy * adx))
|
|
+ ((cdx * cdx + cdy * cdy) * ((adx * bdytail + bdy * adxtail)
|
|
- (ady * bdxtail + bdx * adytail))
|
|
+ 2.0 * (cdx * cdxtail + cdy * cdytail) * (adx * bdy - ady * bdx)));
|
|
if ((det >= errbound) || (-det >= errbound)) {
|
|
return det;
|
|
}
|
|
|
|
finnow = fin1;
|
|
finother = fin2;
|
|
|
|
if ((bdxtail != 0.0) || (bdytail != 0.0)
|
|
|| (cdxtail != 0.0) || (cdytail != 0.0)) {
|
|
Square(adx, adxadx1, adxadx0);
|
|
Square(ady, adyady1, adyady0);
|
|
Two_Two_Sum(adxadx1, adxadx0, adyady1, adyady0, aa3, aa[2], aa[1], aa[0]);
|
|
aa[3] = aa3;
|
|
}
|
|
if ((cdxtail != 0.0) || (cdytail != 0.0)
|
|
|| (adxtail != 0.0) || (adytail != 0.0)) {
|
|
Square(bdx, bdxbdx1, bdxbdx0);
|
|
Square(bdy, bdybdy1, bdybdy0);
|
|
Two_Two_Sum(bdxbdx1, bdxbdx0, bdybdy1, bdybdy0, bb3, bb[2], bb[1], bb[0]);
|
|
bb[3] = bb3;
|
|
}
|
|
if ((adxtail != 0.0) || (adytail != 0.0)
|
|
|| (bdxtail != 0.0) || (bdytail != 0.0)) {
|
|
Square(cdx, cdxcdx1, cdxcdx0);
|
|
Square(cdy, cdycdy1, cdycdy0);
|
|
Two_Two_Sum(cdxcdx1, cdxcdx0, cdycdy1, cdycdy0, cc3, cc[2], cc[1], cc[0]);
|
|
cc[3] = cc3;
|
|
}
|
|
|
|
if (adxtail != 0.0) {
|
|
axtbclen = scale_expansion_zeroelim(4, bc, adxtail, axtbc);
|
|
temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, 2.0 * adx,
|
|
temp16a);
|
|
|
|
axtcclen = scale_expansion_zeroelim(4, cc, adxtail, axtcc);
|
|
temp16blen = scale_expansion_zeroelim(axtcclen, axtcc, bdy, temp16b);
|
|
|
|
axtbblen = scale_expansion_zeroelim(4, bb, adxtail, axtbb);
|
|
temp16clen = scale_expansion_zeroelim(axtbblen, axtbb, -cdy, temp16c);
|
|
|
|
temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
|
|
temp16blen, temp16b, temp32a);
|
|
temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
|
|
temp32alen, temp32a, temp48);
|
|
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
|
|
temp48, finother);
|
|
finswap = finnow; finnow = finother; finother = finswap;
|
|
}
|
|
if (adytail != 0.0) {
|
|
aytbclen = scale_expansion_zeroelim(4, bc, adytail, aytbc);
|
|
temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, 2.0 * ady,
|
|
temp16a);
|
|
|
|
aytbblen = scale_expansion_zeroelim(4, bb, adytail, aytbb);
|
|
temp16blen = scale_expansion_zeroelim(aytbblen, aytbb, cdx, temp16b);
|
|
|
|
aytcclen = scale_expansion_zeroelim(4, cc, adytail, aytcc);
|
|
temp16clen = scale_expansion_zeroelim(aytcclen, aytcc, -bdx, temp16c);
|
|
|
|
temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
|
|
temp16blen, temp16b, temp32a);
|
|
temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
|
|
temp32alen, temp32a, temp48);
|
|
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
|
|
temp48, finother);
|
|
finswap = finnow; finnow = finother; finother = finswap;
|
|
}
|
|
if (bdxtail != 0.0) {
|
|
bxtcalen = scale_expansion_zeroelim(4, ca, bdxtail, bxtca);
|
|
temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, 2.0 * bdx,
|
|
temp16a);
|
|
|
|
bxtaalen = scale_expansion_zeroelim(4, aa, bdxtail, bxtaa);
|
|
temp16blen = scale_expansion_zeroelim(bxtaalen, bxtaa, cdy, temp16b);
|
|
|
|
bxtcclen = scale_expansion_zeroelim(4, cc, bdxtail, bxtcc);
|
|
temp16clen = scale_expansion_zeroelim(bxtcclen, bxtcc, -ady, temp16c);
|
|
|
|
temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
|
|
temp16blen, temp16b, temp32a);
|
|
temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
|
|
temp32alen, temp32a, temp48);
|
|
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
|
|
temp48, finother);
|
|
finswap = finnow; finnow = finother; finother = finswap;
|
|
}
|
|
if (bdytail != 0.0) {
|
|
bytcalen = scale_expansion_zeroelim(4, ca, bdytail, bytca);
|
|
temp16alen = scale_expansion_zeroelim(bytcalen, bytca, 2.0 * bdy,
|
|
temp16a);
|
|
|
|
bytcclen = scale_expansion_zeroelim(4, cc, bdytail, bytcc);
|
|
temp16blen = scale_expansion_zeroelim(bytcclen, bytcc, adx, temp16b);
|
|
|
|
bytaalen = scale_expansion_zeroelim(4, aa, bdytail, bytaa);
|
|
temp16clen = scale_expansion_zeroelim(bytaalen, bytaa, -cdx, temp16c);
|
|
|
|
temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
|
|
temp16blen, temp16b, temp32a);
|
|
temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
|
|
temp32alen, temp32a, temp48);
|
|
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
|
|
temp48, finother);
|
|
finswap = finnow; finnow = finother; finother = finswap;
|
|
}
|
|
if (cdxtail != 0.0) {
|
|
cxtablen = scale_expansion_zeroelim(4, ab, cdxtail, cxtab);
|
|
temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, 2.0 * cdx,
|
|
temp16a);
|
|
|
|
cxtbblen = scale_expansion_zeroelim(4, bb, cdxtail, cxtbb);
|
|
temp16blen = scale_expansion_zeroelim(cxtbblen, cxtbb, ady, temp16b);
|
|
|
|
cxtaalen = scale_expansion_zeroelim(4, aa, cdxtail, cxtaa);
|
|
temp16clen = scale_expansion_zeroelim(cxtaalen, cxtaa, -bdy, temp16c);
|
|
|
|
temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
|
|
temp16blen, temp16b, temp32a);
|
|
temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
|
|
temp32alen, temp32a, temp48);
|
|
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
|
|
temp48, finother);
|
|
finswap = finnow; finnow = finother; finother = finswap;
|
|
}
|
|
if (cdytail != 0.0) {
|
|
cytablen = scale_expansion_zeroelim(4, ab, cdytail, cytab);
|
|
temp16alen = scale_expansion_zeroelim(cytablen, cytab, 2.0 * cdy,
|
|
temp16a);
|
|
|
|
cytaalen = scale_expansion_zeroelim(4, aa, cdytail, cytaa);
|
|
temp16blen = scale_expansion_zeroelim(cytaalen, cytaa, bdx, temp16b);
|
|
|
|
cytbblen = scale_expansion_zeroelim(4, bb, cdytail, cytbb);
|
|
temp16clen = scale_expansion_zeroelim(cytbblen, cytbb, -adx, temp16c);
|
|
|
|
temp32alen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
|
|
temp16blen, temp16b, temp32a);
|
|
temp48len = fast_expansion_sum_zeroelim(temp16clen, temp16c,
|
|
temp32alen, temp32a, temp48);
|
|
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
|
|
temp48, finother);
|
|
finswap = finnow; finnow = finother; finother = finswap;
|
|
}
|
|
|
|
if ((adxtail != 0.0) || (adytail != 0.0)) {
|
|
if ((bdxtail != 0.0) || (bdytail != 0.0)
|
|
|| (cdxtail != 0.0) || (cdytail != 0.0)) {
|
|
Two_Product(bdxtail, cdy, ti1, ti0);
|
|
Two_Product(bdx, cdytail, tj1, tj0);
|
|
Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
|
|
u[3] = u3;
|
|
negate = -bdy;
|
|
Two_Product(cdxtail, negate, ti1, ti0);
|
|
negate = -bdytail;
|
|
Two_Product(cdx, negate, tj1, tj0);
|
|
Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
|
|
v[3] = v3;
|
|
bctlen = fast_expansion_sum_zeroelim(4, u, 4, v, bct);
|
|
|
|
Two_Product(bdxtail, cdytail, ti1, ti0);
|
|
Two_Product(cdxtail, bdytail, tj1, tj0);
|
|
Two_Two_Diff(ti1, ti0, tj1, tj0, bctt3, bctt[2], bctt[1], bctt[0]);
|
|
bctt[3] = bctt3;
|
|
bcttlen = 4;
|
|
} else {
|
|
bct[0] = 0.0;
|
|
bctlen = 1;
|
|
bctt[0] = 0.0;
|
|
bcttlen = 1;
|
|
}
|
|
|
|
if (adxtail != 0.0) {
|
|
temp16alen = scale_expansion_zeroelim(axtbclen, axtbc, adxtail, temp16a);
|
|
axtbctlen = scale_expansion_zeroelim(bctlen, bct, adxtail, axtbct);
|
|
temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, 2.0 * adx,
|
|
temp32a);
|
|
temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
|
|
temp32alen, temp32a, temp48);
|
|
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
|
|
temp48, finother);
|
|
finswap = finnow; finnow = finother; finother = finswap;
|
|
if (bdytail != 0.0) {
|
|
temp8len = scale_expansion_zeroelim(4, cc, adxtail, temp8);
|
|
temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail,
|
|
temp16a);
|
|
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
|
|
temp16a, finother);
|
|
finswap = finnow; finnow = finother; finother = finswap;
|
|
}
|
|
if (cdytail != 0.0) {
|
|
temp8len = scale_expansion_zeroelim(4, bb, -adxtail, temp8);
|
|
temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail,
|
|
temp16a);
|
|
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
|
|
temp16a, finother);
|
|
finswap = finnow; finnow = finother; finother = finswap;
|
|
}
|
|
|
|
temp32alen = scale_expansion_zeroelim(axtbctlen, axtbct, adxtail,
|
|
temp32a);
|
|
axtbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adxtail, axtbctt);
|
|
temp16alen = scale_expansion_zeroelim(axtbcttlen, axtbctt, 2.0 * adx,
|
|
temp16a);
|
|
temp16blen = scale_expansion_zeroelim(axtbcttlen, axtbctt, adxtail,
|
|
temp16b);
|
|
temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
|
|
temp16blen, temp16b, temp32b);
|
|
temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
|
|
temp32blen, temp32b, temp64);
|
|
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
|
|
temp64, finother);
|
|
finswap = finnow; finnow = finother; finother = finswap;
|
|
}
|
|
if (adytail != 0.0) {
|
|
temp16alen = scale_expansion_zeroelim(aytbclen, aytbc, adytail, temp16a);
|
|
aytbctlen = scale_expansion_zeroelim(bctlen, bct, adytail, aytbct);
|
|
temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, 2.0 * ady,
|
|
temp32a);
|
|
temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
|
|
temp32alen, temp32a, temp48);
|
|
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
|
|
temp48, finother);
|
|
finswap = finnow; finnow = finother; finother = finswap;
|
|
|
|
|
|
temp32alen = scale_expansion_zeroelim(aytbctlen, aytbct, adytail,
|
|
temp32a);
|
|
aytbcttlen = scale_expansion_zeroelim(bcttlen, bctt, adytail, aytbctt);
|
|
temp16alen = scale_expansion_zeroelim(aytbcttlen, aytbctt, 2.0 * ady,
|
|
temp16a);
|
|
temp16blen = scale_expansion_zeroelim(aytbcttlen, aytbctt, adytail,
|
|
temp16b);
|
|
temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
|
|
temp16blen, temp16b, temp32b);
|
|
temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
|
|
temp32blen, temp32b, temp64);
|
|
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
|
|
temp64, finother);
|
|
finswap = finnow; finnow = finother; finother = finswap;
|
|
}
|
|
}
|
|
if ((bdxtail != 0.0) || (bdytail != 0.0)) {
|
|
if ((cdxtail != 0.0) || (cdytail != 0.0)
|
|
|| (adxtail != 0.0) || (adytail != 0.0)) {
|
|
Two_Product(cdxtail, ady, ti1, ti0);
|
|
Two_Product(cdx, adytail, tj1, tj0);
|
|
Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
|
|
u[3] = u3;
|
|
negate = -cdy;
|
|
Two_Product(adxtail, negate, ti1, ti0);
|
|
negate = -cdytail;
|
|
Two_Product(adx, negate, tj1, tj0);
|
|
Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
|
|
v[3] = v3;
|
|
catlen = fast_expansion_sum_zeroelim(4, u, 4, v, cat);
|
|
|
|
Two_Product(cdxtail, adytail, ti1, ti0);
|
|
Two_Product(adxtail, cdytail, tj1, tj0);
|
|
Two_Two_Diff(ti1, ti0, tj1, tj0, catt3, catt[2], catt[1], catt[0]);
|
|
catt[3] = catt3;
|
|
cattlen = 4;
|
|
} else {
|
|
cat[0] = 0.0;
|
|
catlen = 1;
|
|
catt[0] = 0.0;
|
|
cattlen = 1;
|
|
}
|
|
|
|
if (bdxtail != 0.0) {
|
|
temp16alen = scale_expansion_zeroelim(bxtcalen, bxtca, bdxtail, temp16a);
|
|
bxtcatlen = scale_expansion_zeroelim(catlen, cat, bdxtail, bxtcat);
|
|
temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, 2.0 * bdx,
|
|
temp32a);
|
|
temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
|
|
temp32alen, temp32a, temp48);
|
|
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
|
|
temp48, finother);
|
|
finswap = finnow; finnow = finother; finother = finswap;
|
|
if (cdytail != 0.0) {
|
|
temp8len = scale_expansion_zeroelim(4, aa, bdxtail, temp8);
|
|
temp16alen = scale_expansion_zeroelim(temp8len, temp8, cdytail,
|
|
temp16a);
|
|
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
|
|
temp16a, finother);
|
|
finswap = finnow; finnow = finother; finother = finswap;
|
|
}
|
|
if (adytail != 0.0) {
|
|
temp8len = scale_expansion_zeroelim(4, cc, -bdxtail, temp8);
|
|
temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail,
|
|
temp16a);
|
|
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
|
|
temp16a, finother);
|
|
finswap = finnow; finnow = finother; finother = finswap;
|
|
}
|
|
|
|
temp32alen = scale_expansion_zeroelim(bxtcatlen, bxtcat, bdxtail,
|
|
temp32a);
|
|
bxtcattlen = scale_expansion_zeroelim(cattlen, catt, bdxtail, bxtcatt);
|
|
temp16alen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, 2.0 * bdx,
|
|
temp16a);
|
|
temp16blen = scale_expansion_zeroelim(bxtcattlen, bxtcatt, bdxtail,
|
|
temp16b);
|
|
temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
|
|
temp16blen, temp16b, temp32b);
|
|
temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
|
|
temp32blen, temp32b, temp64);
|
|
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
|
|
temp64, finother);
|
|
finswap = finnow; finnow = finother; finother = finswap;
|
|
}
|
|
if (bdytail != 0.0) {
|
|
temp16alen = scale_expansion_zeroelim(bytcalen, bytca, bdytail, temp16a);
|
|
bytcatlen = scale_expansion_zeroelim(catlen, cat, bdytail, bytcat);
|
|
temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, 2.0 * bdy,
|
|
temp32a);
|
|
temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
|
|
temp32alen, temp32a, temp48);
|
|
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
|
|
temp48, finother);
|
|
finswap = finnow; finnow = finother; finother = finswap;
|
|
|
|
|
|
temp32alen = scale_expansion_zeroelim(bytcatlen, bytcat, bdytail,
|
|
temp32a);
|
|
bytcattlen = scale_expansion_zeroelim(cattlen, catt, bdytail, bytcatt);
|
|
temp16alen = scale_expansion_zeroelim(bytcattlen, bytcatt, 2.0 * bdy,
|
|
temp16a);
|
|
temp16blen = scale_expansion_zeroelim(bytcattlen, bytcatt, bdytail,
|
|
temp16b);
|
|
temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
|
|
temp16blen, temp16b, temp32b);
|
|
temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
|
|
temp32blen, temp32b, temp64);
|
|
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
|
|
temp64, finother);
|
|
finswap = finnow; finnow = finother; finother = finswap;
|
|
}
|
|
}
|
|
if ((cdxtail != 0.0) || (cdytail != 0.0)) {
|
|
if ((adxtail != 0.0) || (adytail != 0.0)
|
|
|| (bdxtail != 0.0) || (bdytail != 0.0)) {
|
|
Two_Product(adxtail, bdy, ti1, ti0);
|
|
Two_Product(adx, bdytail, tj1, tj0);
|
|
Two_Two_Sum(ti1, ti0, tj1, tj0, u3, u[2], u[1], u[0]);
|
|
u[3] = u3;
|
|
negate = -ady;
|
|
Two_Product(bdxtail, negate, ti1, ti0);
|
|
negate = -adytail;
|
|
Two_Product(bdx, negate, tj1, tj0);
|
|
Two_Two_Sum(ti1, ti0, tj1, tj0, v3, v[2], v[1], v[0]);
|
|
v[3] = v3;
|
|
abtlen = fast_expansion_sum_zeroelim(4, u, 4, v, abt);
|
|
|
|
Two_Product(adxtail, bdytail, ti1, ti0);
|
|
Two_Product(bdxtail, adytail, tj1, tj0);
|
|
Two_Two_Diff(ti1, ti0, tj1, tj0, abtt3, abtt[2], abtt[1], abtt[0]);
|
|
abtt[3] = abtt3;
|
|
abttlen = 4;
|
|
} else {
|
|
abt[0] = 0.0;
|
|
abtlen = 1;
|
|
abtt[0] = 0.0;
|
|
abttlen = 1;
|
|
}
|
|
|
|
if (cdxtail != 0.0) {
|
|
temp16alen = scale_expansion_zeroelim(cxtablen, cxtab, cdxtail, temp16a);
|
|
cxtabtlen = scale_expansion_zeroelim(abtlen, abt, cdxtail, cxtabt);
|
|
temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, 2.0 * cdx,
|
|
temp32a);
|
|
temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
|
|
temp32alen, temp32a, temp48);
|
|
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
|
|
temp48, finother);
|
|
finswap = finnow; finnow = finother; finother = finswap;
|
|
if (adytail != 0.0) {
|
|
temp8len = scale_expansion_zeroelim(4, bb, cdxtail, temp8);
|
|
temp16alen = scale_expansion_zeroelim(temp8len, temp8, adytail,
|
|
temp16a);
|
|
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
|
|
temp16a, finother);
|
|
finswap = finnow; finnow = finother; finother = finswap;
|
|
}
|
|
if (bdytail != 0.0) {
|
|
temp8len = scale_expansion_zeroelim(4, aa, -cdxtail, temp8);
|
|
temp16alen = scale_expansion_zeroelim(temp8len, temp8, bdytail,
|
|
temp16a);
|
|
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp16alen,
|
|
temp16a, finother);
|
|
finswap = finnow; finnow = finother; finother = finswap;
|
|
}
|
|
|
|
temp32alen = scale_expansion_zeroelim(cxtabtlen, cxtabt, cdxtail,
|
|
temp32a);
|
|
cxtabttlen = scale_expansion_zeroelim(abttlen, abtt, cdxtail, cxtabtt);
|
|
temp16alen = scale_expansion_zeroelim(cxtabttlen, cxtabtt, 2.0 * cdx,
|
|
temp16a);
|
|
temp16blen = scale_expansion_zeroelim(cxtabttlen, cxtabtt, cdxtail,
|
|
temp16b);
|
|
temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
|
|
temp16blen, temp16b, temp32b);
|
|
temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
|
|
temp32blen, temp32b, temp64);
|
|
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
|
|
temp64, finother);
|
|
finswap = finnow; finnow = finother; finother = finswap;
|
|
}
|
|
if (cdytail != 0.0) {
|
|
temp16alen = scale_expansion_zeroelim(cytablen, cytab, cdytail, temp16a);
|
|
cytabtlen = scale_expansion_zeroelim(abtlen, abt, cdytail, cytabt);
|
|
temp32alen = scale_expansion_zeroelim(cytabtlen, cytabt, 2.0 * cdy,
|
|
temp32a);
|
|
temp48len = fast_expansion_sum_zeroelim(temp16alen, temp16a,
|
|
temp32alen, temp32a, temp48);
|
|
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp48len,
|
|
temp48, finother);
|
|
finswap = finnow; finnow = finother; finother = finswap;
|
|
|
|
|
|
temp32alen = scale_expansion_zeroelim(cytabtlen, cytabt, cdytail,
|
|
temp32a);
|
|
cytabttlen = scale_expansion_zeroelim(abttlen, abtt, cdytail, cytabtt);
|
|
temp16alen = scale_expansion_zeroelim(cytabttlen, cytabtt, 2.0 * cdy,
|
|
temp16a);
|
|
temp16blen = scale_expansion_zeroelim(cytabttlen, cytabtt, cdytail,
|
|
temp16b);
|
|
temp32blen = fast_expansion_sum_zeroelim(temp16alen, temp16a,
|
|
temp16blen, temp16b, temp32b);
|
|
temp64len = fast_expansion_sum_zeroelim(temp32alen, temp32a,
|
|
temp32blen, temp32b, temp64);
|
|
finlength = fast_expansion_sum_zeroelim(finlength, finnow, temp64len,
|
|
temp64, finother);
|
|
finswap = finnow; finnow = finother; finother = finswap;
|
|
}
|
|
}
|
|
|
|
return finnow[finlength - 1];
|
|
}
|
|
|
|
REAL incircle(pa, pb, pc, pd)
|
|
point pa;
|
|
point pb;
|
|
point pc;
|
|
point pd;
|
|
{
|
|
REAL adx, bdx, cdx, ady, bdy, cdy;
|
|
REAL bdxcdy, cdxbdy, cdxady, adxcdy, adxbdy, bdxady;
|
|
REAL alift, blift, clift;
|
|
REAL det;
|
|
REAL permanent, errbound;
|
|
|
|
incirclecount++;
|
|
|
|
adx = pa[0] - pd[0];
|
|
bdx = pb[0] - pd[0];
|
|
cdx = pc[0] - pd[0];
|
|
ady = pa[1] - pd[1];
|
|
bdy = pb[1] - pd[1];
|
|
cdy = pc[1] - pd[1];
|
|
|
|
bdxcdy = bdx * cdy;
|
|
cdxbdy = cdx * bdy;
|
|
alift = adx * adx + ady * ady;
|
|
|
|
cdxady = cdx * ady;
|
|
adxcdy = adx * cdy;
|
|
blift = bdx * bdx + bdy * bdy;
|
|
|
|
adxbdy = adx * bdy;
|
|
bdxady = bdx * ady;
|
|
clift = cdx * cdx + cdy * cdy;
|
|
|
|
det = alift * (bdxcdy - cdxbdy)
|
|
+ blift * (cdxady - adxcdy)
|
|
+ clift * (adxbdy - bdxady);
|
|
|
|
if (noexact) {
|
|
return det;
|
|
}
|
|
|
|
permanent = (Absolute(bdxcdy) + Absolute(cdxbdy)) * alift
|
|
+ (Absolute(cdxady) + Absolute(adxcdy)) * blift
|
|
+ (Absolute(adxbdy) + Absolute(bdxady)) * clift;
|
|
errbound = iccerrboundA * permanent;
|
|
if ((det > errbound) || (-det > errbound)) {
|
|
return det;
|
|
}
|
|
|
|
return incircleadapt(pa, pb, pc, pd, permanent);
|
|
}
|
|
|
|
/** **/
|
|
/** **/
|
|
/********* Determinant evaluation routines end here *********/
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* triangleinit() Initialize some variables. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
void triangleinit()
|
|
{
|
|
points.maxitems = triangles.maxitems = shelles.maxitems = viri.maxitems =
|
|
badsegments.maxitems = badtriangles.maxitems = splaynodes.maxitems = 0l;
|
|
points.itembytes = triangles.itembytes = shelles.itembytes = viri.itembytes =
|
|
badsegments.itembytes = badtriangles.itembytes = splaynodes.itembytes = 0;
|
|
recenttri.tri = (triangle *) NULL; /* No triangle has been visited yet. */
|
|
samples = 1; /* Point location should take at least one sample. */
|
|
checksegments = 0; /* There are no segments in the triangulation yet. */
|
|
incirclecount = counterclockcount = hyperbolacount = 0;
|
|
circumcentercount = circletopcount = 0;
|
|
randomseed = 1;
|
|
|
|
exactinit(); /* Initialize exact arithmetic constants. */
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* randomnation() Generate a random number between 0 and `choices' - 1. */
|
|
/* */
|
|
/* This is a simple linear congruential random number generator. Hence, it */
|
|
/* is a bad random number generator, but good enough for most randomized */
|
|
/* geometric algorithms. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
unsigned long randomnation(choices)
|
|
unsigned int choices;
|
|
{
|
|
randomseed = (randomseed * 1366l + 150889l) % 714025l;
|
|
return randomseed / (714025l / choices + 1);
|
|
}
|
|
|
|
/********* Mesh quality testing routines begin here *********/
|
|
/** **/
|
|
/** **/
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* checkmesh() Test the mesh for topological consistency. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
#ifndef REDUCED
|
|
|
|
void checkmesh()
|
|
{
|
|
struct triedge triangleloop;
|
|
struct triedge oppotri, oppooppotri;
|
|
point triorg, tridest, triapex;
|
|
point oppoorg, oppodest;
|
|
int horrors;
|
|
int saveexact;
|
|
triangle ptr; /* Temporary variable used by sym(). */
|
|
|
|
/* Temporarily turn on exact arithmetic if it's off. */
|
|
saveexact = noexact;
|
|
noexact = 0;
|
|
if (!quiet) {
|
|
printf(" Checking consistency of mesh...\n");
|
|
}
|
|
horrors = 0;
|
|
/* Run through the list of triangles, checking each one. */
|
|
traversalinit(&triangles);
|
|
triangleloop.tri = triangletraverse();
|
|
while (triangleloop.tri != (triangle *) NULL) {
|
|
/* Check all three edges of the triangle. */
|
|
for (triangleloop.orient = 0; triangleloop.orient < 3;
|
|
triangleloop.orient++) {
|
|
org(triangleloop, triorg);
|
|
dest(triangleloop, tridest);
|
|
if (triangleloop.orient == 0) { /* Only test for inversion once. */
|
|
/* Test if the triangle is flat or inverted. */
|
|
apex(triangleloop, triapex);
|
|
if (counterclockwise(triorg, tridest, triapex) <= 0.0) {
|
|
printf(" !! !! Inverted ");
|
|
printtriangle(&triangleloop);
|
|
horrors++;
|
|
}
|
|
}
|
|
/* Find the neighboring triangle on this edge. */
|
|
sym(triangleloop, oppotri);
|
|
if (oppotri.tri != dummytri) {
|
|
/* Check that the triangle's neighbor knows it's a neighbor. */
|
|
sym(oppotri, oppooppotri);
|
|
if ((triangleloop.tri != oppooppotri.tri)
|
|
|| (triangleloop.orient != oppooppotri.orient)) {
|
|
printf(" !! !! Asymmetric triangle-triangle bond:\n");
|
|
if (triangleloop.tri == oppooppotri.tri) {
|
|
printf(" (Right triangle, wrong orientation)\n");
|
|
}
|
|
printf(" First ");
|
|
printtriangle(&triangleloop);
|
|
printf(" Second (nonreciprocating) ");
|
|
printtriangle(&oppotri);
|
|
horrors++;
|
|
}
|
|
/* Check that both triangles agree on the identities */
|
|
/* of their shared vertices. */
|
|
org(oppotri, oppoorg);
|
|
dest(oppotri, oppodest);
|
|
if ((triorg != oppodest) || (tridest != oppoorg)) {
|
|
printf(" !! !! Mismatched edge coordinates between two triangles:\n"
|
|
);
|
|
printf(" First mismatched ");
|
|
printtriangle(&triangleloop);
|
|
printf(" Second mismatched ");
|
|
printtriangle(&oppotri);
|
|
horrors++;
|
|
}
|
|
}
|
|
}
|
|
triangleloop.tri = triangletraverse();
|
|
}
|
|
if (horrors == 0) {
|
|
if (!quiet) {
|
|
printf(" In my studied opinion, the mesh appears to be consistent.\n");
|
|
}
|
|
} else if (horrors == 1) {
|
|
printf(" !! !! !! !! Precisely one festering wound discovered.\n");
|
|
} else {
|
|
printf(" !! !! !! !! %d abominations witnessed.\n", horrors);
|
|
}
|
|
/* Restore the status of exact arithmetic. */
|
|
noexact = saveexact;
|
|
}
|
|
|
|
#endif /* not REDUCED */
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* checkdelaunay() Ensure that the mesh is (constrained) Delaunay. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
#ifndef REDUCED
|
|
|
|
void checkdelaunay()
|
|
{
|
|
struct triedge triangleloop;
|
|
struct triedge oppotri;
|
|
struct edge opposhelle;
|
|
point triorg, tridest, triapex;
|
|
point oppoapex;
|
|
int shouldbedelaunay;
|
|
int horrors;
|
|
int saveexact;
|
|
triangle ptr; /* Temporary variable used by sym(). */
|
|
shelle sptr; /* Temporary variable used by tspivot(). */
|
|
|
|
/* Temporarily turn on exact arithmetic if it's off. */
|
|
saveexact = noexact;
|
|
noexact = 0;
|
|
if (!quiet) {
|
|
printf(" Checking Delaunay property of mesh...\n");
|
|
}
|
|
horrors = 0;
|
|
/* Run through the list of triangles, checking each one. */
|
|
traversalinit(&triangles);
|
|
triangleloop.tri = triangletraverse();
|
|
while (triangleloop.tri != (triangle *) NULL) {
|
|
/* Check all three edges of the triangle. */
|
|
for (triangleloop.orient = 0; triangleloop.orient < 3;
|
|
triangleloop.orient++) {
|
|
org(triangleloop, triorg);
|
|
dest(triangleloop, tridest);
|
|
apex(triangleloop, triapex);
|
|
sym(triangleloop, oppotri);
|
|
apex(oppotri, oppoapex);
|
|
/* Only test that the edge is locally Delaunay if there is an */
|
|
/* adjoining triangle whose pointer is larger (to ensure that */
|
|
/* each pair isn't tested twice). */
|
|
shouldbedelaunay = (oppotri.tri != dummytri)
|
|
&& (triapex != (point) NULL) && (oppoapex != (point) NULL)
|
|
&& (triangleloop.tri < oppotri.tri);
|
|
if (checksegments && shouldbedelaunay) {
|
|
/* If a shell edge separates the triangles, then the edge is */
|
|
/* constrained, so no local Delaunay test should be done. */
|
|
tspivot(triangleloop, opposhelle);
|
|
if (opposhelle.sh != dummysh){
|
|
shouldbedelaunay = 0;
|
|
}
|
|
}
|
|
if (shouldbedelaunay) {
|
|
if (incircle(triorg, tridest, triapex, oppoapex) > 0.0) {
|
|
printf(" !! !! Non-Delaunay pair of triangles:\n");
|
|
printf(" First non-Delaunay ");
|
|
printtriangle(&triangleloop);
|
|
printf(" Second non-Delaunay ");
|
|
printtriangle(&oppotri);
|
|
horrors++;
|
|
}
|
|
}
|
|
}
|
|
triangleloop.tri = triangletraverse();
|
|
}
|
|
if (horrors == 0) {
|
|
if (!quiet) {
|
|
printf(
|
|
" By virtue of my perceptive intelligence, I declare the mesh Delaunay.\n");
|
|
}
|
|
} else if (horrors == 1) {
|
|
printf(
|
|
" !! !! !! !! Precisely one terrifying transgression identified.\n");
|
|
} else {
|
|
printf(" !! !! !! !! %d obscenities viewed with horror.\n", horrors);
|
|
}
|
|
/* Restore the status of exact arithmetic. */
|
|
noexact = saveexact;
|
|
}
|
|
|
|
#endif /* not REDUCED */
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* enqueuebadtri() Add a bad triangle to the end of a queue. */
|
|
/* */
|
|
/* The queue is actually a set of 64 queues. I use multiple queues to give */
|
|
/* priority to smaller angles. I originally implemented a heap, but the */
|
|
/* queues are (to my surprise) much faster. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
#ifndef CDT_ONLY
|
|
|
|
void enqueuebadtri(instri, angle, insapex, insorg, insdest)
|
|
struct triedge *instri;
|
|
REAL angle;
|
|
point insapex;
|
|
point insorg;
|
|
point insdest;
|
|
{
|
|
struct badface *newface;
|
|
int queuenumber;
|
|
|
|
if (verbose > 2) {
|
|
printf(" Queueing bad triangle:\n");
|
|
printf(" (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", insorg[0],
|
|
insorg[1], insdest[0], insdest[1], insapex[0], insapex[1]);
|
|
}
|
|
/* Allocate space for the bad triangle. */
|
|
newface = (struct badface *) poolalloc(&badtriangles);
|
|
triedgecopy(*instri, newface->badfacetri);
|
|
newface->key = angle;
|
|
newface->faceapex = insapex;
|
|
newface->faceorg = insorg;
|
|
newface->facedest = insdest;
|
|
newface->nextface = (struct badface *) NULL;
|
|
/* Determine the appropriate queue to put the bad triangle into. */
|
|
if (angle > 0.6) {
|
|
queuenumber = (int) (160.0 * (angle - 0.6));
|
|
if (queuenumber > 63) {
|
|
queuenumber = 63;
|
|
}
|
|
} else {
|
|
/* It's not a bad angle; put the triangle in the lowest-priority queue. */
|
|
queuenumber = 0;
|
|
}
|
|
/* Add the triangle to the end of a queue. */
|
|
*queuetail[queuenumber] = newface;
|
|
/* Maintain a pointer to the NULL pointer at the end of the queue. */
|
|
queuetail[queuenumber] = &newface->nextface;
|
|
}
|
|
|
|
#endif /* not CDT_ONLY */
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* dequeuebadtri() Remove a triangle from the front of the queue. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
#ifndef CDT_ONLY
|
|
|
|
struct badface *dequeuebadtri()
|
|
{
|
|
struct badface *result;
|
|
int queuenumber;
|
|
|
|
/* Look for a nonempty queue. */
|
|
for (queuenumber = 63; queuenumber >= 0; queuenumber--) {
|
|
result = queuefront[queuenumber];
|
|
if (result != (struct badface *) NULL) {
|
|
/* Remove the triangle from the queue. */
|
|
queuefront[queuenumber] = result->nextface;
|
|
/* Maintain a pointer to the NULL pointer at the end of the queue. */
|
|
if (queuefront[queuenumber] == (struct badface *) NULL) {
|
|
queuetail[queuenumber] = &queuefront[queuenumber];
|
|
}
|
|
return result;
|
|
}
|
|
}
|
|
return (struct badface *) NULL;
|
|
}
|
|
|
|
#endif /* not CDT_ONLY */
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* checkedge4encroach() Check a segment to see if it is encroached; add */
|
|
/* it to the list if it is. */
|
|
/* */
|
|
/* An encroached segment is an unflippable edge that has a point in its */
|
|
/* diametral circle (that is, it faces an angle greater than 90 degrees). */
|
|
/* This definition is due to Ruppert. */
|
|
/* */
|
|
/* Returns a nonzero value if the edge is encroached. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
#ifndef CDT_ONLY
|
|
|
|
int checkedge4encroach(testedge)
|
|
struct edge *testedge;
|
|
{
|
|
struct triedge neighbortri;
|
|
struct edge testsym;
|
|
struct edge *badedge;
|
|
int addtolist;
|
|
int sides;
|
|
point eorg, edest, eapex;
|
|
triangle ptr; /* Temporary variable used by stpivot(). */
|
|
|
|
addtolist = 0;
|
|
sides = 0;
|
|
|
|
sorg(*testedge, eorg);
|
|
sdest(*testedge, edest);
|
|
/* Check one neighbor of the shell edge. */
|
|
stpivot(*testedge, neighbortri);
|
|
/* Does the neighbor exist, or is this a boundary edge? */
|
|
if (neighbortri.tri != dummytri) {
|
|
sides++;
|
|
/* Find a vertex opposite this edge. */
|
|
apex(neighbortri, eapex);
|
|
/* Check whether the vertex is inside the diametral circle of the */
|
|
/* shell edge. Pythagoras' Theorem is used to check whether the */
|
|
/* angle at the vertex is greater than 90 degrees. */
|
|
if (eapex[0] * (eorg[0] + edest[0]) + eapex[1] * (eorg[1] + edest[1]) >
|
|
eapex[0] * eapex[0] + eorg[0] * edest[0] +
|
|
eapex[1] * eapex[1] + eorg[1] * edest[1]) {
|
|
addtolist = 1;
|
|
}
|
|
}
|
|
/* Check the other neighbor of the shell edge. */
|
|
ssym(*testedge, testsym);
|
|
stpivot(testsym, neighbortri);
|
|
/* Does the neighbor exist, or is this a boundary edge? */
|
|
if (neighbortri.tri != dummytri) {
|
|
sides++;
|
|
/* Find the other vertex opposite this edge. */
|
|
apex(neighbortri, eapex);
|
|
/* Check whether the vertex is inside the diametral circle of the */
|
|
/* shell edge. Pythagoras' Theorem is used to check whether the */
|
|
/* angle at the vertex is greater than 90 degrees. */
|
|
if (eapex[0] * (eorg[0] + edest[0]) +
|
|
eapex[1] * (eorg[1] + edest[1]) >
|
|
eapex[0] * eapex[0] + eorg[0] * edest[0] +
|
|
eapex[1] * eapex[1] + eorg[1] * edest[1]) {
|
|
addtolist += 2;
|
|
}
|
|
}
|
|
|
|
if (addtolist && (!nobisect || ((nobisect == 1) && (sides == 2)))) {
|
|
if (verbose > 2) {
|
|
printf(" Queueing encroached segment (%.12g, %.12g) (%.12g, %.12g).\n",
|
|
eorg[0], eorg[1], edest[0], edest[1]);
|
|
}
|
|
/* Add the shell edge to the list of encroached segments. */
|
|
/* Be sure to get the orientation right. */
|
|
badedge = (struct edge *) poolalloc(&badsegments);
|
|
if (addtolist == 1) {
|
|
shellecopy(*testedge, *badedge);
|
|
} else {
|
|
shellecopy(testsym, *badedge);
|
|
}
|
|
}
|
|
return addtolist;
|
|
}
|
|
|
|
#endif /* not CDT_ONLY */
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* testtriangle() Test a face for quality measures. */
|
|
/* */
|
|
/* Tests a triangle to see if it satisfies the minimum angle condition and */
|
|
/* the maximum area condition. Triangles that aren't up to spec are added */
|
|
/* to the bad triangle queue. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
#ifndef CDT_ONLY
|
|
|
|
void testtriangle(testtri)
|
|
struct triedge *testtri;
|
|
{
|
|
struct triedge sametesttri;
|
|
struct edge edge1, edge2;
|
|
point torg, tdest, tapex;
|
|
point anglevertex;
|
|
REAL dxod, dyod, dxda, dyda, dxao, dyao;
|
|
REAL dxod2, dyod2, dxda2, dyda2, dxao2, dyao2;
|
|
REAL apexlen, orglen, destlen;
|
|
REAL angle;
|
|
REAL area;
|
|
shelle sptr; /* Temporary variable used by tspivot(). */
|
|
|
|
org(*testtri, torg);
|
|
dest(*testtri, tdest);
|
|
apex(*testtri, tapex);
|
|
dxod = torg[0] - tdest[0];
|
|
dyod = torg[1] - tdest[1];
|
|
dxda = tdest[0] - tapex[0];
|
|
dyda = tdest[1] - tapex[1];
|
|
dxao = tapex[0] - torg[0];
|
|
dyao = tapex[1] - torg[1];
|
|
dxod2 = dxod * dxod;
|
|
dyod2 = dyod * dyod;
|
|
dxda2 = dxda * dxda;
|
|
dyda2 = dyda * dyda;
|
|
dxao2 = dxao * dxao;
|
|
dyao2 = dyao * dyao;
|
|
/* Find the lengths of the triangle's three edges. */
|
|
apexlen = dxod2 + dyod2;
|
|
orglen = dxda2 + dyda2;
|
|
destlen = dxao2 + dyao2;
|
|
if ((apexlen < orglen) && (apexlen < destlen)) {
|
|
/* The edge opposite the apex is shortest. */
|
|
/* Find the square of the cosine of the angle at the apex. */
|
|
angle = dxda * dxao + dyda * dyao;
|
|
angle = angle * angle / (orglen * destlen);
|
|
anglevertex = tapex;
|
|
lnext(*testtri, sametesttri);
|
|
tspivot(sametesttri, edge1);
|
|
lnextself(sametesttri);
|
|
tspivot(sametesttri, edge2);
|
|
} else if (orglen < destlen) {
|
|
/* The edge opposite the origin is shortest. */
|
|
/* Find the square of the cosine of the angle at the origin. */
|
|
angle = dxod * dxao + dyod * dyao;
|
|
angle = angle * angle / (apexlen * destlen);
|
|
anglevertex = torg;
|
|
tspivot(*testtri, edge1);
|
|
lprev(*testtri, sametesttri);
|
|
tspivot(sametesttri, edge2);
|
|
} else {
|
|
/* The edge opposite the destination is shortest. */
|
|
/* Find the square of the cosine of the angle at the destination. */
|
|
angle = dxod * dxda + dyod * dyda;
|
|
angle = angle * angle / (apexlen * orglen);
|
|
anglevertex = tdest;
|
|
tspivot(*testtri, edge1);
|
|
lnext(*testtri, sametesttri);
|
|
tspivot(sametesttri, edge2);
|
|
}
|
|
/* Check if both edges that form the angle are segments. */
|
|
if ((edge1.sh != dummysh) && (edge2.sh != dummysh)) {
|
|
/* The angle is a segment intersection. */
|
|
if ((angle > 0.9924) && !quiet) { /* Roughly 5 degrees. */
|
|
if (angle > 1.0) {
|
|
/* Beware of a floating exception in acos(). */
|
|
angle = 1.0;
|
|
}
|
|
/* Find the actual angle in degrees, for printing. */
|
|
angle = acos(sqrt(angle)) * (180.0 / PI);
|
|
printf(
|
|
"Warning: Small angle (%.4g degrees) between segments at point\n",
|
|
angle);
|
|
printf(" (%.12g, %.12g)\n", anglevertex[0], anglevertex[1]);
|
|
}
|
|
/* Don't add this bad triangle to the list; there's nothing that */
|
|
/* can be done about a small angle between two segments. */
|
|
angle = 0.0;
|
|
}
|
|
/* Check whether the angle is smaller than permitted. */
|
|
if (angle > goodangle) {
|
|
/* Add this triangle to the list of bad triangles. */
|
|
enqueuebadtri(testtri, angle, tapex, torg, tdest);
|
|
return;
|
|
}
|
|
if (vararea || fixedarea) {
|
|
/* Check whether the area is larger than permitted. */
|
|
area = 0.5 * (dxod * dyda - dyod * dxda);
|
|
if (fixedarea && (area > maxarea)) {
|
|
/* Add this triangle to the list of bad triangles. */
|
|
enqueuebadtri(testtri, angle, tapex, torg, tdest);
|
|
} else if (vararea) {
|
|
/* Nonpositive area constraints are treated as unconstrained. */
|
|
if ((area > areabound(*testtri)) && (areabound(*testtri) > 0.0)) {
|
|
/* Add this triangle to the list of bad triangles. */
|
|
enqueuebadtri(testtri, angle, tapex, torg, tdest);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
#endif /* not CDT_ONLY */
|
|
|
|
/** **/
|
|
/** **/
|
|
/********* Mesh quality testing routines end here *********/
|
|
|
|
/********* Point location routines begin here *********/
|
|
/** **/
|
|
/** **/
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* makepointmap() Construct a mapping from points to triangles to improve */
|
|
/* the speed of point location for segment insertion. */
|
|
/* */
|
|
/* Traverses all the triangles, and provides each corner of each triangle */
|
|
/* with a pointer to that triangle. Of course, pointers will be */
|
|
/* overwritten by other pointers because (almost) each point is a corner */
|
|
/* of several triangles, but in the end every point will point to some */
|
|
/* triangle that contains it. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
void makepointmap()
|
|
{
|
|
struct triedge triangleloop;
|
|
point triorg;
|
|
|
|
if (verbose) {
|
|
printf(" Constructing mapping from points to triangles.\n");
|
|
}
|
|
traversalinit(&triangles);
|
|
triangleloop.tri = triangletraverse();
|
|
while (triangleloop.tri != (triangle *) NULL) {
|
|
/* Check all three points of the triangle. */
|
|
for (triangleloop.orient = 0; triangleloop.orient < 3;
|
|
triangleloop.orient++) {
|
|
org(triangleloop, triorg);
|
|
setpoint2tri(triorg, encode(triangleloop));
|
|
}
|
|
triangleloop.tri = triangletraverse();
|
|
}
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* preciselocate() Find a triangle or edge containing a given point. */
|
|
/* */
|
|
/* Begins its search from `searchtri'. It is important that `searchtri' */
|
|
/* be a handle with the property that `searchpoint' is strictly to the left */
|
|
/* of the edge denoted by `searchtri', or is collinear with that edge and */
|
|
/* does not intersect that edge. (In particular, `searchpoint' should not */
|
|
/* be the origin or destination of that edge.) */
|
|
/* */
|
|
/* These conditions are imposed because preciselocate() is normally used in */
|
|
/* one of two situations: */
|
|
/* */
|
|
/* (1) To try to find the location to insert a new point. Normally, we */
|
|
/* know an edge that the point is strictly to the left of. In the */
|
|
/* incremental Delaunay algorithm, that edge is a bounding box edge. */
|
|
/* In Ruppert's Delaunay refinement algorithm for quality meshing, */
|
|
/* that edge is the shortest edge of the triangle whose circumcenter */
|
|
/* is being inserted. */
|
|
/* */
|
|
/* (2) To try to find an existing point. In this case, any edge on the */
|
|
/* convex hull is a good starting edge. The possibility that the */
|
|
/* vertex one seeks is an endpoint of the starting edge must be */
|
|
/* screened out before preciselocate() is called. */
|
|
/* */
|
|
/* On completion, `searchtri' is a triangle that contains `searchpoint'. */
|
|
/* */
|
|
/* This implementation differs from that given by Guibas and Stolfi. It */
|
|
/* walks from triangle to triangle, crossing an edge only if `searchpoint' */
|
|
/* is on the other side of the line containing that edge. After entering */
|
|
/* a triangle, there are two edges by which one can leave that triangle. */
|
|
/* If both edges are valid (`searchpoint' is on the other side of both */
|
|
/* edges), one of the two is chosen by drawing a line perpendicular to */
|
|
/* the entry edge (whose endpoints are `forg' and `fdest') passing through */
|
|
/* `fapex'. Depending on which side of this perpendicular `searchpoint' */
|
|
/* falls on, an exit edge is chosen. */
|
|
/* */
|
|
/* This implementation is empirically faster than the Guibas and Stolfi */
|
|
/* point location routine (which I originally used), which tends to spiral */
|
|
/* in toward its target. */
|
|
/* */
|
|
/* Returns ONVERTEX if the point lies on an existing vertex. `searchtri' */
|
|
/* is a handle whose origin is the existing vertex. */
|
|
/* */
|
|
/* Returns ONEDGE if the point lies on a mesh edge. `searchtri' is a */
|
|
/* handle whose primary edge is the edge on which the point lies. */
|
|
/* */
|
|
/* Returns INTRIANGLE if the point lies strictly within a triangle. */
|
|
/* `searchtri' is a handle on the triangle that contains the point. */
|
|
/* */
|
|
/* Returns OUTSIDE if the point lies outside the mesh. `searchtri' is a */
|
|
/* handle whose primary edge the point is to the right of. This might */
|
|
/* occur when the circumcenter of a triangle falls just slightly outside */
|
|
/* the mesh due to floating-point roundoff error. It also occurs when */
|
|
/* seeking a hole or region point that a foolish user has placed outside */
|
|
/* the mesh. */
|
|
/* */
|
|
/* WARNING: This routine is designed for convex triangulations, and will */
|
|
/* not generally work after the holes and concavities have been carved. */
|
|
/* However, it can still be used to find the circumcenter of a triangle, as */
|
|
/* long as the search is begun from the triangle in question. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
enum locateresult preciselocate(searchpoint, searchtri)
|
|
point searchpoint;
|
|
struct triedge *searchtri;
|
|
{
|
|
struct triedge backtracktri;
|
|
point forg, fdest, fapex;
|
|
point swappoint;
|
|
REAL orgorient, destorient;
|
|
int moveleft;
|
|
triangle ptr; /* Temporary variable used by sym(). */
|
|
|
|
if (verbose > 2) {
|
|
printf(" Searching for point (%.12g, %.12g).\n",
|
|
searchpoint[0], searchpoint[1]);
|
|
}
|
|
/* Where are we? */
|
|
org(*searchtri, forg);
|
|
dest(*searchtri, fdest);
|
|
apex(*searchtri, fapex);
|
|
while (1) {
|
|
if (verbose > 2) {
|
|
printf(" At (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
|
|
forg[0], forg[1], fdest[0], fdest[1], fapex[0], fapex[1]);
|
|
}
|
|
/* Check whether the apex is the point we seek. */
|
|
if ((fapex[0] == searchpoint[0]) && (fapex[1] == searchpoint[1])) {
|
|
lprevself(*searchtri);
|
|
return ONVERTEX;
|
|
}
|
|
/* Does the point lie on the other side of the line defined by the */
|
|
/* triangle edge opposite the triangle's destination? */
|
|
destorient = counterclockwise(forg, fapex, searchpoint);
|
|
/* Does the point lie on the other side of the line defined by the */
|
|
/* triangle edge opposite the triangle's origin? */
|
|
orgorient = counterclockwise(fapex, fdest, searchpoint);
|
|
if (destorient > 0.0) {
|
|
if (orgorient > 0.0) {
|
|
/* Move left if the inner product of (fapex - searchpoint) and */
|
|
/* (fdest - forg) is positive. This is equivalent to drawing */
|
|
/* a line perpendicular to the line (forg, fdest) passing */
|
|
/* through `fapex', and determining which side of this line */
|
|
/* `searchpoint' falls on. */
|
|
moveleft = (fapex[0] - searchpoint[0]) * (fdest[0] - forg[0]) +
|
|
(fapex[1] - searchpoint[1]) * (fdest[1] - forg[1]) > 0.0;
|
|
} else {
|
|
moveleft = 1;
|
|
}
|
|
} else {
|
|
if (orgorient > 0.0) {
|
|
moveleft = 0;
|
|
} else {
|
|
/* The point we seek must be on the boundary of or inside this */
|
|
/* triangle. */
|
|
if (destorient == 0.0) {
|
|
lprevself(*searchtri);
|
|
return ONEDGE;
|
|
}
|
|
if (orgorient == 0.0) {
|
|
lnextself(*searchtri);
|
|
return ONEDGE;
|
|
}
|
|
return INTRIANGLE;
|
|
}
|
|
}
|
|
|
|
/* Move to another triangle. Leave a trace `backtracktri' in case */
|
|
/* floating-point roundoff or some such bogey causes us to walk */
|
|
/* off a boundary of the triangulation. We can just bounce off */
|
|
/* the boundary as if it were an elastic band. */
|
|
if (moveleft) {
|
|
lprev(*searchtri, backtracktri);
|
|
fdest = fapex;
|
|
} else {
|
|
lnext(*searchtri, backtracktri);
|
|
forg = fapex;
|
|
}
|
|
sym(backtracktri, *searchtri);
|
|
|
|
/* Check for walking off the edge. */
|
|
if (searchtri->tri == dummytri) {
|
|
/* Turn around. */
|
|
triedgecopy(backtracktri, *searchtri);
|
|
swappoint = forg;
|
|
forg = fdest;
|
|
fdest = swappoint;
|
|
apex(*searchtri, fapex);
|
|
/* Check if the point really is beyond the triangulation boundary. */
|
|
destorient = counterclockwise(forg, fapex, searchpoint);
|
|
orgorient = counterclockwise(fapex, fdest, searchpoint);
|
|
if ((orgorient < 0.0) && (destorient < 0.0)) {
|
|
return OUTSIDE;
|
|
}
|
|
} else {
|
|
apex(*searchtri, fapex);
|
|
}
|
|
}
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* locate() Find a triangle or edge containing a given point. */
|
|
/* */
|
|
/* Searching begins from one of: the input `searchtri', a recently */
|
|
/* encountered triangle `recenttri', or from a triangle chosen from a */
|
|
/* random sample. The choice is made by determining which triangle's */
|
|
/* origin is closest to the point we are searcing for. Normally, */
|
|
/* `searchtri' should be a handle on the convex hull of the triangulation. */
|
|
/* */
|
|
/* Details on the random sampling method can be found in the Mucke, Saias, */
|
|
/* and Zhu paper cited in the header of this code. */
|
|
/* */
|
|
/* On completion, `searchtri' is a triangle that contains `searchpoint'. */
|
|
/* */
|
|
/* Returns ONVERTEX if the point lies on an existing vertex. `searchtri' */
|
|
/* is a handle whose origin is the existing vertex. */
|
|
/* */
|
|
/* Returns ONEDGE if the point lies on a mesh edge. `searchtri' is a */
|
|
/* handle whose primary edge is the edge on which the point lies. */
|
|
/* */
|
|
/* Returns INTRIANGLE if the point lies strictly within a triangle. */
|
|
/* `searchtri' is a handle on the triangle that contains the point. */
|
|
/* */
|
|
/* Returns OUTSIDE if the point lies outside the mesh. `searchtri' is a */
|
|
/* handle whose primary edge the point is to the right of. This might */
|
|
/* occur when the circumcenter of a triangle falls just slightly outside */
|
|
/* the mesh due to floating-point roundoff error. It also occurs when */
|
|
/* seeking a hole or region point that a foolish user has placed outside */
|
|
/* the mesh. */
|
|
/* */
|
|
/* WARNING: This routine is designed for convex triangulations, and will */
|
|
/* not generally work after the holes and concavities have been carved. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
enum locateresult locate(searchpoint, searchtri)
|
|
point searchpoint;
|
|
struct triedge *searchtri;
|
|
{
|
|
VOID **sampleblock;
|
|
triangle *firsttri;
|
|
struct triedge sampletri;
|
|
point torg, tdest;
|
|
unsigned long alignptr;
|
|
REAL searchdist, dist;
|
|
REAL ahead;
|
|
long sampleblocks, samplesperblock, samplenum;
|
|
long triblocks;
|
|
long i, j;
|
|
triangle ptr; /* Temporary variable used by sym(). */
|
|
|
|
if (verbose > 2) {
|
|
printf(" Randomly sampling for a triangle near point (%.12g, %.12g).\n",
|
|
searchpoint[0], searchpoint[1]);
|
|
}
|
|
/* Record the distance from the suggested starting triangle to the */
|
|
/* point we seek. */
|
|
org(*searchtri, torg);
|
|
searchdist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0])
|
|
+ (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]);
|
|
if (verbose > 2) {
|
|
printf(" Boundary triangle has origin (%.12g, %.12g).\n",
|
|
torg[0], torg[1]);
|
|
}
|
|
|
|
/* If a recently encountered triangle has been recorded and has not been */
|
|
/* deallocated, test it as a good starting point. */
|
|
if (recenttri.tri != (triangle *) NULL) {
|
|
if (recenttri.tri[3] != (triangle) NULL) {
|
|
org(recenttri, torg);
|
|
if ((torg[0] == searchpoint[0]) && (torg[1] == searchpoint[1])) {
|
|
triedgecopy(recenttri, *searchtri);
|
|
return ONVERTEX;
|
|
}
|
|
dist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0])
|
|
+ (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]);
|
|
if (dist < searchdist) {
|
|
triedgecopy(recenttri, *searchtri);
|
|
searchdist = dist;
|
|
if (verbose > 2) {
|
|
printf(" Choosing recent triangle with origin (%.12g, %.12g).\n",
|
|
torg[0], torg[1]);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
/* The number of random samples taken is proportional to the cube root of */
|
|
/* the number of triangles in the mesh. The next bit of code assumes */
|
|
/* that the number of triangles increases monotonically. */
|
|
while (SAMPLEFACTOR * samples * samples * samples < triangles.items) {
|
|
samples++;
|
|
}
|
|
triblocks = (triangles.maxitems + TRIPERBLOCK - 1) / TRIPERBLOCK;
|
|
samplesperblock = 1 + (samples / triblocks);
|
|
sampleblocks = samples / samplesperblock;
|
|
sampleblock = triangles.firstblock;
|
|
sampletri.orient = 0;
|
|
for (i = 0; i < sampleblocks; i++) {
|
|
alignptr = (unsigned long) (sampleblock + 1);
|
|
firsttri = (triangle *) (alignptr + (unsigned long) triangles.alignbytes
|
|
- (alignptr % (unsigned long) triangles.alignbytes));
|
|
for (j = 0; j < samplesperblock; j++) {
|
|
if (i == triblocks - 1) {
|
|
samplenum = randomnation((int)
|
|
(triangles.maxitems - (i * TRIPERBLOCK)));
|
|
} else {
|
|
samplenum = randomnation(TRIPERBLOCK);
|
|
}
|
|
sampletri.tri = (triangle *)
|
|
(firsttri + (samplenum * triangles.itemwords));
|
|
if (sampletri.tri[3] != (triangle) NULL) {
|
|
org(sampletri, torg);
|
|
dist = (searchpoint[0] - torg[0]) * (searchpoint[0] - torg[0])
|
|
+ (searchpoint[1] - torg[1]) * (searchpoint[1] - torg[1]);
|
|
if (dist < searchdist) {
|
|
triedgecopy(sampletri, *searchtri);
|
|
searchdist = dist;
|
|
if (verbose > 2) {
|
|
printf(" Choosing triangle with origin (%.12g, %.12g).\n",
|
|
torg[0], torg[1]);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
sampleblock = (VOID **) *sampleblock;
|
|
}
|
|
/* Where are we? */
|
|
org(*searchtri, torg);
|
|
dest(*searchtri, tdest);
|
|
/* Check the starting triangle's vertices. */
|
|
if ((torg[0] == searchpoint[0]) && (torg[1] == searchpoint[1])) {
|
|
return ONVERTEX;
|
|
}
|
|
if ((tdest[0] == searchpoint[0]) && (tdest[1] == searchpoint[1])) {
|
|
lnextself(*searchtri);
|
|
return ONVERTEX;
|
|
}
|
|
/* Orient `searchtri' to fit the preconditions of calling preciselocate(). */
|
|
ahead = counterclockwise(torg, tdest, searchpoint);
|
|
if (ahead < 0.0) {
|
|
/* Turn around so that `searchpoint' is to the left of the */
|
|
/* edge specified by `searchtri'. */
|
|
symself(*searchtri);
|
|
} else if (ahead == 0.0) {
|
|
/* Check if `searchpoint' is between `torg' and `tdest'. */
|
|
if (((torg[0] < searchpoint[0]) == (searchpoint[0] < tdest[0]))
|
|
&& ((torg[1] < searchpoint[1]) == (searchpoint[1] < tdest[1]))) {
|
|
return ONEDGE;
|
|
}
|
|
}
|
|
return preciselocate(searchpoint, searchtri);
|
|
}
|
|
|
|
/** **/
|
|
/** **/
|
|
/********* Point location routines end here *********/
|
|
|
|
/********* Mesh transformation routines begin here *********/
|
|
/** **/
|
|
/** **/
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* insertshelle() Create a new shell edge and insert it between two */
|
|
/* triangles. */
|
|
/* */
|
|
/* The new shell edge is inserted at the edge described by the handle */
|
|
/* `tri'. Its vertices are properly initialized. The marker `shellemark' */
|
|
/* is applied to the shell edge and, if appropriate, its vertices. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
void insertshelle(tri, shellemark)
|
|
struct triedge *tri; /* Edge at which to insert the new shell edge. */
|
|
int shellemark; /* Marker for the new shell edge. */
|
|
{
|
|
struct triedge oppotri;
|
|
struct edge newshelle;
|
|
point triorg, tridest;
|
|
triangle ptr; /* Temporary variable used by sym(). */
|
|
shelle sptr; /* Temporary variable used by tspivot(). */
|
|
|
|
/* Mark points if possible. */
|
|
org(*tri, triorg);
|
|
dest(*tri, tridest);
|
|
if (pointmark(triorg) == 0) {
|
|
setpointmark(triorg, shellemark);
|
|
}
|
|
if (pointmark(tridest) == 0) {
|
|
setpointmark(tridest, shellemark);
|
|
}
|
|
/* Check if there's already a shell edge here. */
|
|
tspivot(*tri, newshelle);
|
|
if (newshelle.sh == dummysh) {
|
|
/* Make new shell edge and initialize its vertices. */
|
|
makeshelle(&newshelle);
|
|
setsorg(newshelle, tridest);
|
|
setsdest(newshelle, triorg);
|
|
/* Bond new shell edge to the two triangles it is sandwiched between. */
|
|
/* Note that the facing triangle `oppotri' might be equal to */
|
|
/* `dummytri' (outer space), but the new shell edge is bonded to it */
|
|
/* all the same. */
|
|
tsbond(*tri, newshelle);
|
|
sym(*tri, oppotri);
|
|
ssymself(newshelle);
|
|
tsbond(oppotri, newshelle);
|
|
setmark(newshelle, shellemark);
|
|
if (verbose > 2) {
|
|
printf(" Inserting new ");
|
|
printshelle(&newshelle);
|
|
}
|
|
} else {
|
|
if (mark(newshelle) == 0) {
|
|
setmark(newshelle, shellemark);
|
|
}
|
|
}
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* Terminology */
|
|
/* */
|
|
/* A "local transformation" replaces a small set of triangles with another */
|
|
/* set of triangles. This may or may not involve inserting or deleting a */
|
|
/* point. */
|
|
/* */
|
|
/* The term "casing" is used to describe the set of triangles that are */
|
|
/* attached to the triangles being transformed, but are not transformed */
|
|
/* themselves. Think of the casing as a fixed hollow structure inside */
|
|
/* which all the action happens. A "casing" is only defined relative to */
|
|
/* a single transformation; each occurrence of a transformation will */
|
|
/* involve a different casing. */
|
|
/* */
|
|
/* A "shell" is similar to a "casing". The term "shell" describes the set */
|
|
/* of shell edges (if any) that are attached to the triangles being */
|
|
/* transformed. However, I sometimes use "shell" to refer to a single */
|
|
/* shell edge, so don't get confused. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* flip() Transform two triangles to two different triangles by flipping */
|
|
/* an edge within a quadrilateral. */
|
|
/* */
|
|
/* Imagine the original triangles, abc and bad, oriented so that the */
|
|
/* shared edge ab lies in a horizontal plane, with the point b on the left */
|
|
/* and the point a on the right. The point c lies below the edge, and the */
|
|
/* point d lies above the edge. The `flipedge' handle holds the edge ab */
|
|
/* of triangle abc, and is directed left, from vertex a to vertex b. */
|
|
/* */
|
|
/* The triangles abc and bad are deleted and replaced by the triangles cdb */
|
|
/* and dca. The triangles that represent abc and bad are NOT deallocated; */
|
|
/* they are reused for dca and cdb, respectively. Hence, any handles that */
|
|
/* may have held the original triangles are still valid, although not */
|
|
/* directed as they were before. */
|
|
/* */
|
|
/* Upon completion of this routine, the `flipedge' handle holds the edge */
|
|
/* dc of triangle dca, and is directed down, from vertex d to vertex c. */
|
|
/* (Hence, the two triangles have rotated counterclockwise.) */
|
|
/* */
|
|
/* WARNING: This transformation is geometrically valid only if the */
|
|
/* quadrilateral adbc is convex. Furthermore, this transformation is */
|
|
/* valid only if there is not a shell edge between the triangles abc and */
|
|
/* bad. This routine does not check either of these preconditions, and */
|
|
/* it is the responsibility of the calling routine to ensure that they are */
|
|
/* met. If they are not, the streets shall be filled with wailing and */
|
|
/* gnashing of teeth. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
void flip(flipedge)
|
|
struct triedge *flipedge; /* Handle for the triangle abc. */
|
|
{
|
|
struct triedge botleft, botright;
|
|
struct triedge topleft, topright;
|
|
struct triedge top;
|
|
struct triedge botlcasing, botrcasing;
|
|
struct triedge toplcasing, toprcasing;
|
|
struct edge botlshelle, botrshelle;
|
|
struct edge toplshelle, toprshelle;
|
|
point leftpoint, rightpoint, botpoint;
|
|
point farpoint;
|
|
triangle ptr; /* Temporary variable used by sym(). */
|
|
shelle sptr; /* Temporary variable used by tspivot(). */
|
|
|
|
/* Identify the vertices of the quadrilateral. */
|
|
org(*flipedge, rightpoint);
|
|
dest(*flipedge, leftpoint);
|
|
apex(*flipedge, botpoint);
|
|
sym(*flipedge, top);
|
|
#ifdef SELF_CHECK
|
|
if (top.tri == dummytri) {
|
|
printf("Internal error in flip(): Attempt to flip on boundary.\n");
|
|
lnextself(*flipedge);
|
|
return;
|
|
}
|
|
if (checksegments) {
|
|
tspivot(*flipedge, toplshelle);
|
|
if (toplshelle.sh != dummysh) {
|
|
printf("Internal error in flip(): Attempt to flip a segment.\n");
|
|
lnextself(*flipedge);
|
|
return;
|
|
}
|
|
}
|
|
#endif /* SELF_CHECK */
|
|
apex(top, farpoint);
|
|
|
|
/* Identify the casing of the quadrilateral. */
|
|
lprev(top, topleft);
|
|
sym(topleft, toplcasing);
|
|
lnext(top, topright);
|
|
sym(topright, toprcasing);
|
|
lnext(*flipedge, botleft);
|
|
sym(botleft, botlcasing);
|
|
lprev(*flipedge, botright);
|
|
sym(botright, botrcasing);
|
|
/* Rotate the quadrilateral one-quarter turn counterclockwise. */
|
|
bond(topleft, botlcasing);
|
|
bond(botleft, botrcasing);
|
|
bond(botright, toprcasing);
|
|
bond(topright, toplcasing);
|
|
|
|
if (checksegments) {
|
|
/* Check for shell edges and rebond them to the quadrilateral. */
|
|
tspivot(topleft, toplshelle);
|
|
tspivot(botleft, botlshelle);
|
|
tspivot(botright, botrshelle);
|
|
tspivot(topright, toprshelle);
|
|
if (toplshelle.sh == dummysh) {
|
|
tsdissolve(topright);
|
|
} else {
|
|
tsbond(topright, toplshelle);
|
|
}
|
|
if (botlshelle.sh == dummysh) {
|
|
tsdissolve(topleft);
|
|
} else {
|
|
tsbond(topleft, botlshelle);
|
|
}
|
|
if (botrshelle.sh == dummysh) {
|
|
tsdissolve(botleft);
|
|
} else {
|
|
tsbond(botleft, botrshelle);
|
|
}
|
|
if (toprshelle.sh == dummysh) {
|
|
tsdissolve(botright);
|
|
} else {
|
|
tsbond(botright, toprshelle);
|
|
}
|
|
}
|
|
|
|
/* New point assignments for the rotated quadrilateral. */
|
|
setorg(*flipedge, farpoint);
|
|
setdest(*flipedge, botpoint);
|
|
setapex(*flipedge, rightpoint);
|
|
setorg(top, botpoint);
|
|
setdest(top, farpoint);
|
|
setapex(top, leftpoint);
|
|
if (verbose > 2) {
|
|
printf(" Edge flip results in left ");
|
|
lnextself(topleft);
|
|
printtriangle(&topleft);
|
|
printf(" and right ");
|
|
printtriangle(flipedge);
|
|
}
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* insertsite() Insert a vertex into a Delaunay triangulation, */
|
|
/* performing flips as necessary to maintain the Delaunay */
|
|
/* property. */
|
|
/* */
|
|
/* The point `insertpoint' is located. If `searchtri.tri' is not NULL, */
|
|
/* the search for the containing triangle begins from `searchtri'. If */
|
|
/* `searchtri.tri' is NULL, a full point location procedure is called. */
|
|
/* If `insertpoint' is found inside a triangle, the triangle is split into */
|
|
/* three; if `insertpoint' lies on an edge, the edge is split in two, */
|
|
/* thereby splitting the two adjacent triangles into four. Edge flips are */
|
|
/* used to restore the Delaunay property. If `insertpoint' lies on an */
|
|
/* existing vertex, no action is taken, and the value DUPLICATEPOINT is */
|
|
/* returned. On return, `searchtri' is set to a handle whose origin is the */
|
|
/* existing vertex. */
|
|
/* */
|
|
/* Normally, the parameter `splitedge' is set to NULL, implying that no */
|
|
/* segment should be split. In this case, if `insertpoint' is found to */
|
|
/* lie on a segment, no action is taken, and the value VIOLATINGPOINT is */
|
|
/* returned. On return, `searchtri' is set to a handle whose primary edge */
|
|
/* is the violated segment. */
|
|
/* */
|
|
/* If the calling routine wishes to split a segment by inserting a point in */
|
|
/* it, the parameter `splitedge' should be that segment. In this case, */
|
|
/* `searchtri' MUST be the triangle handle reached by pivoting from that */
|
|
/* segment; no point location is done. */
|
|
/* */
|
|
/* `segmentflaws' and `triflaws' are flags that indicate whether or not */
|
|
/* there should be checks for the creation of encroached segments or bad */
|
|
/* quality faces. If a newly inserted point encroaches upon segments, */
|
|
/* these segments are added to the list of segments to be split if */
|
|
/* `segmentflaws' is set. If bad triangles are created, these are added */
|
|
/* to the queue if `triflaws' is set. */
|
|
/* */
|
|
/* If a duplicate point or violated segment does not prevent the point */
|
|
/* from being inserted, the return value will be ENCROACHINGPOINT if the */
|
|
/* point encroaches upon a segment (and checking is enabled), or */
|
|
/* SUCCESSFULPOINT otherwise. In either case, `searchtri' is set to a */
|
|
/* handle whose origin is the newly inserted vertex. */
|
|
/* */
|
|
/* insertsite() does not use flip() for reasons of speed; some */
|
|
/* information can be reused from edge flip to edge flip, like the */
|
|
/* locations of shell edges. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
enum insertsiteresult insertsite(insertpoint, searchtri, splitedge,
|
|
segmentflaws, triflaws)
|
|
point insertpoint;
|
|
struct triedge *searchtri;
|
|
struct edge *splitedge;
|
|
int segmentflaws;
|
|
int triflaws;
|
|
{
|
|
struct triedge horiz;
|
|
struct triedge top;
|
|
struct triedge botleft, botright;
|
|
struct triedge topleft, topright;
|
|
struct triedge newbotleft, newbotright;
|
|
struct triedge newtopright;
|
|
struct triedge botlcasing, botrcasing;
|
|
struct triedge toplcasing, toprcasing;
|
|
struct triedge testtri;
|
|
struct edge botlshelle, botrshelle;
|
|
struct edge toplshelle, toprshelle;
|
|
struct edge brokenshelle;
|
|
struct edge checkshelle;
|
|
struct edge rightedge;
|
|
struct edge newedge;
|
|
struct edge *encroached;
|
|
point first;
|
|
point leftpoint, rightpoint, botpoint, toppoint, farpoint;
|
|
REAL attrib;
|
|
REAL area;
|
|
enum insertsiteresult success;
|
|
enum locateresult intersect;
|
|
int doflip;
|
|
int mirrorflag;
|
|
int i;
|
|
triangle ptr; /* Temporary variable used by sym(). */
|
|
shelle sptr; /* Temporary variable used by spivot() and tspivot(). */
|
|
|
|
if (verbose > 1) {
|
|
printf(" Inserting (%.12g, %.12g).\n", insertpoint[0], insertpoint[1]);
|
|
}
|
|
if (splitedge == (struct edge *) NULL) {
|
|
/* Find the location of the point to be inserted. Check if a good */
|
|
/* starting triangle has already been provided by the caller. */
|
|
if (searchtri->tri == (triangle *) NULL) {
|
|
/* Find a boundary triangle. */
|
|
horiz.tri = dummytri;
|
|
horiz.orient = 0;
|
|
symself(horiz);
|
|
/* Search for a triangle containing `insertpoint'. */
|
|
intersect = locate(insertpoint, &horiz);
|
|
} else {
|
|
/* Start searching from the triangle provided by the caller. */
|
|
triedgecopy(*searchtri, horiz);
|
|
intersect = preciselocate(insertpoint, &horiz);
|
|
}
|
|
} else {
|
|
/* The calling routine provides the edge in which the point is inserted. */
|
|
triedgecopy(*searchtri, horiz);
|
|
intersect = ONEDGE;
|
|
}
|
|
if (intersect == ONVERTEX) {
|
|
/* There's already a vertex there. Return in `searchtri' a triangle */
|
|
/* whose origin is the existing vertex. */
|
|
triedgecopy(horiz, *searchtri);
|
|
triedgecopy(horiz, recenttri);
|
|
return DUPLICATEPOINT;
|
|
}
|
|
if ((intersect == ONEDGE) || (intersect == OUTSIDE)) {
|
|
/* The vertex falls on an edge or boundary. */
|
|
if (checksegments && (splitedge == (struct edge *) NULL)) {
|
|
/* Check whether the vertex falls on a shell edge. */
|
|
tspivot(horiz, brokenshelle);
|
|
if (brokenshelle.sh != dummysh) {
|
|
/* The vertex falls on a shell edge. */
|
|
if (segmentflaws) {
|
|
if (nobisect == 0) {
|
|
/* Add the shell edge to the list of encroached segments. */
|
|
encroached = (struct edge *) poolalloc(&badsegments);
|
|
shellecopy(brokenshelle, *encroached);
|
|
} else if ((nobisect == 1) && (intersect == ONEDGE)) {
|
|
/* This segment may be split only if it is an internal boundary. */
|
|
sym(horiz, testtri);
|
|
if (testtri.tri != dummytri) {
|
|
/* Add the shell edge to the list of encroached segments. */
|
|
encroached = (struct edge *) poolalloc(&badsegments);
|
|
shellecopy(brokenshelle, *encroached);
|
|
}
|
|
}
|
|
}
|
|
/* Return a handle whose primary edge contains the point, */
|
|
/* which has not been inserted. */
|
|
triedgecopy(horiz, *searchtri);
|
|
triedgecopy(horiz, recenttri);
|
|
return VIOLATINGPOINT;
|
|
}
|
|
}
|
|
/* Insert the point on an edge, dividing one triangle into two (if */
|
|
/* the edge lies on a boundary) or two triangles into four. */
|
|
lprev(horiz, botright);
|
|
sym(botright, botrcasing);
|
|
sym(horiz, topright);
|
|
/* Is there a second triangle? (Or does this edge lie on a boundary?) */
|
|
mirrorflag = topright.tri != dummytri;
|
|
if (mirrorflag) {
|
|
lnextself(topright);
|
|
sym(topright, toprcasing);
|
|
maketriangle(&newtopright);
|
|
} else {
|
|
/* Splitting the boundary edge increases the number of boundary edges. */
|
|
hullsize++;
|
|
}
|
|
maketriangle(&newbotright);
|
|
|
|
/* Set the vertices of changed and new triangles. */
|
|
org(horiz, rightpoint);
|
|
dest(horiz, leftpoint);
|
|
apex(horiz, botpoint);
|
|
setorg(newbotright, botpoint);
|
|
setdest(newbotright, rightpoint);
|
|
setapex(newbotright, insertpoint);
|
|
setorg(horiz, insertpoint);
|
|
for (i = 0; i < eextras; i++) {
|
|
/* Set the element attributes of a new triangle. */
|
|
setelemattribute(newbotright, i, elemattribute(botright, i));
|
|
}
|
|
if (vararea) {
|
|
/* Set the area constraint of a new triangle. */
|
|
setareabound(newbotright, areabound(botright));
|
|
}
|
|
if (mirrorflag) {
|
|
dest(topright, toppoint);
|
|
setorg(newtopright, rightpoint);
|
|
setdest(newtopright, toppoint);
|
|
setapex(newtopright, insertpoint);
|
|
setorg(topright, insertpoint);
|
|
for (i = 0; i < eextras; i++) {
|
|
/* Set the element attributes of another new triangle. */
|
|
setelemattribute(newtopright, i, elemattribute(topright, i));
|
|
}
|
|
if (vararea) {
|
|
/* Set the area constraint of another new triangle. */
|
|
setareabound(newtopright, areabound(topright));
|
|
}
|
|
}
|
|
|
|
/* There may be shell edges that need to be bonded */
|
|
/* to the new triangle(s). */
|
|
if (checksegments) {
|
|
tspivot(botright, botrshelle);
|
|
if (botrshelle.sh != dummysh) {
|
|
tsdissolve(botright);
|
|
tsbond(newbotright, botrshelle);
|
|
}
|
|
if (mirrorflag) {
|
|
tspivot(topright, toprshelle);
|
|
if (toprshelle.sh != dummysh) {
|
|
tsdissolve(topright);
|
|
tsbond(newtopright, toprshelle);
|
|
}
|
|
}
|
|
}
|
|
|
|
/* Bond the new triangle(s) to the surrounding triangles. */
|
|
bond(newbotright, botrcasing);
|
|
lprevself(newbotright);
|
|
bond(newbotright, botright);
|
|
lprevself(newbotright);
|
|
if (mirrorflag) {
|
|
bond(newtopright, toprcasing);
|
|
lnextself(newtopright);
|
|
bond(newtopright, topright);
|
|
lnextself(newtopright);
|
|
bond(newtopright, newbotright);
|
|
}
|
|
|
|
if (splitedge != (struct edge *) NULL) {
|
|
/* Split the shell edge into two. */
|
|
setsdest(*splitedge, insertpoint);
|
|
ssymself(*splitedge);
|
|
spivot(*splitedge, rightedge);
|
|
insertshelle(&newbotright, mark(*splitedge));
|
|
tspivot(newbotright, newedge);
|
|
sbond(*splitedge, newedge);
|
|
ssymself(newedge);
|
|
sbond(newedge, rightedge);
|
|
ssymself(*splitedge);
|
|
}
|
|
|
|
#ifdef SELF_CHECK
|
|
if (counterclockwise(rightpoint, leftpoint, botpoint) < 0.0) {
|
|
printf("Internal error in insertsite():\n");
|
|
printf(" Clockwise triangle prior to edge point insertion (bottom).\n");
|
|
}
|
|
if (mirrorflag) {
|
|
if (counterclockwise(leftpoint, rightpoint, toppoint) < 0.0) {
|
|
printf("Internal error in insertsite():\n");
|
|
printf(" Clockwise triangle prior to edge point insertion (top).\n");
|
|
}
|
|
if (counterclockwise(rightpoint, toppoint, insertpoint) < 0.0) {
|
|
printf("Internal error in insertsite():\n");
|
|
printf(" Clockwise triangle after edge point insertion (top right).\n"
|
|
);
|
|
}
|
|
if (counterclockwise(toppoint, leftpoint, insertpoint) < 0.0) {
|
|
printf("Internal error in insertsite():\n");
|
|
printf(" Clockwise triangle after edge point insertion (top left).\n"
|
|
);
|
|
}
|
|
}
|
|
if (counterclockwise(leftpoint, botpoint, insertpoint) < 0.0) {
|
|
printf("Internal error in insertsite():\n");
|
|
printf(" Clockwise triangle after edge point insertion (bottom left).\n"
|
|
);
|
|
}
|
|
if (counterclockwise(botpoint, rightpoint, insertpoint) < 0.0) {
|
|
printf("Internal error in insertsite():\n");
|
|
printf(
|
|
" Clockwise triangle after edge point insertion (bottom right).\n");
|
|
}
|
|
#endif /* SELF_CHECK */
|
|
if (verbose > 2) {
|
|
printf(" Updating bottom left ");
|
|
printtriangle(&botright);
|
|
if (mirrorflag) {
|
|
printf(" Updating top left ");
|
|
printtriangle(&topright);
|
|
printf(" Creating top right ");
|
|
printtriangle(&newtopright);
|
|
}
|
|
printf(" Creating bottom right ");
|
|
printtriangle(&newbotright);
|
|
}
|
|
|
|
/* Position `horiz' on the first edge to check for */
|
|
/* the Delaunay property. */
|
|
lnextself(horiz);
|
|
} else {
|
|
/* Insert the point in a triangle, splitting it into three. */
|
|
lnext(horiz, botleft);
|
|
lprev(horiz, botright);
|
|
sym(botleft, botlcasing);
|
|
sym(botright, botrcasing);
|
|
maketriangle(&newbotleft);
|
|
maketriangle(&newbotright);
|
|
|
|
/* Set the vertices of changed and new triangles. */
|
|
org(horiz, rightpoint);
|
|
dest(horiz, leftpoint);
|
|
apex(horiz, botpoint);
|
|
setorg(newbotleft, leftpoint);
|
|
setdest(newbotleft, botpoint);
|
|
setapex(newbotleft, insertpoint);
|
|
setorg(newbotright, botpoint);
|
|
setdest(newbotright, rightpoint);
|
|
setapex(newbotright, insertpoint);
|
|
setapex(horiz, insertpoint);
|
|
for (i = 0; i < eextras; i++) {
|
|
/* Set the element attributes of the new triangles. */
|
|
attrib = elemattribute(horiz, i);
|
|
setelemattribute(newbotleft, i, attrib);
|
|
setelemattribute(newbotright, i, attrib);
|
|
}
|
|
if (vararea) {
|
|
/* Set the area constraint of the new triangles. */
|
|
area = areabound(horiz);
|
|
setareabound(newbotleft, area);
|
|
setareabound(newbotright, area);
|
|
}
|
|
|
|
/* There may be shell edges that need to be bonded */
|
|
/* to the new triangles. */
|
|
if (checksegments) {
|
|
tspivot(botleft, botlshelle);
|
|
if (botlshelle.sh != dummysh) {
|
|
tsdissolve(botleft);
|
|
tsbond(newbotleft, botlshelle);
|
|
}
|
|
tspivot(botright, botrshelle);
|
|
if (botrshelle.sh != dummysh) {
|
|
tsdissolve(botright);
|
|
tsbond(newbotright, botrshelle);
|
|
}
|
|
}
|
|
|
|
/* Bond the new triangles to the surrounding triangles. */
|
|
bond(newbotleft, botlcasing);
|
|
bond(newbotright, botrcasing);
|
|
lnextself(newbotleft);
|
|
lprevself(newbotright);
|
|
bond(newbotleft, newbotright);
|
|
lnextself(newbotleft);
|
|
bond(botleft, newbotleft);
|
|
lprevself(newbotright);
|
|
bond(botright, newbotright);
|
|
|
|
#ifdef SELF_CHECK
|
|
if (counterclockwise(rightpoint, leftpoint, botpoint) < 0.0) {
|
|
printf("Internal error in insertsite():\n");
|
|
printf(" Clockwise triangle prior to point insertion.\n");
|
|
}
|
|
if (counterclockwise(rightpoint, leftpoint, insertpoint) < 0.0) {
|
|
printf("Internal error in insertsite():\n");
|
|
printf(" Clockwise triangle after point insertion (top).\n");
|
|
}
|
|
if (counterclockwise(leftpoint, botpoint, insertpoint) < 0.0) {
|
|
printf("Internal error in insertsite():\n");
|
|
printf(" Clockwise triangle after point insertion (left).\n");
|
|
}
|
|
if (counterclockwise(botpoint, rightpoint, insertpoint) < 0.0) {
|
|
printf("Internal error in insertsite():\n");
|
|
printf(" Clockwise triangle after point insertion (right).\n");
|
|
}
|
|
#endif /* SELF_CHECK */
|
|
if (verbose > 2) {
|
|
printf(" Updating top ");
|
|
printtriangle(&horiz);
|
|
printf(" Creating left ");
|
|
printtriangle(&newbotleft);
|
|
printf(" Creating right ");
|
|
printtriangle(&newbotright);
|
|
}
|
|
}
|
|
|
|
/* The insertion is successful by default, unless an encroached */
|
|
/* edge is found. */
|
|
success = SUCCESSFULPOINT;
|
|
/* Circle around the newly inserted vertex, checking each edge opposite */
|
|
/* it for the Delaunay property. Non-Delaunay edges are flipped. */
|
|
/* `horiz' is always the edge being checked. `first' marks where to */
|
|
/* stop circling. */
|
|
org(horiz, first);
|
|
rightpoint = first;
|
|
dest(horiz, leftpoint);
|
|
/* Circle until finished. */
|
|
while (1) {
|
|
/* By default, the edge will be flipped. */
|
|
doflip = 1;
|
|
if (checksegments) {
|
|
/* Check for a segment, which cannot be flipped. */
|
|
tspivot(horiz, checkshelle);
|
|
if (checkshelle.sh != dummysh) {
|
|
/* The edge is a segment and cannot be flipped. */
|
|
doflip = 0;
|
|
#ifndef CDT_ONLY
|
|
if (segmentflaws) {
|
|
/* Does the new point encroach upon this segment? */
|
|
if (checkedge4encroach(&checkshelle)) {
|
|
success = ENCROACHINGPOINT;
|
|
}
|
|
}
|
|
#endif /* not CDT_ONLY */
|
|
}
|
|
}
|
|
if (doflip) {
|
|
/* Check if the edge is a boundary edge. */
|
|
sym(horiz, top);
|
|
if (top.tri == dummytri) {
|
|
/* The edge is a boundary edge and cannot be flipped. */
|
|
doflip = 0;
|
|
} else {
|
|
/* Find the point on the other side of the edge. */
|
|
apex(top, farpoint);
|
|
/* In the incremental Delaunay triangulation algorithm, any of */
|
|
/* `leftpoint', `rightpoint', and `farpoint' could be vertices */
|
|
/* of the triangular bounding box. These vertices must be */
|
|
/* treated as if they are infinitely distant, even though their */
|
|
/* "coordinates" are not. */
|
|
if ((leftpoint == infpoint1) || (leftpoint == infpoint2)
|
|
|| (leftpoint == infpoint3)) {
|
|
/* `leftpoint' is infinitely distant. Check the convexity of */
|
|
/* the boundary of the triangulation. 'farpoint' might be */
|
|
/* infinite as well, but trust me, this same condition */
|
|
/* should be applied. */
|
|
doflip = counterclockwise(insertpoint, rightpoint, farpoint) > 0.0;
|
|
} else if ((rightpoint == infpoint1) || (rightpoint == infpoint2)
|
|
|| (rightpoint == infpoint3)) {
|
|
/* `rightpoint' is infinitely distant. Check the convexity of */
|
|
/* the boundary of the triangulation. 'farpoint' might be */
|
|
/* infinite as well, but trust me, this same condition */
|
|
/* should be applied. */
|
|
doflip = counterclockwise(farpoint, leftpoint, insertpoint) > 0.0;
|
|
} else if ((farpoint == infpoint1) || (farpoint == infpoint2)
|
|
|| (farpoint == infpoint3)) {
|
|
/* `farpoint' is infinitely distant and cannot be inside */
|
|
/* the circumcircle of the triangle `horiz'. */
|
|
doflip = 0;
|
|
} else {
|
|
/* Test whether the edge is locally Delaunay. */
|
|
doflip = incircle(leftpoint, insertpoint, rightpoint, farpoint)
|
|
> 0.0;
|
|
}
|
|
if (doflip) {
|
|
/* We made it! Flip the edge `horiz' by rotating its containing */
|
|
/* quadrilateral (the two triangles adjacent to `horiz'). */
|
|
/* Identify the casing of the quadrilateral. */
|
|
lprev(top, topleft);
|
|
sym(topleft, toplcasing);
|
|
lnext(top, topright);
|
|
sym(topright, toprcasing);
|
|
lnext(horiz, botleft);
|
|
sym(botleft, botlcasing);
|
|
lprev(horiz, botright);
|
|
sym(botright, botrcasing);
|
|
/* Rotate the quadrilateral one-quarter turn counterclockwise. */
|
|
bond(topleft, botlcasing);
|
|
bond(botleft, botrcasing);
|
|
bond(botright, toprcasing);
|
|
bond(topright, toplcasing);
|
|
if (checksegments) {
|
|
/* Check for shell edges and rebond them to the quadrilateral. */
|
|
tspivot(topleft, toplshelle);
|
|
tspivot(botleft, botlshelle);
|
|
tspivot(botright, botrshelle);
|
|
tspivot(topright, toprshelle);
|
|
if (toplshelle.sh == dummysh) {
|
|
tsdissolve(topright);
|
|
} else {
|
|
tsbond(topright, toplshelle);
|
|
}
|
|
if (botlshelle.sh == dummysh) {
|
|
tsdissolve(topleft);
|
|
} else {
|
|
tsbond(topleft, botlshelle);
|
|
}
|
|
if (botrshelle.sh == dummysh) {
|
|
tsdissolve(botleft);
|
|
} else {
|
|
tsbond(botleft, botrshelle);
|
|
}
|
|
if (toprshelle.sh == dummysh) {
|
|
tsdissolve(botright);
|
|
} else {
|
|
tsbond(botright, toprshelle);
|
|
}
|
|
}
|
|
/* New point assignments for the rotated quadrilateral. */
|
|
setorg(horiz, farpoint);
|
|
setdest(horiz, insertpoint);
|
|
setapex(horiz, rightpoint);
|
|
setorg(top, insertpoint);
|
|
setdest(top, farpoint);
|
|
setapex(top, leftpoint);
|
|
for (i = 0; i < eextras; i++) {
|
|
/* Take the average of the two triangles' attributes. */
|
|
attrib = (REAL)(0.5 * (elemattribute(top, i) + elemattribute(horiz, i)));
|
|
setelemattribute(top, i, attrib);
|
|
setelemattribute(horiz, i, attrib);
|
|
}
|
|
if (vararea) {
|
|
if ((areabound(top) <= 0.0) || (areabound(horiz) <= 0.0)) {
|
|
area = -1.0;
|
|
} else {
|
|
/* Take the average of the two triangles' area constraints. */
|
|
/* This prevents small area constraints from migrating a */
|
|
/* long, long way from their original location due to flips. */
|
|
area = (REAL)(0.5 * (areabound(top) + areabound(horiz)));
|
|
}
|
|
setareabound(top, area);
|
|
setareabound(horiz, area);
|
|
}
|
|
#ifdef SELF_CHECK
|
|
if (insertpoint != (point) NULL) {
|
|
if (counterclockwise(leftpoint, insertpoint, rightpoint) < 0.0) {
|
|
printf("Internal error in insertsite():\n");
|
|
printf(" Clockwise triangle prior to edge flip (bottom).\n");
|
|
}
|
|
/* The following test has been removed because constrainededge() */
|
|
/* sometimes generates inverted triangles that insertsite() */
|
|
/* removes. */
|
|
/*
|
|
if (counterclockwise(rightpoint, farpoint, leftpoint) < 0.0) {
|
|
printf("Internal error in insertsite():\n");
|
|
printf(" Clockwise triangle prior to edge flip (top).\n");
|
|
}
|
|
*/
|
|
if (counterclockwise(farpoint, leftpoint, insertpoint) < 0.0) {
|
|
printf("Internal error in insertsite():\n");
|
|
printf(" Clockwise triangle after edge flip (left).\n");
|
|
}
|
|
if (counterclockwise(insertpoint, rightpoint, farpoint) < 0.0) {
|
|
printf("Internal error in insertsite():\n");
|
|
printf(" Clockwise triangle after edge flip (right).\n");
|
|
}
|
|
}
|
|
#endif /* SELF_CHECK */
|
|
if (verbose > 2) {
|
|
printf(" Edge flip results in left ");
|
|
lnextself(topleft);
|
|
printtriangle(&topleft);
|
|
printf(" and right ");
|
|
printtriangle(&horiz);
|
|
}
|
|
/* On the next iterations, consider the two edges that were */
|
|
/* exposed (this is, are now visible to the newly inserted */
|
|
/* point) by the edge flip. */
|
|
lprevself(horiz);
|
|
leftpoint = farpoint;
|
|
}
|
|
}
|
|
}
|
|
if (!doflip) {
|
|
/* The handle `horiz' is accepted as locally Delaunay. */
|
|
#ifndef CDT_ONLY
|
|
if (triflaws) {
|
|
/* Check the triangle `horiz' for quality. */
|
|
testtriangle(&horiz);
|
|
}
|
|
#endif /* not CDT_ONLY */
|
|
/* Look for the next edge around the newly inserted point. */
|
|
lnextself(horiz);
|
|
sym(horiz, testtri);
|
|
/* Check for finishing a complete revolution about the new point, or */
|
|
/* falling off the edge of the triangulation. The latter will */
|
|
/* happen when a point is inserted at a boundary. */
|
|
if ((leftpoint == first) || (testtri.tri == dummytri)) {
|
|
/* We're done. Return a triangle whose origin is the new point. */
|
|
lnext(horiz, *searchtri);
|
|
lnext(horiz, recenttri);
|
|
return success;
|
|
}
|
|
/* Finish finding the next edge around the newly inserted point. */
|
|
lnext(testtri, horiz);
|
|
rightpoint = leftpoint;
|
|
dest(horiz, leftpoint);
|
|
}
|
|
}
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* triangulatepolygon() Find the Delaunay triangulation of a polygon that */
|
|
/* has a certain "nice" shape. This includes the */
|
|
/* polygons that result from deletion of a point or */
|
|
/* insertion of a segment. */
|
|
/* */
|
|
/* This is a conceptually difficult routine. The starting assumption is */
|
|
/* that we have a polygon with n sides. n - 1 of these sides are currently */
|
|
/* represented as edges in the mesh. One side, called the "base", need not */
|
|
/* be. */
|
|
/* */
|
|
/* Inside the polygon is a structure I call a "fan", consisting of n - 1 */
|
|
/* triangles that share a common origin. For each of these triangles, the */
|
|
/* edge opposite the origin is one of the sides of the polygon. The */
|
|
/* primary edge of each triangle is the edge directed from the origin to */
|
|
/* the destination; note that this is not the same edge that is a side of */
|
|
/* the polygon. `firstedge' is the primary edge of the first triangle. */
|
|
/* From there, the triangles follow in counterclockwise order about the */
|
|
/* polygon, until `lastedge', the primary edge of the last triangle. */
|
|
/* `firstedge' and `lastedge' are probably connected to other triangles */
|
|
/* beyond the extremes of the fan, but their identity is not important, as */
|
|
/* long as the fan remains connected to them. */
|
|
/* */
|
|
/* Imagine the polygon oriented so that its base is at the bottom. This */
|
|
/* puts `firstedge' on the far right, and `lastedge' on the far left. */
|
|
/* The right vertex of the base is the destination of `firstedge', and the */
|
|
/* left vertex of the base is the apex of `lastedge'. */
|
|
/* */
|
|
/* The challenge now is to find the right sequence of edge flips to */
|
|
/* transform the fan into a Delaunay triangulation of the polygon. Each */
|
|
/* edge flip effectively removes one triangle from the fan, committing it */
|
|
/* to the polygon. The resulting polygon has one fewer edge. If `doflip' */
|
|
/* is set, the final flip will be performed, resulting in a fan of one */
|
|
/* (useless?) triangle. If `doflip' is not set, the final flip is not */
|
|
/* performed, resulting in a fan of two triangles, and an unfinished */
|
|
/* triangular polygon that is not yet filled out with a single triangle. */
|
|
/* On completion of the routine, `lastedge' is the last remaining triangle, */
|
|
/* or the leftmost of the last two. */
|
|
/* */
|
|
/* Although the flips are performed in the order described above, the */
|
|
/* decisions about what flips to perform are made in precisely the reverse */
|
|
/* order. The recursive triangulatepolygon() procedure makes a decision, */
|
|
/* uses up to two recursive calls to triangulate the "subproblems" */
|
|
/* (polygons with fewer edges), and then performs an edge flip. */
|
|
/* */
|
|
/* The "decision" it makes is which vertex of the polygon should be */
|
|
/* connected to the base. This decision is made by testing every possible */
|
|
/* vertex. Once the best vertex is found, the two edges that connect this */
|
|
/* vertex to the base become the bases for two smaller polygons. These */
|
|
/* are triangulated recursively. Unfortunately, this approach can take */
|
|
/* O(n^2) time not only in the worst case, but in many common cases. It's */
|
|
/* rarely a big deal for point deletion, where n is rarely larger than ten, */
|
|
/* but it could be a big deal for segment insertion, especially if there's */
|
|
/* a lot of long segments that each cut many triangles. I ought to code */
|
|
/* a faster algorithm some time. */
|
|
/* */
|
|
/* The `edgecount' parameter is the number of sides of the polygon, */
|
|
/* including its base. `triflaws' is a flag that determines whether the */
|
|
/* new triangles should be tested for quality, and enqueued if they are */
|
|
/* bad. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
void triangulatepolygon(firstedge, lastedge, edgecount, doflip, triflaws)
|
|
struct triedge *firstedge;
|
|
struct triedge *lastedge;
|
|
int edgecount;
|
|
int doflip;
|
|
int triflaws;
|
|
{
|
|
struct triedge testtri;
|
|
struct triedge besttri;
|
|
struct triedge tempedge;
|
|
point leftbasepoint, rightbasepoint;
|
|
point testpoint;
|
|
point bestpoint;
|
|
int bestnumber;
|
|
int i;
|
|
triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */
|
|
|
|
/* Identify the base vertices. */
|
|
apex(*lastedge, leftbasepoint);
|
|
dest(*firstedge, rightbasepoint);
|
|
if (verbose > 2) {
|
|
printf(" Triangulating interior polygon at edge\n");
|
|
printf(" (%.12g, %.12g) (%.12g, %.12g)\n", leftbasepoint[0],
|
|
leftbasepoint[1], rightbasepoint[0], rightbasepoint[1]);
|
|
}
|
|
/* Find the best vertex to connect the base to. */
|
|
onext(*firstedge, besttri);
|
|
dest(besttri, bestpoint);
|
|
triedgecopy(besttri, testtri);
|
|
bestnumber = 1;
|
|
for (i = 2; i <= edgecount - 2; i++) {
|
|
onextself(testtri);
|
|
dest(testtri, testpoint);
|
|
/* Is this a better vertex? */
|
|
if (incircle(leftbasepoint, rightbasepoint, bestpoint, testpoint) > 0.0) {
|
|
triedgecopy(testtri, besttri);
|
|
bestpoint = testpoint;
|
|
bestnumber = i;
|
|
}
|
|
}
|
|
if (verbose > 2) {
|
|
printf(" Connecting edge to (%.12g, %.12g)\n", bestpoint[0],
|
|
bestpoint[1]);
|
|
}
|
|
if (bestnumber > 1) {
|
|
/* Recursively triangulate the smaller polygon on the right. */
|
|
oprev(besttri, tempedge);
|
|
triangulatepolygon(firstedge, &tempedge, bestnumber + 1, 1, triflaws);
|
|
}
|
|
if (bestnumber < edgecount - 2) {
|
|
/* Recursively triangulate the smaller polygon on the left. */
|
|
sym(besttri, tempedge);
|
|
triangulatepolygon(&besttri, lastedge, edgecount - bestnumber, 1,
|
|
triflaws);
|
|
/* Find `besttri' again; it may have been lost to edge flips. */
|
|
sym(tempedge, besttri);
|
|
}
|
|
if (doflip) {
|
|
/* Do one final edge flip. */
|
|
flip(&besttri);
|
|
#ifndef CDT_ONLY
|
|
if (triflaws) {
|
|
/* Check the quality of the newly committed triangle. */
|
|
sym(besttri, testtri);
|
|
testtriangle(&testtri);
|
|
}
|
|
#endif /* not CDT_ONLY */
|
|
}
|
|
/* Return the base triangle. */
|
|
triedgecopy(besttri, *lastedge);
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* deletesite() Delete a vertex from a Delaunay triangulation, ensuring */
|
|
/* that the triangulation remains Delaunay. */
|
|
/* */
|
|
/* The origin of `deltri' is deleted. The union of the triangles adjacent */
|
|
/* to this point is a polygon, for which the Delaunay triangulation is */
|
|
/* found. Two triangles are removed from the mesh. */
|
|
/* */
|
|
/* Only interior points that do not lie on segments (shell edges) or */
|
|
/* boundaries may be deleted. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
#ifndef CDT_ONLY
|
|
|
|
void deletesite(deltri)
|
|
struct triedge *deltri;
|
|
{
|
|
struct triedge countingtri;
|
|
struct triedge firstedge, lastedge;
|
|
struct triedge deltriright;
|
|
struct triedge lefttri, righttri;
|
|
struct triedge leftcasing, rightcasing;
|
|
struct edge leftshelle, rightshelle;
|
|
point delpoint;
|
|
point neworg;
|
|
int edgecount;
|
|
triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */
|
|
shelle sptr; /* Temporary variable used by tspivot(). */
|
|
|
|
org(*deltri, delpoint);
|
|
if (verbose > 1) {
|
|
printf(" Deleting (%.12g, %.12g).\n", delpoint[0], delpoint[1]);
|
|
}
|
|
pointdealloc(delpoint);
|
|
|
|
/* Count the degree of the point being deleted. */
|
|
onext(*deltri, countingtri);
|
|
edgecount = 1;
|
|
while (!triedgeequal(*deltri, countingtri)) {
|
|
#ifdef SELF_CHECK
|
|
if (countingtri.tri == dummytri) {
|
|
printf("Internal error in deletesite():\n");
|
|
printf(" Attempt to delete boundary point.\n");
|
|
internalerror();
|
|
}
|
|
#endif /* SELF_CHECK */
|
|
edgecount++;
|
|
onextself(countingtri);
|
|
}
|
|
|
|
#ifdef SELF_CHECK
|
|
if (edgecount < 3) {
|
|
printf("Internal error in deletesite():\n Point has degree %d.\n",
|
|
edgecount);
|
|
internalerror();
|
|
}
|
|
#endif /* SELF_CHECK */
|
|
if (edgecount > 3) {
|
|
/* Triangulate the polygon defined by the union of all triangles */
|
|
/* adjacent to the point being deleted. Check the quality of */
|
|
/* the resulting triangles. */
|
|
onext(*deltri, firstedge);
|
|
oprev(*deltri, lastedge);
|
|
triangulatepolygon(&firstedge, &lastedge, edgecount, 0, !nobisect);
|
|
}
|
|
/* Splice out two triangles. */
|
|
lprev(*deltri, deltriright);
|
|
dnext(*deltri, lefttri);
|
|
sym(lefttri, leftcasing);
|
|
oprev(deltriright, righttri);
|
|
sym(righttri, rightcasing);
|
|
bond(*deltri, leftcasing);
|
|
bond(deltriright, rightcasing);
|
|
tspivot(lefttri, leftshelle);
|
|
if (leftshelle.sh != dummysh) {
|
|
tsbond(*deltri, leftshelle);
|
|
}
|
|
tspivot(righttri, rightshelle);
|
|
if (rightshelle.sh != dummysh) {
|
|
tsbond(deltriright, rightshelle);
|
|
}
|
|
|
|
/* Set the new origin of `deltri' and check its quality. */
|
|
org(lefttri, neworg);
|
|
setorg(*deltri, neworg);
|
|
if (!nobisect) {
|
|
testtriangle(deltri);
|
|
}
|
|
|
|
/* Delete the two spliced-out triangles. */
|
|
triangledealloc(lefttri.tri);
|
|
triangledealloc(righttri.tri);
|
|
}
|
|
|
|
#endif /* not CDT_ONLY */
|
|
|
|
/** **/
|
|
/** **/
|
|
/********* Mesh transformation routines end here *********/
|
|
|
|
/********* Divide-and-conquer Delaunay triangulation begins here *********/
|
|
/** **/
|
|
/** **/
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* The divide-and-conquer bounding box */
|
|
/* */
|
|
/* I originally implemented the divide-and-conquer and incremental Delaunay */
|
|
/* triangulations using the edge-based data structure presented by Guibas */
|
|
/* and Stolfi. Switching to a triangle-based data structure doubled the */
|
|
/* speed. However, I had to think of a few extra tricks to maintain the */
|
|
/* elegance of the original algorithms. */
|
|
/* */
|
|
/* The "bounding box" used by my variant of the divide-and-conquer */
|
|
/* algorithm uses one triangle for each edge of the convex hull of the */
|
|
/* triangulation. These bounding triangles all share a common apical */
|
|
/* vertex, which is represented by NULL and which represents nothing. */
|
|
/* The bounding triangles are linked in a circular fan about this NULL */
|
|
/* vertex, and the edges on the convex hull of the triangulation appear */
|
|
/* opposite the NULL vertex. You might find it easiest to imagine that */
|
|
/* the NULL vertex is a point in 3D space behind the center of the */
|
|
/* triangulation, and that the bounding triangles form a sort of cone. */
|
|
/* */
|
|
/* This bounding box makes it easy to represent degenerate cases. For */
|
|
/* instance, the triangulation of two vertices is a single edge. This edge */
|
|
/* is represented by two bounding box triangles, one on each "side" of the */
|
|
/* edge. These triangles are also linked together in a fan about the NULL */
|
|
/* vertex. */
|
|
/* */
|
|
/* The bounding box also makes it easy to traverse the convex hull, as the */
|
|
/* divide-and-conquer algorithm needs to do. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* pointsort() Sort an array of points by x-coordinate, using the */
|
|
/* y-coordinate as a secondary key. */
|
|
/* */
|
|
/* Uses quicksort. Randomized O(n log n) time. No, I did not make any of */
|
|
/* the usual quicksort mistakes. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
void pointsort(sortarray, arraysize)
|
|
point *sortarray;
|
|
int arraysize;
|
|
{
|
|
int left, right;
|
|
int pivot;
|
|
REAL pivotx, pivoty;
|
|
point temp;
|
|
|
|
if (arraysize == 2) {
|
|
/* Recursive base case. */
|
|
if ((sortarray[0][0] > sortarray[1][0]) ||
|
|
((sortarray[0][0] == sortarray[1][0]) &&
|
|
(sortarray[0][1] > sortarray[1][1]))) {
|
|
temp = sortarray[1];
|
|
sortarray[1] = sortarray[0];
|
|
sortarray[0] = temp;
|
|
}
|
|
return;
|
|
}
|
|
/* Choose a random pivot to split the array. */
|
|
pivot = (int) randomnation(arraysize);
|
|
pivotx = sortarray[pivot][0];
|
|
pivoty = sortarray[pivot][1];
|
|
/* Split the array. */
|
|
left = -1;
|
|
right = arraysize;
|
|
while (left < right) {
|
|
/* Search for a point whose x-coordinate is too large for the left. */
|
|
do {
|
|
left++;
|
|
} while ((left <= right) && ((sortarray[left][0] < pivotx) ||
|
|
((sortarray[left][0] == pivotx) &&
|
|
(sortarray[left][1] < pivoty))));
|
|
/* Search for a point whose x-coordinate is too small for the right. */
|
|
do {
|
|
right--;
|
|
} while ((left <= right) && ((sortarray[right][0] > pivotx) ||
|
|
((sortarray[right][0] == pivotx) &&
|
|
(sortarray[right][1] > pivoty))));
|
|
if (left < right) {
|
|
/* Swap the left and right points. */
|
|
temp = sortarray[left];
|
|
sortarray[left] = sortarray[right];
|
|
sortarray[right] = temp;
|
|
}
|
|
}
|
|
if (left > 1) {
|
|
/* Recursively sort the left subset. */
|
|
pointsort(sortarray, left);
|
|
}
|
|
if (right < arraysize - 2) {
|
|
/* Recursively sort the right subset. */
|
|
pointsort(&sortarray[right + 1], arraysize - right - 1);
|
|
}
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* pointmedian() An order statistic algorithm, almost. Shuffles an array */
|
|
/* of points so that the first `median' points occur */
|
|
/* lexicographically before the remaining points. */
|
|
/* */
|
|
/* Uses the x-coordinate as the primary key if axis == 0; the y-coordinate */
|
|
/* if axis == 1. Very similar to the pointsort() procedure, but runs in */
|
|
/* randomized linear time. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
void pointmedian(sortarray, arraysize, median, axis)
|
|
point *sortarray;
|
|
int arraysize;
|
|
int median;
|
|
int axis;
|
|
{
|
|
int left, right;
|
|
int pivot;
|
|
REAL pivot1, pivot2;
|
|
point temp;
|
|
|
|
if (arraysize == 2) {
|
|
/* Recursive base case. */
|
|
if ((sortarray[0][axis] > sortarray[1][axis]) ||
|
|
((sortarray[0][axis] == sortarray[1][axis]) &&
|
|
(sortarray[0][1 - axis] > sortarray[1][1 - axis]))) {
|
|
temp = sortarray[1];
|
|
sortarray[1] = sortarray[0];
|
|
sortarray[0] = temp;
|
|
}
|
|
return;
|
|
}
|
|
/* Choose a random pivot to split the array. */
|
|
pivot = (int) randomnation(arraysize);
|
|
pivot1 = sortarray[pivot][axis];
|
|
pivot2 = sortarray[pivot][1 - axis];
|
|
/* Split the array. */
|
|
left = -1;
|
|
right = arraysize;
|
|
while (left < right) {
|
|
/* Search for a point whose x-coordinate is too large for the left. */
|
|
do {
|
|
left++;
|
|
} while ((left <= right) && ((sortarray[left][axis] < pivot1) ||
|
|
((sortarray[left][axis] == pivot1) &&
|
|
(sortarray[left][1 - axis] < pivot2))));
|
|
/* Search for a point whose x-coordinate is too small for the right. */
|
|
do {
|
|
right--;
|
|
} while ((left <= right) && ((sortarray[right][axis] > pivot1) ||
|
|
((sortarray[right][axis] == pivot1) &&
|
|
(sortarray[right][1 - axis] > pivot2))));
|
|
if (left < right) {
|
|
/* Swap the left and right points. */
|
|
temp = sortarray[left];
|
|
sortarray[left] = sortarray[right];
|
|
sortarray[right] = temp;
|
|
}
|
|
}
|
|
/* Unlike in pointsort(), at most one of the following */
|
|
/* conditionals is true. */
|
|
if (left > median) {
|
|
/* Recursively shuffle the left subset. */
|
|
pointmedian(sortarray, left, median, axis);
|
|
}
|
|
if (right < median - 1) {
|
|
/* Recursively shuffle the right subset. */
|
|
pointmedian(&sortarray[right + 1], arraysize - right - 1,
|
|
median - right - 1, axis);
|
|
}
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* alternateaxes() Sorts the points as appropriate for the divide-and- */
|
|
/* conquer algorithm with alternating cuts. */
|
|
/* */
|
|
/* Partitions by x-coordinate if axis == 0; by y-coordinate if axis == 1. */
|
|
/* For the base case, subsets containing only two or three points are */
|
|
/* always sorted by x-coordinate. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
void alternateaxes(sortarray, arraysize, axis)
|
|
point *sortarray;
|
|
int arraysize;
|
|
int axis;
|
|
{
|
|
int divider;
|
|
|
|
divider = arraysize >> 1;
|
|
if (arraysize <= 3) {
|
|
/* Recursive base case: subsets of two or three points will be */
|
|
/* handled specially, and should always be sorted by x-coordinate. */
|
|
axis = 0;
|
|
}
|
|
/* Partition with a horizontal or vertical cut. */
|
|
pointmedian(sortarray, arraysize, divider, axis);
|
|
/* Recursively partition the subsets with a cross cut. */
|
|
if (arraysize - divider >= 2) {
|
|
if (divider >= 2) {
|
|
alternateaxes(sortarray, divider, 1 - axis);
|
|
}
|
|
alternateaxes(&sortarray[divider], arraysize - divider, 1 - axis);
|
|
}
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* mergehulls() Merge two adjacent Delaunay triangulations into a */
|
|
/* single Delaunay triangulation. */
|
|
/* */
|
|
/* This is similar to the algorithm given by Guibas and Stolfi, but uses */
|
|
/* a triangle-based, rather than edge-based, data structure. */
|
|
/* */
|
|
/* The algorithm walks up the gap between the two triangulations, knitting */
|
|
/* them together. As they are merged, some of their bounding triangles */
|
|
/* are converted into real triangles of the triangulation. The procedure */
|
|
/* pulls each hull's bounding triangles apart, then knits them together */
|
|
/* like the teeth of two gears. The Delaunay property determines, at each */
|
|
/* step, whether the next "tooth" is a bounding triangle of the left hull */
|
|
/* or the right. When a bounding triangle becomes real, its apex is */
|
|
/* changed from NULL to a real point. */
|
|
/* */
|
|
/* Only two new triangles need to be allocated. These become new bounding */
|
|
/* triangles at the top and bottom of the seam. They are used to connect */
|
|
/* the remaining bounding triangles (those that have not been converted */
|
|
/* into real triangles) into a single fan. */
|
|
/* */
|
|
/* On entry, `farleft' and `innerleft' are bounding triangles of the left */
|
|
/* triangulation. The origin of `farleft' is the leftmost vertex, and */
|
|
/* the destination of `innerleft' is the rightmost vertex of the */
|
|
/* triangulation. Similarly, `innerright' and `farright' are bounding */
|
|
/* triangles of the right triangulation. The origin of `innerright' and */
|
|
/* destination of `farright' are the leftmost and rightmost vertices. */
|
|
/* */
|
|
/* On completion, the origin of `farleft' is the leftmost vertex of the */
|
|
/* merged triangulation, and the destination of `farright' is the rightmost */
|
|
/* vertex. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
void mergehulls(farleft, innerleft, innerright, farright, axis)
|
|
struct triedge *farleft;
|
|
struct triedge *innerleft;
|
|
struct triedge *innerright;
|
|
struct triedge *farright;
|
|
int axis;
|
|
{
|
|
struct triedge leftcand, rightcand;
|
|
struct triedge baseedge;
|
|
struct triedge nextedge;
|
|
struct triedge sidecasing, topcasing, outercasing;
|
|
struct triedge checkedge;
|
|
point innerleftdest;
|
|
point innerrightorg;
|
|
point innerleftapex, innerrightapex;
|
|
point farleftpt, farrightpt;
|
|
point farleftapex, farrightapex;
|
|
point lowerleft, lowerright;
|
|
point upperleft, upperright;
|
|
point nextapex;
|
|
point checkvertex;
|
|
int changemade;
|
|
int badedge;
|
|
int leftfinished, rightfinished;
|
|
triangle ptr; /* Temporary variable used by sym(). */
|
|
|
|
dest(*innerleft, innerleftdest);
|
|
apex(*innerleft, innerleftapex);
|
|
org(*innerright, innerrightorg);
|
|
apex(*innerright, innerrightapex);
|
|
/* Special treatment for horizontal cuts. */
|
|
if (dwyer && (axis == 1)) {
|
|
org(*farleft, farleftpt);
|
|
apex(*farleft, farleftapex);
|
|
dest(*farright, farrightpt);
|
|
apex(*farright, farrightapex);
|
|
/* The pointers to the extremal points are shifted to point to the */
|
|
/* topmost and bottommost point of each hull, rather than the */
|
|
/* leftmost and rightmost points. */
|
|
while (farleftapex[1] < farleftpt[1]) {
|
|
lnextself(*farleft);
|
|
symself(*farleft);
|
|
farleftpt = farleftapex;
|
|
apex(*farleft, farleftapex);
|
|
}
|
|
sym(*innerleft, checkedge);
|
|
apex(checkedge, checkvertex);
|
|
while (checkvertex[1] > innerleftdest[1]) {
|
|
lnext(checkedge, *innerleft);
|
|
innerleftapex = innerleftdest;
|
|
innerleftdest = checkvertex;
|
|
sym(*innerleft, checkedge);
|
|
apex(checkedge, checkvertex);
|
|
}
|
|
while (innerrightapex[1] < innerrightorg[1]) {
|
|
lnextself(*innerright);
|
|
symself(*innerright);
|
|
innerrightorg = innerrightapex;
|
|
apex(*innerright, innerrightapex);
|
|
}
|
|
sym(*farright, checkedge);
|
|
apex(checkedge, checkvertex);
|
|
while (checkvertex[1] > farrightpt[1]) {
|
|
lnext(checkedge, *farright);
|
|
farrightapex = farrightpt;
|
|
farrightpt = checkvertex;
|
|
sym(*farright, checkedge);
|
|
apex(checkedge, checkvertex);
|
|
}
|
|
}
|
|
/* Find a line tangent to and below both hulls. */
|
|
do {
|
|
changemade = 0;
|
|
/* Make innerleftdest the "bottommost" point of the left hull. */
|
|
if (counterclockwise(innerleftdest, innerleftapex, innerrightorg) > 0.0) {
|
|
lprevself(*innerleft);
|
|
symself(*innerleft);
|
|
innerleftdest = innerleftapex;
|
|
apex(*innerleft, innerleftapex);
|
|
changemade = 1;
|
|
}
|
|
/* Make innerrightorg the "bottommost" point of the right hull. */
|
|
if (counterclockwise(innerrightapex, innerrightorg, innerleftdest) > 0.0) {
|
|
lnextself(*innerright);
|
|
symself(*innerright);
|
|
innerrightorg = innerrightapex;
|
|
apex(*innerright, innerrightapex);
|
|
changemade = 1;
|
|
}
|
|
} while (changemade);
|
|
/* Find the two candidates to be the next "gear tooth". */
|
|
sym(*innerleft, leftcand);
|
|
sym(*innerright, rightcand);
|
|
/* Create the bottom new bounding triangle. */
|
|
maketriangle(&baseedge);
|
|
/* Connect it to the bounding boxes of the left and right triangulations. */
|
|
bond(baseedge, *innerleft);
|
|
lnextself(baseedge);
|
|
bond(baseedge, *innerright);
|
|
lnextself(baseedge);
|
|
setorg(baseedge, innerrightorg);
|
|
setdest(baseedge, innerleftdest);
|
|
/* Apex is intentionally left NULL. */
|
|
if (verbose > 2) {
|
|
printf(" Creating base bounding ");
|
|
printtriangle(&baseedge);
|
|
}
|
|
/* Fix the extreme triangles if necessary. */
|
|
org(*farleft, farleftpt);
|
|
if (innerleftdest == farleftpt) {
|
|
lnext(baseedge, *farleft);
|
|
}
|
|
dest(*farright, farrightpt);
|
|
if (innerrightorg == farrightpt) {
|
|
lprev(baseedge, *farright);
|
|
}
|
|
/* The vertices of the current knitting edge. */
|
|
lowerleft = innerleftdest;
|
|
lowerright = innerrightorg;
|
|
/* The candidate vertices for knitting. */
|
|
apex(leftcand, upperleft);
|
|
apex(rightcand, upperright);
|
|
/* Walk up the gap between the two triangulations, knitting them together. */
|
|
while (1) {
|
|
/* Have we reached the top? (This isn't quite the right question, */
|
|
/* because even though the left triangulation might seem finished now, */
|
|
/* moving up on the right triangulation might reveal a new point of */
|
|
/* the left triangulation. And vice-versa.) */
|
|
leftfinished = counterclockwise(upperleft, lowerleft, lowerright) <= 0.0;
|
|
rightfinished = counterclockwise(upperright, lowerleft, lowerright) <= 0.0;
|
|
if (leftfinished && rightfinished) {
|
|
/* Create the top new bounding triangle. */
|
|
maketriangle(&nextedge);
|
|
setorg(nextedge, lowerleft);
|
|
setdest(nextedge, lowerright);
|
|
/* Apex is intentionally left NULL. */
|
|
/* Connect it to the bounding boxes of the two triangulations. */
|
|
bond(nextedge, baseedge);
|
|
lnextself(nextedge);
|
|
bond(nextedge, rightcand);
|
|
lnextself(nextedge);
|
|
bond(nextedge, leftcand);
|
|
if (verbose > 2) {
|
|
printf(" Creating top bounding ");
|
|
printtriangle(&baseedge);
|
|
}
|
|
/* Special treatment for horizontal cuts. */
|
|
if (dwyer && (axis == 1)) {
|
|
org(*farleft, farleftpt);
|
|
apex(*farleft, farleftapex);
|
|
dest(*farright, farrightpt);
|
|
apex(*farright, farrightapex);
|
|
sym(*farleft, checkedge);
|
|
apex(checkedge, checkvertex);
|
|
/* The pointers to the extremal points are restored to the leftmost */
|
|
/* and rightmost points (rather than topmost and bottommost). */
|
|
while (checkvertex[0] < farleftpt[0]) {
|
|
lprev(checkedge, *farleft);
|
|
farleftapex = farleftpt;
|
|
farleftpt = checkvertex;
|
|
sym(*farleft, checkedge);
|
|
apex(checkedge, checkvertex);
|
|
}
|
|
while (farrightapex[0] > farrightpt[0]) {
|
|
lprevself(*farright);
|
|
symself(*farright);
|
|
farrightpt = farrightapex;
|
|
apex(*farright, farrightapex);
|
|
}
|
|
}
|
|
return;
|
|
}
|
|
/* Consider eliminating edges from the left triangulation. */
|
|
if (!leftfinished) {
|
|
/* What vertex would be exposed if an edge were deleted? */
|
|
lprev(leftcand, nextedge);
|
|
symself(nextedge);
|
|
apex(nextedge, nextapex);
|
|
/* If nextapex is NULL, then no vertex would be exposed; the */
|
|
/* triangulation would have been eaten right through. */
|
|
if (nextapex != (point) NULL) {
|
|
/* Check whether the edge is Delaunay. */
|
|
badedge = incircle(lowerleft, lowerright, upperleft, nextapex) > 0.0;
|
|
while (badedge) {
|
|
/* Eliminate the edge with an edge flip. As a result, the */
|
|
/* left triangulation will have one more boundary triangle. */
|
|
lnextself(nextedge);
|
|
sym(nextedge, topcasing);
|
|
lnextself(nextedge);
|
|
sym(nextedge, sidecasing);
|
|
bond(nextedge, topcasing);
|
|
bond(leftcand, sidecasing);
|
|
lnextself(leftcand);
|
|
sym(leftcand, outercasing);
|
|
lprevself(nextedge);
|
|
bond(nextedge, outercasing);
|
|
/* Correct the vertices to reflect the edge flip. */
|
|
setorg(leftcand, lowerleft);
|
|
setdest(leftcand, NULL);
|
|
setapex(leftcand, nextapex);
|
|
setorg(nextedge, NULL);
|
|
setdest(nextedge, upperleft);
|
|
setapex(nextedge, nextapex);
|
|
/* Consider the newly exposed vertex. */
|
|
upperleft = nextapex;
|
|
/* What vertex would be exposed if another edge were deleted? */
|
|
triedgecopy(sidecasing, nextedge);
|
|
apex(nextedge, nextapex);
|
|
if (nextapex != (point) NULL) {
|
|
/* Check whether the edge is Delaunay. */
|
|
badedge = incircle(lowerleft, lowerright, upperleft, nextapex)
|
|
> 0.0;
|
|
} else {
|
|
/* Avoid eating right through the triangulation. */
|
|
badedge = 0;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
/* Consider eliminating edges from the right triangulation. */
|
|
if (!rightfinished) {
|
|
/* What vertex would be exposed if an edge were deleted? */
|
|
lnext(rightcand, nextedge);
|
|
symself(nextedge);
|
|
apex(nextedge, nextapex);
|
|
/* If nextapex is NULL, then no vertex would be exposed; the */
|
|
/* triangulation would have been eaten right through. */
|
|
if (nextapex != (point) NULL) {
|
|
/* Check whether the edge is Delaunay. */
|
|
badedge = incircle(lowerleft, lowerright, upperright, nextapex) > 0.0;
|
|
while (badedge) {
|
|
/* Eliminate the edge with an edge flip. As a result, the */
|
|
/* right triangulation will have one more boundary triangle. */
|
|
lprevself(nextedge);
|
|
sym(nextedge, topcasing);
|
|
lprevself(nextedge);
|
|
sym(nextedge, sidecasing);
|
|
bond(nextedge, topcasing);
|
|
bond(rightcand, sidecasing);
|
|
lprevself(rightcand);
|
|
sym(rightcand, outercasing);
|
|
lnextself(nextedge);
|
|
bond(nextedge, outercasing);
|
|
/* Correct the vertices to reflect the edge flip. */
|
|
setorg(rightcand, NULL);
|
|
setdest(rightcand, lowerright);
|
|
setapex(rightcand, nextapex);
|
|
setorg(nextedge, upperright);
|
|
setdest(nextedge, NULL);
|
|
setapex(nextedge, nextapex);
|
|
/* Consider the newly exposed vertex. */
|
|
upperright = nextapex;
|
|
/* What vertex would be exposed if another edge were deleted? */
|
|
triedgecopy(sidecasing, nextedge);
|
|
apex(nextedge, nextapex);
|
|
if (nextapex != (point) NULL) {
|
|
/* Check whether the edge is Delaunay. */
|
|
badedge = incircle(lowerleft, lowerright, upperright, nextapex)
|
|
> 0.0;
|
|
} else {
|
|
/* Avoid eating right through the triangulation. */
|
|
badedge = 0;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
if (leftfinished || (!rightfinished &&
|
|
(incircle(upperleft, lowerleft, lowerright, upperright) > 0.0))) {
|
|
/* Knit the triangulations, adding an edge from `lowerleft' */
|
|
/* to `upperright'. */
|
|
bond(baseedge, rightcand);
|
|
lprev(rightcand, baseedge);
|
|
setdest(baseedge, lowerleft);
|
|
lowerright = upperright;
|
|
sym(baseedge, rightcand);
|
|
apex(rightcand, upperright);
|
|
} else {
|
|
/* Knit the triangulations, adding an edge from `upperleft' */
|
|
/* to `lowerright'. */
|
|
bond(baseedge, leftcand);
|
|
lnext(leftcand, baseedge);
|
|
setorg(baseedge, lowerright);
|
|
lowerleft = upperleft;
|
|
sym(baseedge, leftcand);
|
|
apex(leftcand, upperleft);
|
|
}
|
|
if (verbose > 2) {
|
|
printf(" Connecting ");
|
|
printtriangle(&baseedge);
|
|
}
|
|
}
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* divconqrecurse() Recursively form a Delaunay triangulation by the */
|
|
/* divide-and-conquer method. */
|
|
/* */
|
|
/* Recursively breaks down the problem into smaller pieces, which are */
|
|
/* knitted together by mergehulls(). The base cases (problems of two or */
|
|
/* three points) are handled specially here. */
|
|
/* */
|
|
/* On completion, `farleft' and `farright' are bounding triangles such that */
|
|
/* the origin of `farleft' is the leftmost vertex (breaking ties by */
|
|
/* choosing the highest leftmost vertex), and the destination of */
|
|
/* `farright' is the rightmost vertex (breaking ties by choosing the */
|
|
/* lowest rightmost vertex). */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
void divconqrecurse(sortarray, vertices, axis, farleft, farright)
|
|
point *sortarray;
|
|
int vertices;
|
|
int axis;
|
|
struct triedge *farleft;
|
|
struct triedge *farright;
|
|
{
|
|
struct triedge midtri, tri1, tri2, tri3;
|
|
struct triedge innerleft, innerright;
|
|
REAL area;
|
|
int divider;
|
|
|
|
if (verbose > 2) {
|
|
printf(" Triangulating %d points.\n", vertices);
|
|
}
|
|
if (vertices == 2) {
|
|
/* The triangulation of two vertices is an edge. An edge is */
|
|
/* represented by two bounding triangles. */
|
|
maketriangle(farleft);
|
|
setorg(*farleft, sortarray[0]);
|
|
setdest(*farleft, sortarray[1]);
|
|
/* The apex is intentionally left NULL. */
|
|
maketriangle(farright);
|
|
setorg(*farright, sortarray[1]);
|
|
setdest(*farright, sortarray[0]);
|
|
/* The apex is intentionally left NULL. */
|
|
bond(*farleft, *farright);
|
|
lprevself(*farleft);
|
|
lnextself(*farright);
|
|
bond(*farleft, *farright);
|
|
lprevself(*farleft);
|
|
lnextself(*farright);
|
|
bond(*farleft, *farright);
|
|
if (verbose > 2) {
|
|
printf(" Creating ");
|
|
printtriangle(farleft);
|
|
printf(" Creating ");
|
|
printtriangle(farright);
|
|
}
|
|
/* Ensure that the origin of `farleft' is sortarray[0]. */
|
|
lprev(*farright, *farleft);
|
|
return;
|
|
} else if (vertices == 3) {
|
|
/* The triangulation of three vertices is either a triangle (with */
|
|
/* three bounding triangles) or two edges (with four bounding */
|
|
/* triangles). In either case, four triangles are created. */
|
|
maketriangle(&midtri);
|
|
maketriangle(&tri1);
|
|
maketriangle(&tri2);
|
|
maketriangle(&tri3);
|
|
area = counterclockwise(sortarray[0], sortarray[1], sortarray[2]);
|
|
if (area == 0.0) {
|
|
/* Three collinear points; the triangulation is two edges. */
|
|
setorg(midtri, sortarray[0]);
|
|
setdest(midtri, sortarray[1]);
|
|
setorg(tri1, sortarray[1]);
|
|
setdest(tri1, sortarray[0]);
|
|
setorg(tri2, sortarray[2]);
|
|
setdest(tri2, sortarray[1]);
|
|
setorg(tri3, sortarray[1]);
|
|
setdest(tri3, sortarray[2]);
|
|
/* All apices are intentionally left NULL. */
|
|
bond(midtri, tri1);
|
|
bond(tri2, tri3);
|
|
lnextself(midtri);
|
|
lprevself(tri1);
|
|
lnextself(tri2);
|
|
lprevself(tri3);
|
|
bond(midtri, tri3);
|
|
bond(tri1, tri2);
|
|
lnextself(midtri);
|
|
lprevself(tri1);
|
|
lnextself(tri2);
|
|
lprevself(tri3);
|
|
bond(midtri, tri1);
|
|
bond(tri2, tri3);
|
|
/* Ensure that the origin of `farleft' is sortarray[0]. */
|
|
triedgecopy(tri1, *farleft);
|
|
/* Ensure that the destination of `farright' is sortarray[2]. */
|
|
triedgecopy(tri2, *farright);
|
|
} else {
|
|
/* The three points are not collinear; the triangulation is one */
|
|
/* triangle, namely `midtri'. */
|
|
setorg(midtri, sortarray[0]);
|
|
setdest(tri1, sortarray[0]);
|
|
setorg(tri3, sortarray[0]);
|
|
/* Apices of tri1, tri2, and tri3 are left NULL. */
|
|
if (area > 0.0) {
|
|
/* The vertices are in counterclockwise order. */
|
|
setdest(midtri, sortarray[1]);
|
|
setorg(tri1, sortarray[1]);
|
|
setdest(tri2, sortarray[1]);
|
|
setapex(midtri, sortarray[2]);
|
|
setorg(tri2, sortarray[2]);
|
|
setdest(tri3, sortarray[2]);
|
|
} else {
|
|
/* The vertices are in clockwise order. */
|
|
setdest(midtri, sortarray[2]);
|
|
setorg(tri1, sortarray[2]);
|
|
setdest(tri2, sortarray[2]);
|
|
setapex(midtri, sortarray[1]);
|
|
setorg(tri2, sortarray[1]);
|
|
setdest(tri3, sortarray[1]);
|
|
}
|
|
/* The topology does not depend on how the vertices are ordered. */
|
|
bond(midtri, tri1);
|
|
lnextself(midtri);
|
|
bond(midtri, tri2);
|
|
lnextself(midtri);
|
|
bond(midtri, tri3);
|
|
lprevself(tri1);
|
|
lnextself(tri2);
|
|
bond(tri1, tri2);
|
|
lprevself(tri1);
|
|
lprevself(tri3);
|
|
bond(tri1, tri3);
|
|
lnextself(tri2);
|
|
lprevself(tri3);
|
|
bond(tri2, tri3);
|
|
/* Ensure that the origin of `farleft' is sortarray[0]. */
|
|
triedgecopy(tri1, *farleft);
|
|
/* Ensure that the destination of `farright' is sortarray[2]. */
|
|
if (area > 0.0) {
|
|
triedgecopy(tri2, *farright);
|
|
} else {
|
|
lnext(*farleft, *farright);
|
|
}
|
|
}
|
|
if (verbose > 2) {
|
|
printf(" Creating ");
|
|
printtriangle(&midtri);
|
|
printf(" Creating ");
|
|
printtriangle(&tri1);
|
|
printf(" Creating ");
|
|
printtriangle(&tri2);
|
|
printf(" Creating ");
|
|
printtriangle(&tri3);
|
|
}
|
|
return;
|
|
} else {
|
|
/* Split the vertices in half. */
|
|
divider = vertices >> 1;
|
|
/* Recursively triangulate each half. */
|
|
divconqrecurse(sortarray, divider, 1 - axis, farleft, &innerleft);
|
|
divconqrecurse(&sortarray[divider], vertices - divider, 1 - axis,
|
|
&innerright, farright);
|
|
if (verbose > 1) {
|
|
printf(" Joining triangulations with %d and %d vertices.\n", divider,
|
|
vertices - divider);
|
|
}
|
|
/* Merge the two triangulations into one. */
|
|
mergehulls(farleft, &innerleft, &innerright, farright, axis);
|
|
}
|
|
}
|
|
|
|
long removeghosts(startghost)
|
|
struct triedge *startghost;
|
|
{
|
|
struct triedge searchedge;
|
|
struct triedge dissolveedge;
|
|
struct triedge deadtri;
|
|
point markorg;
|
|
long hullsize;
|
|
triangle ptr; /* Temporary variable used by sym(). */
|
|
|
|
if (verbose) {
|
|
printf(" Removing ghost triangles.\n");
|
|
}
|
|
/* Find an edge on the convex hull to start point location from. */
|
|
lprev(*startghost, searchedge);
|
|
symself(searchedge);
|
|
dummytri[0] = encode(searchedge);
|
|
/* Remove the bounding box and count the convex hull edges. */
|
|
triedgecopy(*startghost, dissolveedge);
|
|
hullsize = 0;
|
|
do {
|
|
hullsize++;
|
|
lnext(dissolveedge, deadtri);
|
|
lprevself(dissolveedge);
|
|
symself(dissolveedge);
|
|
/* If no PSLG is involved, set the boundary markers of all the points */
|
|
/* on the convex hull. If a PSLG is used, this step is done later. */
|
|
if (!poly) {
|
|
/* Watch out for the case where all the input points are collinear. */
|
|
if (dissolveedge.tri != dummytri) {
|
|
org(dissolveedge, markorg);
|
|
if (pointmark(markorg) == 0) {
|
|
setpointmark(markorg, 1);
|
|
}
|
|
}
|
|
}
|
|
/* Remove a bounding triangle from a convex hull triangle. */
|
|
dissolve(dissolveedge);
|
|
/* Find the next bounding triangle. */
|
|
sym(deadtri, dissolveedge);
|
|
/* Delete the bounding triangle. */
|
|
triangledealloc(deadtri.tri);
|
|
} while (!triedgeequal(dissolveedge, *startghost));
|
|
return hullsize;
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* divconqdelaunay() Form a Delaunay triangulation by the divide-and- */
|
|
/* conquer method. */
|
|
/* */
|
|
/* Sorts the points, calls a recursive procedure to triangulate them, and */
|
|
/* removes the bounding box, setting boundary markers as appropriate. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
long divconqdelaunay()
|
|
{
|
|
point *sortarray;
|
|
struct triedge hullleft, hullright;
|
|
int divider;
|
|
int i, j;
|
|
|
|
/* Allocate an array of pointers to points for sorting. */
|
|
sortarray = (point *) malloc(inpoints * sizeof(point));
|
|
if (sortarray == (point *) NULL) {
|
|
printf("Error: Out of memory.\n");
|
|
exit(1);
|
|
}
|
|
traversalinit(&points);
|
|
for (i = 0; i < inpoints; i++) {
|
|
sortarray[i] = pointtraverse();
|
|
}
|
|
if (verbose) {
|
|
printf(" Sorting points.\n");
|
|
}
|
|
/* Sort the points. */
|
|
pointsort(sortarray, inpoints);
|
|
/* Discard duplicate points, which can really mess up the algorithm. */
|
|
i = 0;
|
|
for (j = 1; j < inpoints; j++) {
|
|
if ((sortarray[i][0] == sortarray[j][0])
|
|
&& (sortarray[i][1] == sortarray[j][1])) {
|
|
if (!quiet) {
|
|
printf(
|
|
"Warning: A duplicate point at (%.12g, %.12g) appeared and was ignored.\n",
|
|
sortarray[j][0], sortarray[j][1]);
|
|
}
|
|
/* Commented out - would eliminate point from output .node file, but causes
|
|
a failure if some segment has this point as an endpoint.
|
|
setpointmark(sortarray[j], DEADPOINT);
|
|
*/
|
|
} else {
|
|
i++;
|
|
sortarray[i] = sortarray[j];
|
|
}
|
|
}
|
|
i++;
|
|
if (dwyer) {
|
|
/* Re-sort the array of points to accommodate alternating cuts. */
|
|
divider = i >> 1;
|
|
if (i - divider >= 2) {
|
|
if (divider >= 2) {
|
|
alternateaxes(sortarray, divider, 1);
|
|
}
|
|
alternateaxes(&sortarray[divider], i - divider, 1);
|
|
}
|
|
}
|
|
if (verbose) {
|
|
printf(" Forming triangulation.\n");
|
|
}
|
|
/* Form the Delaunay triangulation. */
|
|
divconqrecurse(sortarray, i, 0, &hullleft, &hullright);
|
|
free(sortarray);
|
|
|
|
return removeghosts(&hullleft);
|
|
}
|
|
|
|
/** **/
|
|
/** **/
|
|
/********* Divide-and-conquer Delaunay triangulation ends here *********/
|
|
|
|
/********* Incremental Delaunay triangulation begins here *********/
|
|
/** **/
|
|
/** **/
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* boundingbox() Form an "infinite" bounding triangle to insert points */
|
|
/* into. */
|
|
/* */
|
|
/* The points at "infinity" are assigned finite coordinates, which are used */
|
|
/* by the point location routines, but (mostly) ignored by the Delaunay */
|
|
/* edge flip routines. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
#ifndef REDUCED
|
|
|
|
void boundingbox()
|
|
{
|
|
struct triedge inftri; /* Handle for the triangular bounding box. */
|
|
REAL width;
|
|
|
|
if (verbose) {
|
|
printf(" Creating triangular bounding box.\n");
|
|
}
|
|
/* Find the width (or height, whichever is larger) of the triangulation. */
|
|
width = xmax - xmin;
|
|
if (ymax - ymin > width) {
|
|
width = ymax - ymin;
|
|
}
|
|
if (width == 0.0) {
|
|
width = 1.0;
|
|
}
|
|
/* Create the vertices of the bounding box. */
|
|
infpoint1 = (point) malloc(points.itembytes);
|
|
infpoint2 = (point) malloc(points.itembytes);
|
|
infpoint3 = (point) malloc(points.itembytes);
|
|
if ((infpoint1 == (point) NULL) || (infpoint2 == (point) NULL)
|
|
|| (infpoint3 == (point) NULL)) {
|
|
printf("Error: Out of memory.\n");
|
|
exit(1);
|
|
}
|
|
infpoint1[0] = xmin - 50.0 * width;
|
|
infpoint1[1] = ymin - 40.0 * width;
|
|
infpoint2[0] = xmax + 50.0 * width;
|
|
infpoint2[1] = ymin - 40.0 * width;
|
|
infpoint3[0] = 0.5 * (xmin + xmax);
|
|
infpoint3[1] = ymax + 60.0 * width;
|
|
|
|
/* Create the bounding box. */
|
|
maketriangle(&inftri);
|
|
setorg(inftri, infpoint1);
|
|
setdest(inftri, infpoint2);
|
|
setapex(inftri, infpoint3);
|
|
/* Link dummytri to the bounding box so we can always find an */
|
|
/* edge to begin searching (point location) from. */
|
|
dummytri[0] = (triangle) inftri.tri;
|
|
if (verbose > 2) {
|
|
printf(" Creating ");
|
|
printtriangle(&inftri);
|
|
}
|
|
}
|
|
|
|
#endif /* not REDUCED */
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* removebox() Remove the "infinite" bounding triangle, setting boundary */
|
|
/* markers as appropriate. */
|
|
/* */
|
|
/* The triangular bounding box has three boundary triangles (one for each */
|
|
/* side of the bounding box), and a bunch of triangles fanning out from */
|
|
/* the three bounding box vertices (one triangle for each edge of the */
|
|
/* convex hull of the inner mesh). This routine removes these triangles. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
#ifndef REDUCED
|
|
|
|
long removebox()
|
|
{
|
|
struct triedge deadtri;
|
|
struct triedge searchedge;
|
|
struct triedge checkedge;
|
|
struct triedge nextedge, finaledge, dissolveedge;
|
|
point markorg;
|
|
long hullsize;
|
|
triangle ptr; /* Temporary variable used by sym(). */
|
|
|
|
if (verbose) {
|
|
printf(" Removing triangular bounding box.\n");
|
|
}
|
|
/* Find a boundary triangle. */
|
|
nextedge.tri = dummytri;
|
|
nextedge.orient = 0;
|
|
symself(nextedge);
|
|
/* Mark a place to stop. */
|
|
lprev(nextedge, finaledge);
|
|
lnextself(nextedge);
|
|
symself(nextedge);
|
|
/* Find a triangle (on the boundary of the point set) that isn't */
|
|
/* a bounding box triangle. */
|
|
lprev(nextedge, searchedge);
|
|
symself(searchedge);
|
|
/* Check whether nextedge is another boundary triangle */
|
|
/* adjacent to the first one. */
|
|
lnext(nextedge, checkedge);
|
|
symself(checkedge);
|
|
if (checkedge.tri == dummytri) {
|
|
/* Go on to the next triangle. There are only three boundary */
|
|
/* triangles, and this next triangle cannot be the third one, */
|
|
/* so it's safe to stop here. */
|
|
lprevself(searchedge);
|
|
symself(searchedge);
|
|
}
|
|
/* Find a new boundary edge to search from, as the current search */
|
|
/* edge lies on a bounding box triangle and will be deleted. */
|
|
dummytri[0] = encode(searchedge);
|
|
hullsize = -2l;
|
|
while (!triedgeequal(nextedge, finaledge)) {
|
|
hullsize++;
|
|
lprev(nextedge, dissolveedge);
|
|
symself(dissolveedge);
|
|
/* If not using a PSLG, the vertices should be marked now. */
|
|
/* (If using a PSLG, markhull() will do the job.) */
|
|
if (!poly) {
|
|
/* Be careful! One must check for the case where all the input */
|
|
/* points are collinear, and thus all the triangles are part of */
|
|
/* the bounding box. Otherwise, the setpointmark() call below */
|
|
/* will cause a bad pointer reference. */
|
|
if (dissolveedge.tri != dummytri) {
|
|
org(dissolveedge, markorg);
|
|
if (pointmark(markorg) == 0) {
|
|
setpointmark(markorg, 1);
|
|
}
|
|
}
|
|
}
|
|
/* Disconnect the bounding box triangle from the mesh triangle. */
|
|
dissolve(dissolveedge);
|
|
lnext(nextedge, deadtri);
|
|
sym(deadtri, nextedge);
|
|
/* Get rid of the bounding box triangle. */
|
|
triangledealloc(deadtri.tri);
|
|
/* Do we need to turn the corner? */
|
|
if (nextedge.tri == dummytri) {
|
|
/* Turn the corner. */
|
|
triedgecopy(dissolveedge, nextedge);
|
|
}
|
|
}
|
|
triangledealloc(finaledge.tri);
|
|
|
|
free(infpoint1); /* Deallocate the bounding box vertices. */
|
|
free(infpoint2);
|
|
free(infpoint3);
|
|
|
|
return hullsize;
|
|
}
|
|
|
|
#endif /* not REDUCED */
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* incrementaldelaunay() Form a Delaunay triangulation by incrementally */
|
|
/* adding vertices. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
#ifndef REDUCED
|
|
|
|
long incrementaldelaunay()
|
|
{
|
|
struct triedge starttri;
|
|
point pointloop;
|
|
int i;
|
|
|
|
/* Create a triangular bounding box. */
|
|
boundingbox();
|
|
if (verbose) {
|
|
printf(" Incrementally inserting points.\n");
|
|
}
|
|
traversalinit(&points);
|
|
pointloop = pointtraverse();
|
|
i = 1;
|
|
while (pointloop != (point) NULL) {
|
|
/* Find a boundary triangle to search from. */
|
|
starttri.tri = (triangle *) NULL;
|
|
if (insertsite(pointloop, &starttri, (struct edge *) NULL, 0, 0) ==
|
|
DUPLICATEPOINT) {
|
|
if (!quiet) {
|
|
printf(
|
|
"Warning: A duplicate point at (%.12g, %.12g) appeared and was ignored.\n",
|
|
pointloop[0], pointloop[1]);
|
|
}
|
|
/* Commented out - would eliminate point from output .node file.
|
|
setpointmark(pointloop, DEADPOINT);
|
|
*/
|
|
}
|
|
pointloop = pointtraverse();
|
|
i++;
|
|
}
|
|
/* Remove the bounding box. */
|
|
return removebox();
|
|
}
|
|
|
|
#endif /* not REDUCED */
|
|
|
|
/** **/
|
|
/** **/
|
|
/********* Incremental Delaunay triangulation ends here *********/
|
|
|
|
/********* Sweepline Delaunay triangulation begins here *********/
|
|
/** **/
|
|
/** **/
|
|
|
|
#ifndef REDUCED
|
|
|
|
void eventheapinsert(heap, heapsize, newevent)
|
|
struct event **heap;
|
|
int heapsize;
|
|
struct event *newevent;
|
|
{
|
|
REAL eventx, eventy;
|
|
int eventnum;
|
|
int parent;
|
|
int notdone;
|
|
|
|
eventx = newevent->xkey;
|
|
eventy = newevent->ykey;
|
|
eventnum = heapsize;
|
|
notdone = eventnum > 0;
|
|
while (notdone) {
|
|
parent = (eventnum - 1) >> 1;
|
|
if ((heap[parent]->ykey < eventy) ||
|
|
((heap[parent]->ykey == eventy)
|
|
&& (heap[parent]->xkey <= eventx))) {
|
|
notdone = 0;
|
|
} else {
|
|
heap[eventnum] = heap[parent];
|
|
heap[eventnum]->heapposition = eventnum;
|
|
|
|
eventnum = parent;
|
|
notdone = eventnum > 0;
|
|
}
|
|
}
|
|
heap[eventnum] = newevent;
|
|
newevent->heapposition = eventnum;
|
|
}
|
|
|
|
#endif /* not REDUCED */
|
|
|
|
#ifndef REDUCED
|
|
|
|
void eventheapify(heap, heapsize, eventnum)
|
|
struct event **heap;
|
|
int heapsize;
|
|
int eventnum;
|
|
{
|
|
struct event *thisevent;
|
|
REAL eventx, eventy;
|
|
int leftchild, rightchild;
|
|
int smallest;
|
|
int notdone;
|
|
|
|
thisevent = heap[eventnum];
|
|
eventx = thisevent->xkey;
|
|
eventy = thisevent->ykey;
|
|
leftchild = 2 * eventnum + 1;
|
|
notdone = leftchild < heapsize;
|
|
while (notdone) {
|
|
if ((heap[leftchild]->ykey < eventy) ||
|
|
((heap[leftchild]->ykey == eventy)
|
|
&& (heap[leftchild]->xkey < eventx))) {
|
|
smallest = leftchild;
|
|
} else {
|
|
smallest = eventnum;
|
|
}
|
|
rightchild = leftchild + 1;
|
|
if (rightchild < heapsize) {
|
|
if ((heap[rightchild]->ykey < heap[smallest]->ykey) ||
|
|
((heap[rightchild]->ykey == heap[smallest]->ykey)
|
|
&& (heap[rightchild]->xkey < heap[smallest]->xkey))) {
|
|
smallest = rightchild;
|
|
}
|
|
}
|
|
if (smallest == eventnum) {
|
|
notdone = 0;
|
|
} else {
|
|
heap[eventnum] = heap[smallest];
|
|
heap[eventnum]->heapposition = eventnum;
|
|
heap[smallest] = thisevent;
|
|
thisevent->heapposition = smallest;
|
|
|
|
eventnum = smallest;
|
|
leftchild = 2 * eventnum + 1;
|
|
notdone = leftchild < heapsize;
|
|
}
|
|
}
|
|
}
|
|
|
|
#endif /* not REDUCED */
|
|
|
|
#ifndef REDUCED
|
|
|
|
void eventheapdelete(heap, heapsize, eventnum)
|
|
struct event **heap;
|
|
int heapsize;
|
|
int eventnum;
|
|
{
|
|
struct event *moveevent;
|
|
REAL eventx, eventy;
|
|
int parent;
|
|
int notdone;
|
|
|
|
moveevent = heap[heapsize - 1];
|
|
if (eventnum > 0) {
|
|
eventx = moveevent->xkey;
|
|
eventy = moveevent->ykey;
|
|
do {
|
|
parent = (eventnum - 1) >> 1;
|
|
if ((heap[parent]->ykey < eventy) ||
|
|
((heap[parent]->ykey == eventy)
|
|
&& (heap[parent]->xkey <= eventx))) {
|
|
notdone = 0;
|
|
} else {
|
|
heap[eventnum] = heap[parent];
|
|
heap[eventnum]->heapposition = eventnum;
|
|
|
|
eventnum = parent;
|
|
notdone = eventnum > 0;
|
|
}
|
|
} while (notdone);
|
|
}
|
|
heap[eventnum] = moveevent;
|
|
moveevent->heapposition = eventnum;
|
|
eventheapify(heap, heapsize - 1, eventnum);
|
|
}
|
|
|
|
#endif /* not REDUCED */
|
|
|
|
#ifndef REDUCED
|
|
|
|
void createeventheap(eventheap, events, freeevents)
|
|
struct event ***eventheap;
|
|
struct event **events;
|
|
struct event **freeevents;
|
|
{
|
|
point thispoint;
|
|
int maxevents;
|
|
int i;
|
|
|
|
maxevents = (3 * inpoints) / 2;
|
|
*eventheap = (struct event **) malloc(maxevents * sizeof(struct event *));
|
|
if (*eventheap == (struct event **) NULL) {
|
|
printf("Error: Out of memory.\n");
|
|
exit(1);
|
|
}
|
|
*events = (struct event *) malloc(maxevents * sizeof(struct event));
|
|
if (*events == (struct event *) NULL) {
|
|
printf("Error: Out of memory.\n");
|
|
exit(1);
|
|
}
|
|
traversalinit(&points);
|
|
for (i = 0; i < inpoints; i++) {
|
|
thispoint = pointtraverse();
|
|
(*events)[i].eventptr = (VOID *) thispoint;
|
|
(*events)[i].xkey = thispoint[0];
|
|
(*events)[i].ykey = thispoint[1];
|
|
eventheapinsert(*eventheap, i, *events + i);
|
|
}
|
|
*freeevents = (struct event *) NULL;
|
|
for (i = maxevents - 1; i >= inpoints; i--) {
|
|
(*events)[i].eventptr = (VOID *) *freeevents;
|
|
*freeevents = *events + i;
|
|
}
|
|
}
|
|
|
|
#endif /* not REDUCED */
|
|
|
|
#ifndef REDUCED
|
|
|
|
int rightofhyperbola(fronttri, newsite)
|
|
struct triedge *fronttri;
|
|
point newsite;
|
|
{
|
|
point leftpoint, rightpoint;
|
|
REAL dxa, dya, dxb, dyb;
|
|
|
|
hyperbolacount++;
|
|
|
|
dest(*fronttri, leftpoint);
|
|
apex(*fronttri, rightpoint);
|
|
if ((leftpoint[1] < rightpoint[1])
|
|
|| ((leftpoint[1] == rightpoint[1]) && (leftpoint[0] < rightpoint[0]))) {
|
|
if (newsite[0] >= rightpoint[0]) {
|
|
return 1;
|
|
}
|
|
} else {
|
|
if (newsite[0] <= leftpoint[0]) {
|
|
return 0;
|
|
}
|
|
}
|
|
dxa = leftpoint[0] - newsite[0];
|
|
dya = leftpoint[1] - newsite[1];
|
|
dxb = rightpoint[0] - newsite[0];
|
|
dyb = rightpoint[1] - newsite[1];
|
|
return dya * (dxb * dxb + dyb * dyb) > dyb * (dxa * dxa + dya * dya);
|
|
}
|
|
|
|
#endif /* not REDUCED */
|
|
|
|
#ifndef REDUCED
|
|
|
|
REAL circletop(pa, pb, pc, ccwabc)
|
|
point pa;
|
|
point pb;
|
|
point pc;
|
|
REAL ccwabc;
|
|
{
|
|
REAL xac, yac, xbc, ybc, xab, yab;
|
|
REAL aclen2, bclen2, ablen2;
|
|
|
|
circletopcount++;
|
|
|
|
xac = pa[0] - pc[0];
|
|
yac = pa[1] - pc[1];
|
|
xbc = pb[0] - pc[0];
|
|
ybc = pb[1] - pc[1];
|
|
xab = pa[0] - pb[0];
|
|
yab = pa[1] - pb[1];
|
|
aclen2 = xac * xac + yac * yac;
|
|
bclen2 = xbc * xbc + ybc * ybc;
|
|
ablen2 = xab * xab + yab * yab;
|
|
return pc[1] + (xac * bclen2 - xbc * aclen2 + sqrt(aclen2 * bclen2 * ablen2))
|
|
/ (2.0 * ccwabc);
|
|
}
|
|
|
|
#endif /* not REDUCED */
|
|
|
|
#ifndef REDUCED
|
|
|
|
void check4deadevent(checktri, freeevents, eventheap, heapsize)
|
|
struct triedge *checktri;
|
|
struct event **freeevents;
|
|
struct event **eventheap;
|
|
int *heapsize;
|
|
{
|
|
struct event *deadevent;
|
|
point eventpoint;
|
|
int eventnum;
|
|
|
|
org(*checktri, eventpoint);
|
|
if (eventpoint != (point) NULL) {
|
|
deadevent = (struct event *) eventpoint;
|
|
eventnum = deadevent->heapposition;
|
|
deadevent->eventptr = (VOID *) *freeevents;
|
|
*freeevents = deadevent;
|
|
eventheapdelete(eventheap, *heapsize, eventnum);
|
|
(*heapsize)--;
|
|
setorg(*checktri, NULL);
|
|
}
|
|
}
|
|
|
|
#endif /* not REDUCED */
|
|
|
|
#ifndef REDUCED
|
|
|
|
struct splaynode *splay(splaytree, searchpoint, searchtri)
|
|
struct splaynode *splaytree;
|
|
point searchpoint;
|
|
struct triedge *searchtri;
|
|
{
|
|
struct splaynode *child, *grandchild;
|
|
struct splaynode *lefttree, *righttree;
|
|
struct splaynode *leftright;
|
|
point checkpoint;
|
|
int rightofroot, rightofchild;
|
|
|
|
if (splaytree == (struct splaynode *) NULL) {
|
|
return (struct splaynode *) NULL;
|
|
}
|
|
dest(splaytree->keyedge, checkpoint);
|
|
if (checkpoint == splaytree->keydest) {
|
|
rightofroot = rightofhyperbola(&splaytree->keyedge, searchpoint);
|
|
if (rightofroot) {
|
|
triedgecopy(splaytree->keyedge, *searchtri);
|
|
child = splaytree->rchild;
|
|
} else {
|
|
child = splaytree->lchild;
|
|
}
|
|
if (child == (struct splaynode *) NULL) {
|
|
return splaytree;
|
|
}
|
|
dest(child->keyedge, checkpoint);
|
|
if (checkpoint != child->keydest) {
|
|
child = splay(child, searchpoint, searchtri);
|
|
if (child == (struct splaynode *) NULL) {
|
|
if (rightofroot) {
|
|
splaytree->rchild = (struct splaynode *) NULL;
|
|
} else {
|
|
splaytree->lchild = (struct splaynode *) NULL;
|
|
}
|
|
return splaytree;
|
|
}
|
|
}
|
|
rightofchild = rightofhyperbola(&child->keyedge, searchpoint);
|
|
if (rightofchild) {
|
|
triedgecopy(child->keyedge, *searchtri);
|
|
grandchild = splay(child->rchild, searchpoint, searchtri);
|
|
child->rchild = grandchild;
|
|
} else {
|
|
grandchild = splay(child->lchild, searchpoint, searchtri);
|
|
child->lchild = grandchild;
|
|
}
|
|
if (grandchild == (struct splaynode *) NULL) {
|
|
if (rightofroot) {
|
|
splaytree->rchild = child->lchild;
|
|
child->lchild = splaytree;
|
|
} else {
|
|
splaytree->lchild = child->rchild;
|
|
child->rchild = splaytree;
|
|
}
|
|
return child;
|
|
}
|
|
if (rightofchild) {
|
|
if (rightofroot) {
|
|
splaytree->rchild = child->lchild;
|
|
child->lchild = splaytree;
|
|
} else {
|
|
splaytree->lchild = grandchild->rchild;
|
|
grandchild->rchild = splaytree;
|
|
}
|
|
child->rchild = grandchild->lchild;
|
|
grandchild->lchild = child;
|
|
} else {
|
|
if (rightofroot) {
|
|
splaytree->rchild = grandchild->lchild;
|
|
grandchild->lchild = splaytree;
|
|
} else {
|
|
splaytree->lchild = child->rchild;
|
|
child->rchild = splaytree;
|
|
}
|
|
child->lchild = grandchild->rchild;
|
|
grandchild->rchild = child;
|
|
}
|
|
return grandchild;
|
|
} else {
|
|
lefttree = splay(splaytree->lchild, searchpoint, searchtri);
|
|
righttree = splay(splaytree->rchild, searchpoint, searchtri);
|
|
|
|
pooldealloc(&splaynodes, (VOID *) splaytree);
|
|
if (lefttree == (struct splaynode *) NULL) {
|
|
return righttree;
|
|
} else if (righttree == (struct splaynode *) NULL) {
|
|
return lefttree;
|
|
} else if (lefttree->rchild == (struct splaynode *) NULL) {
|
|
lefttree->rchild = righttree->lchild;
|
|
righttree->lchild = lefttree;
|
|
return righttree;
|
|
} else if (righttree->lchild == (struct splaynode *) NULL) {
|
|
righttree->lchild = lefttree->rchild;
|
|
lefttree->rchild = righttree;
|
|
return lefttree;
|
|
} else {
|
|
/* printf("Holy Toledo!!!\n"); */
|
|
leftright = lefttree->rchild;
|
|
while (leftright->rchild != (struct splaynode *) NULL) {
|
|
leftright = leftright->rchild;
|
|
}
|
|
leftright->rchild = righttree;
|
|
return lefttree;
|
|
}
|
|
}
|
|
}
|
|
|
|
#endif /* not REDUCED */
|
|
|
|
#ifndef REDUCED
|
|
|
|
struct splaynode *splayinsert(splayroot, newkey, searchpoint)
|
|
struct splaynode *splayroot;
|
|
struct triedge *newkey;
|
|
point searchpoint;
|
|
{
|
|
struct splaynode *newsplaynode;
|
|
|
|
newsplaynode = (struct splaynode *) poolalloc(&splaynodes);
|
|
triedgecopy(*newkey, newsplaynode->keyedge);
|
|
dest(*newkey, newsplaynode->keydest);
|
|
if (splayroot == (struct splaynode *) NULL) {
|
|
newsplaynode->lchild = (struct splaynode *) NULL;
|
|
newsplaynode->rchild = (struct splaynode *) NULL;
|
|
} else if (rightofhyperbola(&splayroot->keyedge, searchpoint)) {
|
|
newsplaynode->lchild = splayroot;
|
|
newsplaynode->rchild = splayroot->rchild;
|
|
splayroot->rchild = (struct splaynode *) NULL;
|
|
} else {
|
|
newsplaynode->lchild = splayroot->lchild;
|
|
newsplaynode->rchild = splayroot;
|
|
splayroot->lchild = (struct splaynode *) NULL;
|
|
}
|
|
return newsplaynode;
|
|
}
|
|
|
|
#endif /* not REDUCED */
|
|
|
|
#ifndef REDUCED
|
|
|
|
struct splaynode *circletopinsert(splayroot, newkey, pa, pb, pc, topy)
|
|
struct splaynode *splayroot;
|
|
struct triedge *newkey;
|
|
point pa;
|
|
point pb;
|
|
point pc;
|
|
REAL topy;
|
|
{
|
|
REAL ccwabc;
|
|
REAL xac, yac, xbc, ybc;
|
|
REAL aclen2, bclen2;
|
|
REAL searchpoint[2];
|
|
struct triedge dummytri;
|
|
|
|
ccwabc = counterclockwise(pa, pb, pc);
|
|
xac = pa[0] - pc[0];
|
|
yac = pa[1] - pc[1];
|
|
xbc = pb[0] - pc[0];
|
|
ybc = pb[1] - pc[1];
|
|
aclen2 = xac * xac + yac * yac;
|
|
bclen2 = xbc * xbc + ybc * ybc;
|
|
searchpoint[0] = pc[0] - (yac * bclen2 - ybc * aclen2) / (2.0 * ccwabc);
|
|
searchpoint[1] = topy;
|
|
return splayinsert(splay(splayroot, (point) searchpoint, &dummytri), newkey,
|
|
(point) searchpoint);
|
|
}
|
|
|
|
#endif /* not REDUCED */
|
|
|
|
#ifndef REDUCED
|
|
|
|
struct splaynode *frontlocate(splayroot, bottommost, searchpoint, searchtri,
|
|
farright)
|
|
struct splaynode *splayroot;
|
|
struct triedge *bottommost;
|
|
point searchpoint;
|
|
struct triedge *searchtri;
|
|
int *farright;
|
|
{
|
|
int farrightflag;
|
|
triangle ptr; /* Temporary variable used by onext(). */
|
|
|
|
triedgecopy(*bottommost, *searchtri);
|
|
splayroot = splay(splayroot, searchpoint, searchtri);
|
|
|
|
farrightflag = 0;
|
|
while (!farrightflag && rightofhyperbola(searchtri, searchpoint)) {
|
|
onextself(*searchtri);
|
|
farrightflag = triedgeequal(*searchtri, *bottommost);
|
|
}
|
|
*farright = farrightflag;
|
|
return splayroot;
|
|
}
|
|
|
|
#endif /* not REDUCED */
|
|
|
|
#ifndef REDUCED
|
|
|
|
long sweeplinedelaunay()
|
|
{
|
|
struct event **eventheap;
|
|
struct event *events;
|
|
struct event *freeevents;
|
|
struct event *nextevent;
|
|
struct event *newevent;
|
|
struct splaynode *splayroot;
|
|
struct triedge bottommost;
|
|
struct triedge searchtri;
|
|
struct triedge fliptri;
|
|
struct triedge lefttri, righttri, farlefttri, farrighttri;
|
|
struct triedge inserttri;
|
|
point firstpoint, secondpoint;
|
|
point nextpoint, lastpoint;
|
|
point connectpoint;
|
|
point leftpoint, midpoint, rightpoint;
|
|
REAL lefttest, righttest;
|
|
int heapsize;
|
|
int check4events, farrightflag;
|
|
triangle ptr; /* Temporary variable used by sym(), onext(), and oprev(). */
|
|
|
|
poolinit(&splaynodes, sizeof(struct splaynode), SPLAYNODEPERBLOCK, POINTER,
|
|
0);
|
|
splayroot = (struct splaynode *) NULL;
|
|
|
|
if (verbose) {
|
|
printf(" Placing points in event heap.\n");
|
|
}
|
|
createeventheap(&eventheap, &events, &freeevents);
|
|
heapsize = inpoints;
|
|
|
|
if (verbose) {
|
|
printf(" Forming triangulation.\n");
|
|
}
|
|
maketriangle(&lefttri);
|
|
maketriangle(&righttri);
|
|
bond(lefttri, righttri);
|
|
lnextself(lefttri);
|
|
lprevself(righttri);
|
|
bond(lefttri, righttri);
|
|
lnextself(lefttri);
|
|
lprevself(righttri);
|
|
bond(lefttri, righttri);
|
|
firstpoint = (point) eventheap[0]->eventptr;
|
|
eventheap[0]->eventptr = (VOID *) freeevents;
|
|
freeevents = eventheap[0];
|
|
eventheapdelete(eventheap, heapsize, 0);
|
|
heapsize--;
|
|
do {
|
|
if (heapsize == 0) {
|
|
printf("Error: Input points are all identical.\n");
|
|
exit(1);
|
|
}
|
|
secondpoint = (point) eventheap[0]->eventptr;
|
|
eventheap[0]->eventptr = (VOID *) freeevents;
|
|
freeevents = eventheap[0];
|
|
eventheapdelete(eventheap, heapsize, 0);
|
|
heapsize--;
|
|
if ((firstpoint[0] == secondpoint[0])
|
|
&& (firstpoint[1] == secondpoint[1])) {
|
|
printf(
|
|
"Warning: A duplicate point at (%.12g, %.12g) appeared and was ignored.\n",
|
|
secondpoint[0], secondpoint[1]);
|
|
/* Commented out - would eliminate point from output .node file.
|
|
setpointmark(secondpoint, DEADPOINT);
|
|
*/
|
|
}
|
|
} while ((firstpoint[0] == secondpoint[0])
|
|
&& (firstpoint[1] == secondpoint[1]));
|
|
setorg(lefttri, firstpoint);
|
|
setdest(lefttri, secondpoint);
|
|
setorg(righttri, secondpoint);
|
|
setdest(righttri, firstpoint);
|
|
lprev(lefttri, bottommost);
|
|
lastpoint = secondpoint;
|
|
while (heapsize > 0) {
|
|
nextevent = eventheap[0];
|
|
eventheapdelete(eventheap, heapsize, 0);
|
|
heapsize--;
|
|
check4events = 1;
|
|
if (nextevent->xkey < xmin) {
|
|
decode(nextevent->eventptr, fliptri);
|
|
oprev(fliptri, farlefttri);
|
|
check4deadevent(&farlefttri, &freeevents, eventheap, &heapsize);
|
|
onext(fliptri, farrighttri);
|
|
check4deadevent(&farrighttri, &freeevents, eventheap, &heapsize);
|
|
|
|
if (triedgeequal(farlefttri, bottommost)) {
|
|
lprev(fliptri, bottommost);
|
|
}
|
|
flip(&fliptri);
|
|
setapex(fliptri, NULL);
|
|
lprev(fliptri, lefttri);
|
|
lnext(fliptri, righttri);
|
|
sym(lefttri, farlefttri);
|
|
|
|
if (randomnation(SAMPLERATE) == 0) {
|
|
symself(fliptri);
|
|
dest(fliptri, leftpoint);
|
|
apex(fliptri, midpoint);
|
|
org(fliptri, rightpoint);
|
|
splayroot = circletopinsert(splayroot, &lefttri, leftpoint, midpoint,
|
|
rightpoint, nextevent->ykey);
|
|
}
|
|
} else {
|
|
nextpoint = (point) nextevent->eventptr;
|
|
if ((nextpoint[0] == lastpoint[0]) && (nextpoint[1] == lastpoint[1])) {
|
|
printf(
|
|
"Warning: A duplicate point at (%.12g, %.12g) appeared and was ignored.\n",
|
|
nextpoint[0], nextpoint[1]);
|
|
/* Commented out - would eliminate point from output .node file.
|
|
setpointmark(nextpoint, DEADPOINT);
|
|
*/
|
|
check4events = 0;
|
|
} else {
|
|
lastpoint = nextpoint;
|
|
|
|
splayroot = frontlocate(splayroot, &bottommost, nextpoint, &searchtri,
|
|
&farrightflag);
|
|
/*
|
|
triedgecopy(bottommost, searchtri);
|
|
farrightflag = 0;
|
|
while (!farrightflag && rightofhyperbola(&searchtri, nextpoint)) {
|
|
onextself(searchtri);
|
|
farrightflag = triedgeequal(searchtri, bottommost);
|
|
}
|
|
*/
|
|
|
|
check4deadevent(&searchtri, &freeevents, eventheap, &heapsize);
|
|
|
|
triedgecopy(searchtri, farrighttri);
|
|
sym(searchtri, farlefttri);
|
|
maketriangle(&lefttri);
|
|
maketriangle(&righttri);
|
|
dest(farrighttri, connectpoint);
|
|
setorg(lefttri, connectpoint);
|
|
setdest(lefttri, nextpoint);
|
|
setorg(righttri, nextpoint);
|
|
setdest(righttri, connectpoint);
|
|
bond(lefttri, righttri);
|
|
lnextself(lefttri);
|
|
lprevself(righttri);
|
|
bond(lefttri, righttri);
|
|
lnextself(lefttri);
|
|
lprevself(righttri);
|
|
bond(lefttri, farlefttri);
|
|
bond(righttri, farrighttri);
|
|
if (!farrightflag && triedgeequal(farrighttri, bottommost)) {
|
|
triedgecopy(lefttri, bottommost);
|
|
}
|
|
|
|
if (randomnation(SAMPLERATE) == 0) {
|
|
splayroot = splayinsert(splayroot, &lefttri, nextpoint);
|
|
} else if (randomnation(SAMPLERATE) == 0) {
|
|
lnext(righttri, inserttri);
|
|
splayroot = splayinsert(splayroot, &inserttri, nextpoint);
|
|
}
|
|
}
|
|
}
|
|
nextevent->eventptr = (VOID *) freeevents;
|
|
freeevents = nextevent;
|
|
|
|
if (check4events) {
|
|
apex(farlefttri, leftpoint);
|
|
dest(lefttri, midpoint);
|
|
apex(lefttri, rightpoint);
|
|
lefttest = counterclockwise(leftpoint, midpoint, rightpoint);
|
|
if (lefttest > 0.0) {
|
|
newevent = freeevents;
|
|
freeevents = (struct event *) freeevents->eventptr;
|
|
newevent->xkey = xminextreme;
|
|
newevent->ykey = circletop(leftpoint, midpoint, rightpoint,
|
|
lefttest);
|
|
newevent->eventptr = (VOID *) encode(lefttri);
|
|
eventheapinsert(eventheap, heapsize, newevent);
|
|
heapsize++;
|
|
setorg(lefttri, newevent);
|
|
}
|
|
apex(righttri, leftpoint);
|
|
org(righttri, midpoint);
|
|
apex(farrighttri, rightpoint);
|
|
righttest = counterclockwise(leftpoint, midpoint, rightpoint);
|
|
if (righttest > 0.0) {
|
|
newevent = freeevents;
|
|
freeevents = (struct event *) freeevents->eventptr;
|
|
newevent->xkey = xminextreme;
|
|
newevent->ykey = circletop(leftpoint, midpoint, rightpoint,
|
|
righttest);
|
|
newevent->eventptr = (VOID *) encode(farrighttri);
|
|
eventheapinsert(eventheap, heapsize, newevent);
|
|
heapsize++;
|
|
setorg(farrighttri, newevent);
|
|
}
|
|
}
|
|
}
|
|
|
|
pooldeinit(&splaynodes);
|
|
lprevself(bottommost);
|
|
return removeghosts(&bottommost);
|
|
}
|
|
|
|
#endif /* not REDUCED */
|
|
|
|
/** **/
|
|
/** **/
|
|
/********* Sweepline Delaunay triangulation ends here *********/
|
|
|
|
/********* General mesh construction routines begin here *********/
|
|
/** **/
|
|
/** **/
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* delaunay() Form a Delaunay triangulation. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
long delaunay()
|
|
{
|
|
eextras = 0;
|
|
initializetrisegpools();
|
|
|
|
#ifdef REDUCED
|
|
if (!quiet) {
|
|
printf(
|
|
"Constructing Delaunay triangulation by divide-and-conquer method.\n");
|
|
}
|
|
return divconqdelaunay();
|
|
#else /* not REDUCED */
|
|
if (!quiet) {
|
|
printf("Constructing Delaunay triangulation ");
|
|
if (incremental) {
|
|
printf("by incremental method.\n");
|
|
} else if (sweepline) {
|
|
printf("by sweepline method.\n");
|
|
} else {
|
|
printf("by divide-and-conquer method.\n");
|
|
}
|
|
}
|
|
if (incremental) {
|
|
return incrementaldelaunay();
|
|
} else if (sweepline) {
|
|
return sweeplinedelaunay();
|
|
} else {
|
|
return divconqdelaunay();
|
|
}
|
|
#endif /* not REDUCED */
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* reconstruct() Reconstruct a triangulation from its .ele (and possibly */
|
|
/* .poly) file. Used when the -r switch is used. */
|
|
/* */
|
|
/* Reads an .ele file and reconstructs the original mesh. If the -p switch */
|
|
/* is used, this procedure will also read a .poly file and reconstruct the */
|
|
/* shell edges of the original mesh. If the -a switch is used, this */
|
|
/* procedure will also read an .area file and set a maximum area constraint */
|
|
/* on each triangle. */
|
|
/* */
|
|
/* Points that are not corners of triangles, such as nodes on edges of */
|
|
/* subparametric elements, are discarded. */
|
|
/* */
|
|
/* This routine finds the adjacencies between triangles (and shell edges) */
|
|
/* by forming one stack of triangles for each vertex. Each triangle is on */
|
|
/* three different stacks simultaneously. Each triangle's shell edge */
|
|
/* pointers are used to link the items in each stack. This memory-saving */
|
|
/* feature makes the code harder to read. The most important thing to keep */
|
|
/* in mind is that each triangle is removed from a stack precisely when */
|
|
/* the corresponding pointer is adjusted to refer to a shell edge rather */
|
|
/* than the next triangle of the stack. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
#ifndef CDT_ONLY
|
|
|
|
#ifdef TRILIBRARY
|
|
|
|
int reconstruct(trianglelist, triangleattriblist, trianglearealist, elements,
|
|
corners, attribs, segmentlist, segmentmarkerlist,
|
|
numberofsegments)
|
|
int *trianglelist;
|
|
REAL *triangleattriblist;
|
|
REAL *trianglearealist;
|
|
int elements;
|
|
int corners;
|
|
int attribs;
|
|
int *segmentlist;
|
|
int *segmentmarkerlist;
|
|
int numberofsegments;
|
|
|
|
#else /* not TRILIBRARY */
|
|
|
|
long reconstruct(elefilename, areafilename, polyfilename, polyfile)
|
|
char *elefilename;
|
|
char *areafilename;
|
|
char *polyfilename;
|
|
FILE *polyfile;
|
|
|
|
#endif /* not TRILIBRARY */
|
|
|
|
{
|
|
#ifdef TRILIBRARY
|
|
int pointindex;
|
|
int attribindex;
|
|
#else /* not TRILIBRARY */
|
|
FILE *elefile;
|
|
FILE *areafile;
|
|
char inputline[INPUTLINESIZE];
|
|
char *stringptr;
|
|
int areaelements;
|
|
#endif /* not TRILIBRARY */
|
|
struct triedge triangleloop;
|
|
struct triedge triangleleft;
|
|
struct triedge checktri;
|
|
struct triedge checkleft;
|
|
struct triedge checkneighbor;
|
|
struct edge shelleloop;
|
|
triangle *vertexarray;
|
|
triangle *prevlink;
|
|
triangle nexttri;
|
|
point tdest, tapex;
|
|
point checkdest, checkapex;
|
|
point shorg;
|
|
point killpoint;
|
|
REAL area;
|
|
int corner[3];
|
|
int end[2];
|
|
int killpointindex;
|
|
int incorners;
|
|
int segmentmarkers;
|
|
int boundmarker;
|
|
int aroundpoint;
|
|
long hullsize;
|
|
int notfound;
|
|
int elementnumber, segmentnumber;
|
|
int i, j;
|
|
triangle ptr; /* Temporary variable used by sym(). */
|
|
|
|
#ifdef TRILIBRARY
|
|
inelements = elements;
|
|
incorners = corners;
|
|
if (incorners < 3) {
|
|
printf("Error: Triangles must have at least 3 points.\n");
|
|
exit(1);
|
|
}
|
|
eextras = attribs;
|
|
#else /* not TRILIBRARY */
|
|
/* Read the triangles from an .ele file. */
|
|
if (!quiet) {
|
|
printf("Opening %s.\n", elefilename);
|
|
}
|
|
elefile = fopen(elefilename, "r");
|
|
if (elefile == (FILE *) NULL) {
|
|
printf(" Error: Cannot access file %s.\n", elefilename);
|
|
exit(1);
|
|
}
|
|
/* Read number of triangles, number of points per triangle, and */
|
|
/* number of triangle attributes from .ele file. */
|
|
stringptr = readline(inputline, elefile, elefilename);
|
|
inelements = (int) strtol (stringptr, &stringptr, 0);
|
|
stringptr = findfield(stringptr);
|
|
if (*stringptr == '\0') {
|
|
incorners = 3;
|
|
} else {
|
|
incorners = (int) strtol (stringptr, &stringptr, 0);
|
|
if (incorners < 3) {
|
|
printf("Error: Triangles in %s must have at least 3 points.\n",
|
|
elefilename);
|
|
exit(1);
|
|
}
|
|
}
|
|
stringptr = findfield(stringptr);
|
|
if (*stringptr == '\0') {
|
|
eextras = 0;
|
|
} else {
|
|
eextras = (int) strtol (stringptr, &stringptr, 0);
|
|
}
|
|
#endif /* not TRILIBRARY */
|
|
|
|
initializetrisegpools();
|
|
|
|
/* Create the triangles. */
|
|
for (elementnumber = 1; elementnumber <= inelements; elementnumber++) {
|
|
maketriangle(&triangleloop);
|
|
/* Mark the triangle as living. */
|
|
triangleloop.tri[3] = (triangle) triangleloop.tri;
|
|
}
|
|
|
|
if (poly) {
|
|
#ifdef TRILIBRARY
|
|
insegments = numberofsegments;
|
|
segmentmarkers = segmentmarkerlist != (int *) NULL;
|
|
#else /* not TRILIBRARY */
|
|
/* Read number of segments and number of segment */
|
|
/* boundary markers from .poly file. */
|
|
stringptr = readline(inputline, polyfile, inpolyfilename);
|
|
insegments = (int) strtol (stringptr, &stringptr, 0);
|
|
stringptr = findfield(stringptr);
|
|
if (*stringptr == '\0') {
|
|
segmentmarkers = 0;
|
|
} else {
|
|
segmentmarkers = (int) strtol (stringptr, &stringptr, 0);
|
|
}
|
|
#endif /* not TRILIBRARY */
|
|
|
|
/* Create the shell edges. */
|
|
for (segmentnumber = 1; segmentnumber <= insegments; segmentnumber++) {
|
|
makeshelle(&shelleloop);
|
|
/* Mark the shell edge as living. */
|
|
shelleloop.sh[2] = (shelle) shelleloop.sh;
|
|
}
|
|
}
|
|
|
|
#ifdef TRILIBRARY
|
|
pointindex = 0;
|
|
attribindex = 0;
|
|
#else /* not TRILIBRARY */
|
|
if (vararea) {
|
|
/* Open an .area file, check for consistency with the .ele file. */
|
|
if (!quiet) {
|
|
printf("Opening %s.\n", areafilename);
|
|
}
|
|
areafile = fopen(areafilename, "r");
|
|
if (areafile == (FILE *) NULL) {
|
|
printf(" Error: Cannot access file %s.\n", areafilename);
|
|
exit(1);
|
|
}
|
|
stringptr = readline(inputline, areafile, areafilename);
|
|
areaelements = (int) strtol (stringptr, &stringptr, 0);
|
|
if (areaelements != inelements) {
|
|
printf("Error: %s and %s disagree on number of triangles.\n",
|
|
elefilename, areafilename);
|
|
exit(1);
|
|
}
|
|
}
|
|
#endif /* not TRILIBRARY */
|
|
|
|
if (!quiet) {
|
|
printf("Reconstructing mesh.\n");
|
|
}
|
|
/* Allocate a temporary array that maps each point to some adjacent */
|
|
/* triangle. I took care to allocate all the permanent memory for */
|
|
/* triangles and shell edges first. */
|
|
vertexarray = (triangle *) malloc(points.items * sizeof(triangle));
|
|
if (vertexarray == (triangle *) NULL) {
|
|
printf("Error: Out of memory.\n");
|
|
exit(1);
|
|
}
|
|
/* Each point is initially unrepresented. */
|
|
for (i = 0; i < points.items; i++) {
|
|
vertexarray[i] = (triangle) dummytri;
|
|
}
|
|
|
|
if (verbose) {
|
|
printf(" Assembling triangles.\n");
|
|
}
|
|
/* Read the triangles from the .ele file, and link */
|
|
/* together those that share an edge. */
|
|
traversalinit(&triangles);
|
|
triangleloop.tri = triangletraverse();
|
|
elementnumber = firstnumber;
|
|
while (triangleloop.tri != (triangle *) NULL) {
|
|
#ifdef TRILIBRARY
|
|
/* Copy the triangle's three corners. */
|
|
for (j = 0; j < 3; j++) {
|
|
corner[j] = trianglelist[pointindex++];
|
|
if ((corner[j] < firstnumber) || (corner[j] >= firstnumber + inpoints)) {
|
|
printf("Error: Triangle %d has an invalid vertex index.\n",
|
|
elementnumber);
|
|
exit(1);
|
|
}
|
|
}
|
|
#else /* not TRILIBRARY */
|
|
/* Read triangle number and the triangle's three corners. */
|
|
stringptr = readline(inputline, elefile, elefilename);
|
|
for (j = 0; j < 3; j++) {
|
|
stringptr = findfield(stringptr);
|
|
if (*stringptr == '\0') {
|
|
printf("Error: Triangle %d is missing point %d in %s.\n",
|
|
elementnumber, j + 1, elefilename);
|
|
exit(1);
|
|
} else {
|
|
corner[j] = (int) strtol (stringptr, &stringptr, 0);
|
|
if ((corner[j] < firstnumber) ||
|
|
(corner[j] >= firstnumber + inpoints)) {
|
|
printf("Error: Triangle %d has an invalid vertex index.\n",
|
|
elementnumber);
|
|
exit(1);
|
|
}
|
|
}
|
|
}
|
|
#endif /* not TRILIBRARY */
|
|
|
|
/* Find out about (and throw away) extra nodes. */
|
|
for (j = 3; j < incorners; j++) {
|
|
#ifdef TRILIBRARY
|
|
killpointindex = trianglelist[pointindex++];
|
|
#else /* not TRILIBRARY */
|
|
stringptr = findfield(stringptr);
|
|
if (*stringptr != '\0') {
|
|
killpointindex = (int) strtol (stringptr, &stringptr, 0);
|
|
#endif /* not TRILIBRARY */
|
|
if ((killpointindex >= firstnumber) &&
|
|
(killpointindex < firstnumber + inpoints)) {
|
|
/* Delete the non-corner point if it's not already deleted. */
|
|
killpoint = getpoint(killpointindex);
|
|
if (pointmark(killpoint) != DEADPOINT) {
|
|
pointdealloc(killpoint);
|
|
}
|
|
}
|
|
#ifndef TRILIBRARY
|
|
}
|
|
#endif /* not TRILIBRARY */
|
|
}
|
|
|
|
/* Read the triangle's attributes. */
|
|
for (j = 0; j < eextras; j++) {
|
|
#ifdef TRILIBRARY
|
|
setelemattribute(triangleloop, j, triangleattriblist[attribindex++]);
|
|
#else /* not TRILIBRARY */
|
|
stringptr = findfield(stringptr);
|
|
if (*stringptr == '\0') {
|
|
setelemattribute(triangleloop, j, 0);
|
|
} else {
|
|
setelemattribute(triangleloop, j,
|
|
(REAL) strtod (stringptr, &stringptr));
|
|
}
|
|
#endif /* not TRILIBRARY */
|
|
}
|
|
|
|
if (vararea) {
|
|
#ifdef TRILIBRARY
|
|
area = trianglearealist[elementnumber - firstnumber];
|
|
#else /* not TRILIBRARY */
|
|
/* Read an area constraint from the .area file. */
|
|
stringptr = readline(inputline, areafile, areafilename);
|
|
stringptr = findfield(stringptr);
|
|
if (*stringptr == '\0') {
|
|
area = -1.0; /* No constraint on this triangle. */
|
|
} else {
|
|
area = (REAL) strtod(stringptr, &stringptr);
|
|
}
|
|
#endif /* not TRILIBRARY */
|
|
setareabound(triangleloop, area);
|
|
}
|
|
|
|
/* Set the triangle's vertices. */
|
|
triangleloop.orient = 0;
|
|
setorg(triangleloop, getpoint(corner[0]));
|
|
setdest(triangleloop, getpoint(corner[1]));
|
|
setapex(triangleloop, getpoint(corner[2]));
|
|
/* Try linking the triangle to others that share these vertices. */
|
|
for (triangleloop.orient = 0; triangleloop.orient < 3;
|
|
triangleloop.orient++) {
|
|
/* Take the number for the origin of triangleloop. */
|
|
aroundpoint = corner[triangleloop.orient];
|
|
/* Look for other triangles having this vertex. */
|
|
nexttri = vertexarray[aroundpoint - firstnumber];
|
|
/* Link the current triangle to the next one in the stack. */
|
|
triangleloop.tri[6 + triangleloop.orient] = nexttri;
|
|
/* Push the current triangle onto the stack. */
|
|
vertexarray[aroundpoint - firstnumber] = encode(triangleloop);
|
|
decode(nexttri, checktri);
|
|
if (checktri.tri != dummytri) {
|
|
dest(triangleloop, tdest);
|
|
apex(triangleloop, tapex);
|
|
/* Look for other triangles that share an edge. */
|
|
do {
|
|
dest(checktri, checkdest);
|
|
apex(checktri, checkapex);
|
|
if (tapex == checkdest) {
|
|
/* The two triangles share an edge; bond them together. */
|
|
lprev(triangleloop, triangleleft);
|
|
bond(triangleleft, checktri);
|
|
}
|
|
if (tdest == checkapex) {
|
|
/* The two triangles share an edge; bond them together. */
|
|
lprev(checktri, checkleft);
|
|
bond(triangleloop, checkleft);
|
|
}
|
|
/* Find the next triangle in the stack. */
|
|
nexttri = checktri.tri[6 + checktri.orient];
|
|
decode(nexttri, checktri);
|
|
} while (checktri.tri != dummytri);
|
|
}
|
|
}
|
|
triangleloop.tri = triangletraverse();
|
|
elementnumber++;
|
|
}
|
|
|
|
#ifdef TRILIBRARY
|
|
pointindex = 0;
|
|
#else /* not TRILIBRARY */
|
|
fclose(elefile);
|
|
if (vararea) {
|
|
fclose(areafile);
|
|
}
|
|
#endif /* not TRILIBRARY */
|
|
|
|
hullsize = 0; /* Prepare to count the boundary edges. */
|
|
if (poly) {
|
|
if (verbose) {
|
|
printf(" Marking segments in triangulation.\n");
|
|
}
|
|
/* Read the segments from the .poly file, and link them */
|
|
/* to their neighboring triangles. */
|
|
boundmarker = 0;
|
|
traversalinit(&shelles);
|
|
shelleloop.sh = shelletraverse();
|
|
segmentnumber = firstnumber;
|
|
while (shelleloop.sh != (shelle *) NULL) {
|
|
#ifdef TRILIBRARY
|
|
end[0] = segmentlist[pointindex++];
|
|
end[1] = segmentlist[pointindex++];
|
|
if (segmentmarkers) {
|
|
boundmarker = segmentmarkerlist[segmentnumber - firstnumber];
|
|
}
|
|
#else /* not TRILIBRARY */
|
|
/* Read the endpoints of each segment, and possibly a boundary marker. */
|
|
stringptr = readline(inputline, polyfile, inpolyfilename);
|
|
/* Skip the first (segment number) field. */
|
|
stringptr = findfield(stringptr);
|
|
if (*stringptr == '\0') {
|
|
printf("Error: Segment %d has no endpoints in %s.\n", segmentnumber,
|
|
polyfilename);
|
|
exit(1);
|
|
} else {
|
|
end[0] = (int) strtol (stringptr, &stringptr, 0);
|
|
}
|
|
stringptr = findfield(stringptr);
|
|
if (*stringptr == '\0') {
|
|
printf("Error: Segment %d is missing its second endpoint in %s.\n",
|
|
segmentnumber, polyfilename);
|
|
exit(1);
|
|
} else {
|
|
end[1] = (int) strtol (stringptr, &stringptr, 0);
|
|
}
|
|
if (segmentmarkers) {
|
|
stringptr = findfield(stringptr);
|
|
if (*stringptr == '\0') {
|
|
boundmarker = 0;
|
|
} else {
|
|
boundmarker = (int) strtol (stringptr, &stringptr, 0);
|
|
}
|
|
}
|
|
#endif /* not TRILIBRARY */
|
|
for (j = 0; j < 2; j++) {
|
|
if ((end[j] < firstnumber) || (end[j] >= firstnumber + inpoints)) {
|
|
printf("Error: Segment %d has an invalid vertex index.\n",
|
|
segmentnumber);
|
|
exit(1);
|
|
}
|
|
}
|
|
|
|
/* set the shell edge's vertices. */
|
|
shelleloop.shorient = 0;
|
|
setsorg(shelleloop, getpoint(end[0]));
|
|
setsdest(shelleloop, getpoint(end[1]));
|
|
setmark(shelleloop, boundmarker);
|
|
/* Try linking the shell edge to triangles that share these vertices. */
|
|
for (shelleloop.shorient = 0; shelleloop.shorient < 2;
|
|
shelleloop.shorient++) {
|
|
/* Take the number for the destination of shelleloop. */
|
|
aroundpoint = end[1 - shelleloop.shorient];
|
|
/* Look for triangles having this vertex. */
|
|
prevlink = &vertexarray[aroundpoint - firstnumber];
|
|
nexttri = vertexarray[aroundpoint - firstnumber];
|
|
decode(nexttri, checktri);
|
|
sorg(shelleloop, shorg);
|
|
notfound = 1;
|
|
/* Look for triangles having this edge. Note that I'm only */
|
|
/* comparing each triangle's destination with the shell edge; */
|
|
/* each triangle's apex is handled through a different vertex. */
|
|
/* Because each triangle appears on three vertices' lists, each */
|
|
/* occurrence of a triangle on a list can (and does) represent */
|
|
/* an edge. In this way, most edges are represented twice, and */
|
|
/* every triangle-segment bond is represented once. */
|
|
while (notfound && (checktri.tri != dummytri)) {
|
|
dest(checktri, checkdest);
|
|
if (shorg == checkdest) {
|
|
/* We have a match. Remove this triangle from the list. */
|
|
*prevlink = checktri.tri[6 + checktri.orient];
|
|
/* Bond the shell edge to the triangle. */
|
|
tsbond(checktri, shelleloop);
|
|
/* Check if this is a boundary edge. */
|
|
sym(checktri, checkneighbor);
|
|
if (checkneighbor.tri == dummytri) {
|
|
/* The next line doesn't insert a shell edge (because there's */
|
|
/* already one there), but it sets the boundary markers of */
|
|
/* the existing shell edge and its vertices. */
|
|
insertshelle(&checktri, 1);
|
|
hullsize++;
|
|
}
|
|
notfound = 0;
|
|
}
|
|
/* Find the next triangle in the stack. */
|
|
prevlink = &checktri.tri[6 + checktri.orient];
|
|
nexttri = checktri.tri[6 + checktri.orient];
|
|
decode(nexttri, checktri);
|
|
}
|
|
}
|
|
shelleloop.sh = shelletraverse();
|
|
segmentnumber++;
|
|
}
|
|
}
|
|
|
|
/* Mark the remaining edges as not being attached to any shell edge. */
|
|
/* Also, count the (yet uncounted) boundary edges. */
|
|
for (i = 0; i < points.items; i++) {
|
|
/* Search the stack of triangles adjacent to a point. */
|
|
nexttri = vertexarray[i];
|
|
decode(nexttri, checktri);
|
|
while (checktri.tri != dummytri) {
|
|
/* Find the next triangle in the stack before this */
|
|
/* information gets overwritten. */
|
|
nexttri = checktri.tri[6 + checktri.orient];
|
|
/* No adjacent shell edge. (This overwrites the stack info.) */
|
|
tsdissolve(checktri);
|
|
sym(checktri, checkneighbor);
|
|
if (checkneighbor.tri == dummytri) {
|
|
insertshelle(&checktri, 1);
|
|
hullsize++;
|
|
}
|
|
decode(nexttri, checktri);
|
|
}
|
|
}
|
|
|
|
free(vertexarray);
|
|
return hullsize;
|
|
}
|
|
|
|
#endif /* not CDT_ONLY */
|
|
|
|
/** **/
|
|
/** **/
|
|
/********* General mesh construction routines end here *********/
|
|
|
|
/********* Segment (shell edge) insertion begins here *********/
|
|
/** **/
|
|
/** **/
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* finddirection() Find the first triangle on the path from one point */
|
|
/* to another. */
|
|
/* */
|
|
/* Finds the triangle that intersects a line segment drawn from the */
|
|
/* origin of `searchtri' to the point `endpoint', and returns the result */
|
|
/* in `searchtri'. The origin of `searchtri' does not change, even though */
|
|
/* the triangle returned may differ from the one passed in. This routine */
|
|
/* is used to find the direction to move in to get from one point to */
|
|
/* another. */
|
|
/* */
|
|
/* The return value notes whether the destination or apex of the found */
|
|
/* triangle is collinear with the two points in question. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
enum finddirectionresult finddirection(searchtri, endpoint)
|
|
struct triedge *searchtri;
|
|
point endpoint;
|
|
{
|
|
struct triedge checktri;
|
|
point startpoint;
|
|
point leftpoint, rightpoint;
|
|
REAL leftccw, rightccw;
|
|
int leftflag, rightflag;
|
|
triangle ptr; /* Temporary variable used by onext() and oprev(). */
|
|
|
|
org(*searchtri, startpoint);
|
|
dest(*searchtri, rightpoint);
|
|
apex(*searchtri, leftpoint);
|
|
/* Is `endpoint' to the left? */
|
|
leftccw = counterclockwise(endpoint, startpoint, leftpoint);
|
|
leftflag = leftccw > 0.0;
|
|
/* Is `endpoint' to the right? */
|
|
rightccw = counterclockwise(startpoint, endpoint, rightpoint);
|
|
rightflag = rightccw > 0.0;
|
|
if (leftflag && rightflag) {
|
|
/* `searchtri' faces directly away from `endpoint'. We could go */
|
|
/* left or right. Ask whether it's a triangle or a boundary */
|
|
/* on the left. */
|
|
onext(*searchtri, checktri);
|
|
if (checktri.tri == dummytri) {
|
|
leftflag = 0;
|
|
} else {
|
|
rightflag = 0;
|
|
}
|
|
}
|
|
while (leftflag) {
|
|
/* Turn left until satisfied. */
|
|
onextself(*searchtri);
|
|
if (searchtri->tri == dummytri) {
|
|
printf("Internal error in finddirection(): Unable to find a\n");
|
|
printf(" triangle leading from (%.12g, %.12g) to", startpoint[0],
|
|
startpoint[1]);
|
|
printf(" (%.12g, %.12g).\n", endpoint[0], endpoint[1]);
|
|
internalerror();
|
|
}
|
|
apex(*searchtri, leftpoint);
|
|
rightccw = leftccw;
|
|
leftccw = counterclockwise(endpoint, startpoint, leftpoint);
|
|
leftflag = leftccw > 0.0;
|
|
}
|
|
while (rightflag) {
|
|
/* Turn right until satisfied. */
|
|
oprevself(*searchtri);
|
|
if (searchtri->tri == dummytri) {
|
|
printf("Internal error in finddirection(): Unable to find a\n");
|
|
printf(" triangle leading from (%.12g, %.12g) to", startpoint[0],
|
|
startpoint[1]);
|
|
printf(" (%.12g, %.12g).\n", endpoint[0], endpoint[1]);
|
|
internalerror();
|
|
}
|
|
dest(*searchtri, rightpoint);
|
|
leftccw = rightccw;
|
|
rightccw = counterclockwise(startpoint, endpoint, rightpoint);
|
|
rightflag = rightccw > 0.0;
|
|
}
|
|
if (leftccw == 0.0) {
|
|
return LEFTCOLLINEAR;
|
|
} else if (rightccw == 0.0) {
|
|
return RIGHTCOLLINEAR;
|
|
} else {
|
|
return WITHIN;
|
|
}
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* segmentintersection() Find the intersection of an existing segment */
|
|
/* and a segment that is being inserted. Insert */
|
|
/* a point at the intersection, splitting an */
|
|
/* existing shell edge. */
|
|
/* */
|
|
/* The segment being inserted connects the apex of splittri to endpoint2. */
|
|
/* splitshelle is the shell edge being split, and MUST be opposite */
|
|
/* splittri. Hence, the edge being split connects the origin and */
|
|
/* destination of splittri. */
|
|
/* */
|
|
/* On completion, splittri is a handle having the newly inserted */
|
|
/* intersection point as its origin, and endpoint1 as its destination. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
void segmentintersection(splittri, splitshelle, endpoint2)
|
|
struct triedge *splittri;
|
|
struct edge *splitshelle;
|
|
point endpoint2;
|
|
{
|
|
point endpoint1;
|
|
point torg, tdest;
|
|
point leftpoint, rightpoint;
|
|
point newpoint;
|
|
enum insertsiteresult success;
|
|
enum finddirectionresult collinear;
|
|
REAL ex, ey;
|
|
REAL tx, ty;
|
|
REAL etx, ety;
|
|
REAL split, denom;
|
|
int i;
|
|
triangle ptr; /* Temporary variable used by onext(). */
|
|
|
|
/* Find the other three segment endpoints. */
|
|
apex(*splittri, endpoint1);
|
|
org(*splittri, torg);
|
|
dest(*splittri, tdest);
|
|
/* Segment intersection formulae; see the Antonio reference. */
|
|
tx = tdest[0] - torg[0];
|
|
ty = tdest[1] - torg[1];
|
|
ex = endpoint2[0] - endpoint1[0];
|
|
ey = endpoint2[1] - endpoint1[1];
|
|
etx = torg[0] - endpoint2[0];
|
|
ety = torg[1] - endpoint2[1];
|
|
denom = ty * ex - tx * ey;
|
|
if (denom == 0.0) {
|
|
printf("Internal error in segmentintersection():");
|
|
printf(" Attempt to find intersection of parallel segments.\n");
|
|
internalerror();
|
|
}
|
|
split = (ey * etx - ex * ety) / denom;
|
|
/* Create the new point. */
|
|
newpoint = (point) poolalloc(&points);
|
|
/* Interpolate its coordinate and attributes. */
|
|
for (i = 0; i < 2 + nextras; i++) {
|
|
newpoint[i] = torg[i] + split * (tdest[i] - torg[i]);
|
|
}
|
|
setpointmark(newpoint, mark(*splitshelle));
|
|
if (verbose > 1) {
|
|
printf(
|
|
" Splitting edge (%.12g, %.12g) (%.12g, %.12g) at (%.12g, %.12g).\n",
|
|
torg[0], torg[1], tdest[0], tdest[1], newpoint[0], newpoint[1]);
|
|
}
|
|
/* Insert the intersection point. This should always succeed. */
|
|
success = insertsite(newpoint, splittri, splitshelle, 0, 0);
|
|
if (success != SUCCESSFULPOINT) {
|
|
printf("Internal error in segmentintersection():\n");
|
|
printf(" Failure to split a segment.\n");
|
|
internalerror();
|
|
}
|
|
if (steinerleft > 0) {
|
|
steinerleft--;
|
|
}
|
|
/* Inserting the point may have caused edge flips. We wish to rediscover */
|
|
/* the edge connecting endpoint1 to the new intersection point. */
|
|
collinear = finddirection(splittri, endpoint1);
|
|
dest(*splittri, rightpoint);
|
|
apex(*splittri, leftpoint);
|
|
if ((leftpoint[0] == endpoint1[0]) && (leftpoint[1] == endpoint1[1])) {
|
|
onextself(*splittri);
|
|
} else if ((rightpoint[0] != endpoint1[0]) ||
|
|
(rightpoint[1] != endpoint1[1])) {
|
|
printf("Internal error in segmentintersection():\n");
|
|
printf(" Topological inconsistency after splitting a segment.\n");
|
|
internalerror();
|
|
}
|
|
/* `splittri' should have destination endpoint1. */
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* scoutsegment() Scout the first triangle on the path from one endpoint */
|
|
/* to another, and check for completion (reaching the */
|
|
/* second endpoint), a collinear point, and the */
|
|
/* intersection of two segments. */
|
|
/* */
|
|
/* Returns one if the entire segment is successfully inserted, and zero if */
|
|
/* the job must be finished by conformingedge() or constrainededge(). */
|
|
/* */
|
|
/* If the first triangle on the path has the second endpoint as its */
|
|
/* destination or apex, a shell edge is inserted and the job is done. */
|
|
/* */
|
|
/* If the first triangle on the path has a destination or apex that lies on */
|
|
/* the segment, a shell edge is inserted connecting the first endpoint to */
|
|
/* the collinear point, and the search is continued from the collinear */
|
|
/* point. */
|
|
/* */
|
|
/* If the first triangle on the path has a shell edge opposite its origin, */
|
|
/* then there is a segment that intersects the segment being inserted. */
|
|
/* Their intersection point is inserted, splitting the shell edge. */
|
|
/* */
|
|
/* Otherwise, return zero. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
int scoutsegment(searchtri, endpoint2, newmark)
|
|
struct triedge *searchtri;
|
|
point endpoint2;
|
|
int newmark;
|
|
{
|
|
struct triedge crosstri;
|
|
struct edge crossedge;
|
|
point leftpoint, rightpoint;
|
|
point endpoint1;
|
|
enum finddirectionresult collinear;
|
|
shelle sptr; /* Temporary variable used by tspivot(). */
|
|
|
|
collinear = finddirection(searchtri, endpoint2);
|
|
dest(*searchtri, rightpoint);
|
|
apex(*searchtri, leftpoint);
|
|
if (((leftpoint[0] == endpoint2[0]) && (leftpoint[1] == endpoint2[1])) ||
|
|
((rightpoint[0] == endpoint2[0]) && (rightpoint[1] == endpoint2[1]))) {
|
|
/* The segment is already an edge in the mesh. */
|
|
if ((leftpoint[0] == endpoint2[0]) && (leftpoint[1] == endpoint2[1])) {
|
|
lprevself(*searchtri);
|
|
}
|
|
/* Insert a shell edge, if there isn't already one there. */
|
|
insertshelle(searchtri, newmark);
|
|
return 1;
|
|
} else if (collinear == LEFTCOLLINEAR) {
|
|
/* We've collided with a point between the segment's endpoints. */
|
|
/* Make the collinear point be the triangle's origin. */
|
|
lprevself(*searchtri);
|
|
insertshelle(searchtri, newmark);
|
|
/* Insert the remainder of the segment. */
|
|
return scoutsegment(searchtri, endpoint2, newmark);
|
|
} else if (collinear == RIGHTCOLLINEAR) {
|
|
/* We've collided with a point between the segment's endpoints. */
|
|
insertshelle(searchtri, newmark);
|
|
/* Make the collinear point be the triangle's origin. */
|
|
lnextself(*searchtri);
|
|
/* Insert the remainder of the segment. */
|
|
return scoutsegment(searchtri, endpoint2, newmark);
|
|
} else {
|
|
lnext(*searchtri, crosstri);
|
|
tspivot(crosstri, crossedge);
|
|
/* Check for a crossing segment. */
|
|
if (crossedge.sh == dummysh) {
|
|
return 0;
|
|
} else {
|
|
org(*searchtri, endpoint1);
|
|
/* Insert a point at the intersection. */
|
|
segmentintersection(&crosstri, &crossedge, endpoint2);
|
|
triedgecopy(crosstri, *searchtri);
|
|
insertshelle(searchtri, newmark);
|
|
/* Insert the remainder of the segment. */
|
|
return scoutsegment(searchtri, endpoint2, newmark);
|
|
}
|
|
}
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* conformingedge() Force a segment into a conforming Delaunay */
|
|
/* triangulation by inserting a point at its midpoint, */
|
|
/* and recursively forcing in the two half-segments if */
|
|
/* necessary. */
|
|
/* */
|
|
/* Generates a sequence of edges connecting `endpoint1' to `endpoint2'. */
|
|
/* `newmark' is the boundary marker of the segment, assigned to each new */
|
|
/* splitting point and shell edge. */
|
|
/* */
|
|
/* Note that conformingedge() does not always maintain the conforming */
|
|
/* Delaunay property. Once inserted, segments are locked into place; */
|
|
/* points inserted later (to force other segments in) may render these */
|
|
/* fixed segments non-Delaunay. The conforming Delaunay property will be */
|
|
/* restored by enforcequality() by splitting encroached segments. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
#ifndef REDUCED
|
|
#ifndef CDT_ONLY
|
|
|
|
void conformingedge(endpoint1, endpoint2, newmark)
|
|
point endpoint1;
|
|
point endpoint2;
|
|
int newmark;
|
|
{
|
|
struct triedge searchtri1, searchtri2;
|
|
struct edge brokenshelle;
|
|
point newpoint;
|
|
point midpoint1, midpoint2;
|
|
enum insertsiteresult success;
|
|
int result1, result2;
|
|
int i;
|
|
shelle sptr; /* Temporary variable used by tspivot(). */
|
|
|
|
if (verbose > 2) {
|
|
printf("Forcing segment into triangulation by recursive splitting:\n");
|
|
printf(" (%.12g, %.12g) (%.12g, %.12g)\n", endpoint1[0], endpoint1[1],
|
|
endpoint2[0], endpoint2[1]);
|
|
}
|
|
/* Create a new point to insert in the middle of the segment. */
|
|
newpoint = (point) poolalloc(&points);
|
|
/* Interpolate coordinates and attributes. */
|
|
for (i = 0; i < 2 + nextras; i++) {
|
|
newpoint[i] = 0.5 * (endpoint1[i] + endpoint2[i]);
|
|
}
|
|
setpointmark(newpoint, newmark);
|
|
/* Find a boundary triangle to search from. */
|
|
searchtri1.tri = (triangle *) NULL;
|
|
/* Attempt to insert the new point. */
|
|
success = insertsite(newpoint, &searchtri1, (struct edge *) NULL, 0, 0);
|
|
if (success == DUPLICATEPOINT) {
|
|
if (verbose > 2) {
|
|
printf(" Segment intersects existing point (%.12g, %.12g).\n",
|
|
newpoint[0], newpoint[1]);
|
|
}
|
|
/* Use the point that's already there. */
|
|
pointdealloc(newpoint);
|
|
org(searchtri1, newpoint);
|
|
} else {
|
|
if (success == VIOLATINGPOINT) {
|
|
if (verbose > 2) {
|
|
printf(" Two segments intersect at (%.12g, %.12g).\n",
|
|
newpoint[0], newpoint[1]);
|
|
}
|
|
/* By fluke, we've landed right on another segment. Split it. */
|
|
tspivot(searchtri1, brokenshelle);
|
|
success = insertsite(newpoint, &searchtri1, &brokenshelle, 0, 0);
|
|
if (success != SUCCESSFULPOINT) {
|
|
printf("Internal error in conformingedge():\n");
|
|
printf(" Failure to split a segment.\n");
|
|
internalerror();
|
|
}
|
|
}
|
|
/* The point has been inserted successfully. */
|
|
if (steinerleft > 0) {
|
|
steinerleft--;
|
|
}
|
|
}
|
|
triedgecopy(searchtri1, searchtri2);
|
|
result1 = scoutsegment(&searchtri1, endpoint1, newmark);
|
|
result2 = scoutsegment(&searchtri2, endpoint2, newmark);
|
|
if (!result1) {
|
|
/* The origin of searchtri1 may have changed if a collision with an */
|
|
/* intervening vertex on the segment occurred. */
|
|
org(searchtri1, midpoint1);
|
|
conformingedge(midpoint1, endpoint1, newmark);
|
|
}
|
|
if (!result2) {
|
|
/* The origin of searchtri2 may have changed if a collision with an */
|
|
/* intervening vertex on the segment occurred. */
|
|
org(searchtri2, midpoint2);
|
|
conformingedge(midpoint2, endpoint2, newmark);
|
|
}
|
|
}
|
|
|
|
#endif /* not CDT_ONLY */
|
|
#endif /* not REDUCED */
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* delaunayfixup() Enforce the Delaunay condition at an edge, fanning out */
|
|
/* recursively from an existing point. Pay special */
|
|
/* attention to stacking inverted triangles. */
|
|
/* */
|
|
/* This is a support routine for inserting segments into a constrained */
|
|
/* Delaunay triangulation. */
|
|
/* */
|
|
/* The origin of fixuptri is treated as if it has just been inserted, and */
|
|
/* the local Delaunay condition needs to be enforced. It is only enforced */
|
|
/* in one sector, however, that being the angular range defined by */
|
|
/* fixuptri. */
|
|
/* */
|
|
/* This routine also needs to make decisions regarding the "stacking" of */
|
|
/* triangles. (Read the description of constrainededge() below before */
|
|
/* reading on here, so you understand the algorithm.) If the position of */
|
|
/* the new point (the origin of fixuptri) indicates that the vertex before */
|
|
/* it on the polygon is a reflex vertex, then "stack" the triangle by */
|
|
/* doing nothing. (fixuptri is an inverted triangle, which is how stacked */
|
|
/* triangles are identified.) */
|
|
/* */
|
|
/* Otherwise, check whether the vertex before that was a reflex vertex. */
|
|
/* If so, perform an edge flip, thereby eliminating an inverted triangle */
|
|
/* (popping it off the stack). The edge flip may result in the creation */
|
|
/* of a new inverted triangle, depending on whether or not the new vertex */
|
|
/* is visible to the vertex three edges behind on the polygon. */
|
|
/* */
|
|
/* If neither of the two vertices behind the new vertex are reflex */
|
|
/* vertices, fixuptri and fartri, the triangle opposite it, are not */
|
|
/* inverted; hence, ensure that the edge between them is locally Delaunay. */
|
|
/* */
|
|
/* `leftside' indicates whether or not fixuptri is to the left of the */
|
|
/* segment being inserted. (Imagine that the segment is pointing up from */
|
|
/* endpoint1 to endpoint2.) */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
void delaunayfixup(fixuptri, leftside)
|
|
struct triedge *fixuptri;
|
|
int leftside;
|
|
{
|
|
struct triedge neartri;
|
|
struct triedge fartri;
|
|
struct edge faredge;
|
|
point nearpoint, leftpoint, rightpoint, farpoint;
|
|
triangle ptr; /* Temporary variable used by sym(). */
|
|
shelle sptr; /* Temporary variable used by tspivot(). */
|
|
|
|
lnext(*fixuptri, neartri);
|
|
sym(neartri, fartri);
|
|
/* Check if the edge opposite the origin of fixuptri can be flipped. */
|
|
if (fartri.tri == dummytri) {
|
|
return;
|
|
}
|
|
tspivot(neartri, faredge);
|
|
if (faredge.sh != dummysh) {
|
|
return;
|
|
}
|
|
/* Find all the relevant vertices. */
|
|
apex(neartri, nearpoint);
|
|
org(neartri, leftpoint);
|
|
dest(neartri, rightpoint);
|
|
apex(fartri, farpoint);
|
|
/* Check whether the previous polygon vertex is a reflex vertex. */
|
|
if (leftside) {
|
|
if (counterclockwise(nearpoint, leftpoint, farpoint) <= 0.0) {
|
|
/* leftpoint is a reflex vertex too. Nothing can */
|
|
/* be done until a convex section is found. */
|
|
return;
|
|
}
|
|
} else {
|
|
if (counterclockwise(farpoint, rightpoint, nearpoint) <= 0.0) {
|
|
/* rightpoint is a reflex vertex too. Nothing can */
|
|
/* be done until a convex section is found. */
|
|
return;
|
|
}
|
|
}
|
|
if (counterclockwise(rightpoint, leftpoint, farpoint) > 0.0) {
|
|
/* fartri is not an inverted triangle, and farpoint is not a reflex */
|
|
/* vertex. As there are no reflex vertices, fixuptri isn't an */
|
|
/* inverted triangle, either. Hence, test the edge between the */
|
|
/* triangles to ensure it is locally Delaunay. */
|
|
if (incircle(leftpoint, farpoint, rightpoint, nearpoint) <= 0.0) {
|
|
return;
|
|
}
|
|
/* Not locally Delaunay; go on to an edge flip. */
|
|
} /* else fartri is inverted; remove it from the stack by flipping. */
|
|
flip(&neartri);
|
|
lprevself(*fixuptri); /* Restore the origin of fixuptri after the flip. */
|
|
/* Recursively process the two triangles that result from the flip. */
|
|
delaunayfixup(fixuptri, leftside);
|
|
delaunayfixup(&fartri, leftside);
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* constrainededge() Force a segment into a constrained Delaunay */
|
|
/* triangulation by deleting the triangles it */
|
|
/* intersects, and triangulating the polygons that */
|
|
/* form on each side of it. */
|
|
/* */
|
|
/* Generates a single edge connecting `endpoint1' to `endpoint2'. The */
|
|
/* triangle `starttri' has `endpoint1' as its origin. `newmark' is the */
|
|
/* boundary marker of the segment. */
|
|
/* */
|
|
/* To insert a segment, every triangle whose interior intersects the */
|
|
/* segment is deleted. The union of these deleted triangles is a polygon */
|
|
/* (which is not necessarily monotone, but is close enough), which is */
|
|
/* divided into two polygons by the new segment. This routine's task is */
|
|
/* to generate the Delaunay triangulation of these two polygons. */
|
|
/* */
|
|
/* You might think of this routine's behavior as a two-step process. The */
|
|
/* first step is to walk from endpoint1 to endpoint2, flipping each edge */
|
|
/* encountered. This step creates a fan of edges connected to endpoint1, */
|
|
/* including the desired edge to endpoint2. The second step enforces the */
|
|
/* Delaunay condition on each side of the segment in an incremental manner: */
|
|
/* proceeding along the polygon from endpoint1 to endpoint2 (this is done */
|
|
/* independently on each side of the segment), each vertex is "enforced" */
|
|
/* as if it had just been inserted, but affecting only the previous */
|
|
/* vertices. The result is the same as if the vertices had been inserted */
|
|
/* in the order they appear on the polygon, so the result is Delaunay. */
|
|
/* */
|
|
/* In truth, constrainededge() interleaves these two steps. The procedure */
|
|
/* walks from endpoint1 to endpoint2, and each time an edge is encountered */
|
|
/* and flipped, the newly exposed vertex (at the far end of the flipped */
|
|
/* edge) is "enforced" upon the previously flipped edges, usually affecting */
|
|
/* only one side of the polygon (depending upon which side of the segment */
|
|
/* the vertex falls on). */
|
|
/* */
|
|
/* The algorithm is complicated by the need to handle polygons that are not */
|
|
/* convex. Although the polygon is not necessarily monotone, it can be */
|
|
/* triangulated in a manner similar to the stack-based algorithms for */
|
|
/* monotone polygons. For each reflex vertex (local concavity) of the */
|
|
/* polygon, there will be an inverted triangle formed by one of the edge */
|
|
/* flips. (An inverted triangle is one with negative area - that is, its */
|
|
/* vertices are arranged in clockwise order - and is best thought of as a */
|
|
/* wrinkle in the fabric of the mesh.) Each inverted triangle can be */
|
|
/* thought of as a reflex vertex pushed on the stack, waiting to be fixed */
|
|
/* later. */
|
|
/* */
|
|
/* A reflex vertex is popped from the stack when a vertex is inserted that */
|
|
/* is visible to the reflex vertex. (However, if the vertex behind the */
|
|
/* reflex vertex is not visible to the reflex vertex, a new inverted */
|
|
/* triangle will take its place on the stack.) These details are handled */
|
|
/* by the delaunayfixup() routine above. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
void constrainededge(starttri, endpoint2, newmark)
|
|
struct triedge *starttri;
|
|
point endpoint2;
|
|
int newmark;
|
|
{
|
|
struct triedge fixuptri, fixuptri2;
|
|
struct edge fixupedge;
|
|
point endpoint1;
|
|
point farpoint;
|
|
REAL area;
|
|
int collision;
|
|
int done;
|
|
triangle ptr; /* Temporary variable used by sym() and oprev(). */
|
|
shelle sptr; /* Temporary variable used by tspivot(). */
|
|
|
|
org(*starttri, endpoint1);
|
|
lnext(*starttri, fixuptri);
|
|
flip(&fixuptri);
|
|
/* `collision' indicates whether we have found a point directly */
|
|
/* between endpoint1 and endpoint2. */
|
|
collision = 0;
|
|
done = 0;
|
|
do {
|
|
org(fixuptri, farpoint);
|
|
/* `farpoint' is the extreme point of the polygon we are "digging" */
|
|
/* to get from endpoint1 to endpoint2. */
|
|
if ((farpoint[0] == endpoint2[0]) && (farpoint[1] == endpoint2[1])) {
|
|
oprev(fixuptri, fixuptri2);
|
|
/* Enforce the Delaunay condition around endpoint2. */
|
|
delaunayfixup(&fixuptri, 0);
|
|
delaunayfixup(&fixuptri2, 1);
|
|
done = 1;
|
|
} else {
|
|
/* Check whether farpoint is to the left or right of the segment */
|
|
/* being inserted, to decide which edge of fixuptri to dig */
|
|
/* through next. */
|
|
area = counterclockwise(endpoint1, endpoint2, farpoint);
|
|
if (area == 0.0) {
|
|
/* We've collided with a point between endpoint1 and endpoint2. */
|
|
collision = 1;
|
|
oprev(fixuptri, fixuptri2);
|
|
/* Enforce the Delaunay condition around farpoint. */
|
|
delaunayfixup(&fixuptri, 0);
|
|
delaunayfixup(&fixuptri2, 1);
|
|
done = 1;
|
|
} else {
|
|
if (area > 0.0) { /* farpoint is to the left of the segment. */
|
|
oprev(fixuptri, fixuptri2);
|
|
/* Enforce the Delaunay condition around farpoint, on the */
|
|
/* left side of the segment only. */
|
|
delaunayfixup(&fixuptri2, 1);
|
|
/* Flip the edge that crosses the segment. After the edge is */
|
|
/* flipped, one of its endpoints is the fan vertex, and the */
|
|
/* destination of fixuptri is the fan vertex. */
|
|
lprevself(fixuptri);
|
|
} else { /* farpoint is to the right of the segment. */
|
|
delaunayfixup(&fixuptri, 0);
|
|
/* Flip the edge that crosses the segment. After the edge is */
|
|
/* flipped, one of its endpoints is the fan vertex, and the */
|
|
/* destination of fixuptri is the fan vertex. */
|
|
oprevself(fixuptri);
|
|
}
|
|
/* Check for two intersecting segments. */
|
|
tspivot(fixuptri, fixupedge);
|
|
if (fixupedge.sh == dummysh) {
|
|
flip(&fixuptri); /* May create an inverted triangle on the left. */
|
|
} else {
|
|
/* We've collided with a segment between endpoint1 and endpoint2. */
|
|
collision = 1;
|
|
/* Insert a point at the intersection. */
|
|
segmentintersection(&fixuptri, &fixupedge, endpoint2);
|
|
done = 1;
|
|
}
|
|
}
|
|
}
|
|
} while (!done);
|
|
/* Insert a shell edge to make the segment permanent. */
|
|
insertshelle(&fixuptri, newmark);
|
|
/* If there was a collision with an interceding vertex, install another */
|
|
/* segment connecting that vertex with endpoint2. */
|
|
if (collision) {
|
|
/* Insert the remainder of the segment. */
|
|
if (!scoutsegment(&fixuptri, endpoint2, newmark)) {
|
|
constrainededge(&fixuptri, endpoint2, newmark);
|
|
}
|
|
}
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* insertsegment() Insert a PSLG segment into a triangulation. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
void insertsegment(endpoint1, endpoint2, newmark)
|
|
point endpoint1;
|
|
point endpoint2;
|
|
int newmark;
|
|
{
|
|
struct triedge searchtri1, searchtri2;
|
|
triangle encodedtri;
|
|
point checkpoint;
|
|
triangle ptr; /* Temporary variable used by sym(). */
|
|
|
|
if (verbose > 1) {
|
|
printf(" Connecting (%.12g, %.12g) to (%.12g, %.12g).\n",
|
|
endpoint1[0], endpoint1[1], endpoint2[0], endpoint2[1]);
|
|
}
|
|
|
|
/* Find a triangle whose origin is the segment's first endpoint. */
|
|
checkpoint = (point) NULL;
|
|
encodedtri = point2tri(endpoint1);
|
|
if (encodedtri != (triangle) NULL) {
|
|
decode(encodedtri, searchtri1);
|
|
org(searchtri1, checkpoint);
|
|
}
|
|
if (checkpoint != endpoint1) {
|
|
/* Find a boundary triangle to search from. */
|
|
searchtri1.tri = dummytri;
|
|
searchtri1.orient = 0;
|
|
symself(searchtri1);
|
|
/* Search for the segment's first endpoint by point location. */
|
|
if (locate(endpoint1, &searchtri1) != ONVERTEX) {
|
|
printf(
|
|
"Internal error in insertsegment(): Unable to locate PSLG point\n");
|
|
printf(" (%.12g, %.12g) in triangulation.\n",
|
|
endpoint1[0], endpoint1[1]);
|
|
internalerror();
|
|
}
|
|
}
|
|
/* Remember this triangle to improve subsequent point location. */
|
|
triedgecopy(searchtri1, recenttri);
|
|
/* Scout the beginnings of a path from the first endpoint */
|
|
/* toward the second. */
|
|
if (scoutsegment(&searchtri1, endpoint2, newmark)) {
|
|
/* The segment was easily inserted. */
|
|
return;
|
|
}
|
|
/* The first endpoint may have changed if a collision with an intervening */
|
|
/* vertex on the segment occurred. */
|
|
org(searchtri1, endpoint1);
|
|
|
|
/* Find a triangle whose origin is the segment's second endpoint. */
|
|
checkpoint = (point) NULL;
|
|
encodedtri = point2tri(endpoint2);
|
|
if (encodedtri != (triangle) NULL) {
|
|
decode(encodedtri, searchtri2);
|
|
org(searchtri2, checkpoint);
|
|
}
|
|
if (checkpoint != endpoint2) {
|
|
/* Find a boundary triangle to search from. */
|
|
searchtri2.tri = dummytri;
|
|
searchtri2.orient = 0;
|
|
symself(searchtri2);
|
|
/* Search for the segment's second endpoint by point location. */
|
|
if (locate(endpoint2, &searchtri2) != ONVERTEX) {
|
|
printf(
|
|
"Internal error in insertsegment(): Unable to locate PSLG point\n");
|
|
printf(" (%.12g, %.12g) in triangulation.\n",
|
|
endpoint2[0], endpoint2[1]);
|
|
internalerror();
|
|
}
|
|
}
|
|
/* Remember this triangle to improve subsequent point location. */
|
|
triedgecopy(searchtri2, recenttri);
|
|
/* Scout the beginnings of a path from the second endpoint */
|
|
/* toward the first. */
|
|
if (scoutsegment(&searchtri2, endpoint1, newmark)) {
|
|
/* The segment was easily inserted. */
|
|
return;
|
|
}
|
|
/* The second endpoint may have changed if a collision with an intervening */
|
|
/* vertex on the segment occurred. */
|
|
org(searchtri2, endpoint2);
|
|
|
|
#ifndef REDUCED
|
|
#ifndef CDT_ONLY
|
|
if (splitseg) {
|
|
/* Insert vertices to force the segment into the triangulation. */
|
|
conformingedge(endpoint1, endpoint2, newmark);
|
|
} else {
|
|
#endif /* not CDT_ONLY */
|
|
#endif /* not REDUCED */
|
|
/* Insert the segment directly into the triangulation. */
|
|
constrainededge(&searchtri1, endpoint2, newmark);
|
|
#ifndef REDUCED
|
|
#ifndef CDT_ONLY
|
|
}
|
|
#endif /* not CDT_ONLY */
|
|
#endif /* not REDUCED */
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* markhull() Cover the convex hull of a triangulation with shell edges. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
void markhull()
|
|
{
|
|
struct triedge hulltri;
|
|
struct triedge nexttri;
|
|
struct triedge starttri;
|
|
triangle ptr; /* Temporary variable used by sym() and oprev(). */
|
|
|
|
/* Find a triangle handle on the hull. */
|
|
hulltri.tri = dummytri;
|
|
hulltri.orient = 0;
|
|
symself(hulltri);
|
|
/* Remember where we started so we know when to stop. */
|
|
triedgecopy(hulltri, starttri);
|
|
/* Go once counterclockwise around the convex hull. */
|
|
do {
|
|
/* Create a shell edge if there isn't already one here. */
|
|
insertshelle(&hulltri, 1);
|
|
/* To find the next hull edge, go clockwise around the next vertex. */
|
|
lnextself(hulltri);
|
|
oprev(hulltri, nexttri);
|
|
while (nexttri.tri != dummytri) {
|
|
triedgecopy(nexttri, hulltri);
|
|
oprev(hulltri, nexttri);
|
|
}
|
|
} while (!triedgeequal(hulltri, starttri));
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* formskeleton() Create the shell edges of a triangulation, including */
|
|
/* PSLG edges and edges on the convex hull. */
|
|
/* */
|
|
/* The PSLG edges are read from a .poly file. The return value is the */
|
|
/* number of segments in the file. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
#ifdef TRILIBRARY
|
|
|
|
int formskeleton(segmentlist, segmentmarkerlist, numberofsegments)
|
|
int *segmentlist;
|
|
int *segmentmarkerlist;
|
|
int numberofsegments;
|
|
|
|
#else /* not TRILIBRARY */
|
|
|
|
int formskeleton(polyfile, polyfilename)
|
|
FILE *polyfile;
|
|
char *polyfilename;
|
|
|
|
#endif /* not TRILIBRARY */
|
|
|
|
{
|
|
#ifdef TRILIBRARY
|
|
char polyfilename[6];
|
|
int index;
|
|
#else /* not TRILIBRARY */
|
|
char inputline[INPUTLINESIZE];
|
|
char *stringptr;
|
|
#endif /* not TRILIBRARY */
|
|
point endpoint1, endpoint2;
|
|
int segments;
|
|
int segmentmarkers;
|
|
int end1, end2;
|
|
int boundmarker;
|
|
int i;
|
|
|
|
if (poly) {
|
|
if (!quiet) {
|
|
printf("Inserting segments into Delaunay triangulation.\n");
|
|
}
|
|
#ifdef TRILIBRARY
|
|
strcpy(polyfilename, "input");
|
|
segments = numberofsegments;
|
|
segmentmarkers = segmentmarkerlist != (int *) NULL;
|
|
index = 0;
|
|
#else /* not TRILIBRARY */
|
|
/* Read the segments from a .poly file. */
|
|
/* Read number of segments and number of boundary markers. */
|
|
stringptr = readline(inputline, polyfile, polyfilename);
|
|
segments = (int) strtol (stringptr, &stringptr, 0);
|
|
stringptr = findfield(stringptr);
|
|
if (*stringptr == '\0') {
|
|
segmentmarkers = 0;
|
|
} else {
|
|
segmentmarkers = (int) strtol (stringptr, &stringptr, 0);
|
|
}
|
|
#endif /* not TRILIBRARY */
|
|
/* If segments are to be inserted, compute a mapping */
|
|
/* from points to triangles. */
|
|
if (segments > 0) {
|
|
if (verbose) {
|
|
printf(" Inserting PSLG segments.\n");
|
|
}
|
|
makepointmap();
|
|
}
|
|
|
|
boundmarker = 0;
|
|
/* Read and insert the segments. */
|
|
for (i = 1; i <= segments; i++) {
|
|
#ifdef TRILIBRARY
|
|
end1 = segmentlist[index++];
|
|
end2 = segmentlist[index++];
|
|
if (segmentmarkers) {
|
|
boundmarker = segmentmarkerlist[i - 1];
|
|
}
|
|
#else /* not TRILIBRARY */
|
|
stringptr = readline(inputline, polyfile, inpolyfilename);
|
|
stringptr = findfield(stringptr);
|
|
if (*stringptr == '\0') {
|
|
printf("Error: Segment %d has no endpoints in %s.\n", i,
|
|
polyfilename);
|
|
exit(1);
|
|
} else {
|
|
end1 = (int) strtol (stringptr, &stringptr, 0);
|
|
}
|
|
stringptr = findfield(stringptr);
|
|
if (*stringptr == '\0') {
|
|
printf("Error: Segment %d is missing its second endpoint in %s.\n", i,
|
|
polyfilename);
|
|
exit(1);
|
|
} else {
|
|
end2 = (int) strtol (stringptr, &stringptr, 0);
|
|
}
|
|
if (segmentmarkers) {
|
|
stringptr = findfield(stringptr);
|
|
if (*stringptr == '\0') {
|
|
boundmarker = 0;
|
|
} else {
|
|
boundmarker = (int) strtol (stringptr, &stringptr, 0);
|
|
}
|
|
}
|
|
#endif /* not TRILIBRARY */
|
|
if ((end1 < firstnumber) || (end1 >= firstnumber + inpoints)) {
|
|
if (!quiet) {
|
|
printf("Warning: Invalid first endpoint of segment %d in %s.\n", i,
|
|
polyfilename);
|
|
}
|
|
} else if ((end2 < firstnumber) || (end2 >= firstnumber + inpoints)) {
|
|
if (!quiet) {
|
|
printf("Warning: Invalid second endpoint of segment %d in %s.\n", i,
|
|
polyfilename);
|
|
}
|
|
} else {
|
|
endpoint1 = getpoint(end1);
|
|
endpoint2 = getpoint(end2);
|
|
if ((endpoint1[0] == endpoint2[0]) && (endpoint1[1] == endpoint2[1])) {
|
|
if (!quiet) {
|
|
printf("Warning: Endpoints of segment %d are coincident in %s.\n",
|
|
i, polyfilename);
|
|
}
|
|
} else {
|
|
insertsegment(endpoint1, endpoint2, boundmarker);
|
|
}
|
|
}
|
|
}
|
|
} else {
|
|
segments = 0;
|
|
}
|
|
if (convex || !poly) {
|
|
/* Enclose the convex hull with shell edges. */
|
|
if (verbose) {
|
|
printf(" Enclosing convex hull with segments.\n");
|
|
}
|
|
markhull();
|
|
}
|
|
return segments;
|
|
}
|
|
|
|
/** **/
|
|
/** **/
|
|
/********* Segment (shell edge) insertion ends here *********/
|
|
|
|
/********* Carving out holes and concavities begins here *********/
|
|
/** **/
|
|
/** **/
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* infecthull() Virally infect all of the triangles of the convex hull */
|
|
/* that are not protected by shell edges. Where there are */
|
|
/* shell edges, set boundary markers as appropriate. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
void infecthull()
|
|
{
|
|
struct triedge hulltri;
|
|
struct triedge nexttri;
|
|
struct triedge starttri;
|
|
struct edge hulledge;
|
|
triangle **deadtri;
|
|
point horg, hdest;
|
|
triangle ptr; /* Temporary variable used by sym(). */
|
|
shelle sptr; /* Temporary variable used by tspivot(). */
|
|
|
|
if (verbose) {
|
|
printf(" Marking concavities (external triangles) for elimination.\n");
|
|
}
|
|
/* Find a triangle handle on the hull. */
|
|
hulltri.tri = dummytri;
|
|
hulltri.orient = 0;
|
|
symself(hulltri);
|
|
/* Remember where we started so we know when to stop. */
|
|
triedgecopy(hulltri, starttri);
|
|
/* Go once counterclockwise around the convex hull. */
|
|
do {
|
|
/* Ignore triangles that are already infected. */
|
|
if (!infected(hulltri)) {
|
|
/* Is the triangle protected by a shell edge? */
|
|
tspivot(hulltri, hulledge);
|
|
if (hulledge.sh == dummysh) {
|
|
/* The triangle is not protected; infect it. */
|
|
infect(hulltri);
|
|
deadtri = (triangle **) poolalloc(&viri);
|
|
*deadtri = hulltri.tri;
|
|
} else {
|
|
/* The triangle is protected; set boundary markers if appropriate. */
|
|
if (mark(hulledge) == 0) {
|
|
setmark(hulledge, 1);
|
|
org(hulltri, horg);
|
|
dest(hulltri, hdest);
|
|
if (pointmark(horg) == 0) {
|
|
setpointmark(horg, 1);
|
|
}
|
|
if (pointmark(hdest) == 0) {
|
|
setpointmark(hdest, 1);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
/* To find the next hull edge, go clockwise around the next vertex. */
|
|
lnextself(hulltri);
|
|
oprev(hulltri, nexttri);
|
|
while (nexttri.tri != dummytri) {
|
|
triedgecopy(nexttri, hulltri);
|
|
oprev(hulltri, nexttri);
|
|
}
|
|
} while (!triedgeequal(hulltri, starttri));
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* plague() Spread the virus from all infected triangles to any neighbors */
|
|
/* not protected by shell edges. Delete all infected triangles. */
|
|
/* */
|
|
/* This is the procedure that actually creates holes and concavities. */
|
|
/* */
|
|
/* This procedure operates in two phases. The first phase identifies all */
|
|
/* the triangles that will die, and marks them as infected. They are */
|
|
/* marked to ensure that each triangle is added to the virus pool only */
|
|
/* once, so the procedure will terminate. */
|
|
/* */
|
|
/* The second phase actually eliminates the infected triangles. It also */
|
|
/* eliminates orphaned points. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
void plague()
|
|
{
|
|
struct triedge testtri;
|
|
struct triedge neighbor;
|
|
triangle **virusloop;
|
|
triangle **deadtri;
|
|
struct edge neighborshelle;
|
|
point testpoint;
|
|
point norg, ndest;
|
|
point deadorg, deaddest, deadapex;
|
|
int killorg;
|
|
triangle ptr; /* Temporary variable used by sym() and onext(). */
|
|
shelle sptr; /* Temporary variable used by tspivot(). */
|
|
|
|
if (verbose) {
|
|
printf(" Marking neighbors of marked triangles.\n");
|
|
}
|
|
/* Loop through all the infected triangles, spreading the virus to */
|
|
/* their neighbors, then to their neighbors' neighbors. */
|
|
traversalinit(&viri);
|
|
virusloop = (triangle **) traverse(&viri);
|
|
while (virusloop != (triangle **) NULL) {
|
|
testtri.tri = *virusloop;
|
|
/* A triangle is marked as infected by messing with one of its shell */
|
|
/* edges, setting it to an illegal value. Hence, we have to */
|
|
/* temporarily uninfect this triangle so that we can examine its */
|
|
/* adjacent shell edges. */
|
|
uninfect(testtri);
|
|
if (verbose > 2) {
|
|
/* Assign the triangle an orientation for convenience in */
|
|
/* checking its points. */
|
|
testtri.orient = 0;
|
|
org(testtri, deadorg);
|
|
dest(testtri, deaddest);
|
|
apex(testtri, deadapex);
|
|
printf(" Checking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
|
|
deadorg[0], deadorg[1], deaddest[0], deaddest[1],
|
|
deadapex[0], deadapex[1]);
|
|
}
|
|
/* Check each of the triangle's three neighbors. */
|
|
for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
|
|
/* Find the neighbor. */
|
|
sym(testtri, neighbor);
|
|
/* Check for a shell between the triangle and its neighbor. */
|
|
tspivot(testtri, neighborshelle);
|
|
/* Check if the neighbor is nonexistent or already infected. */
|
|
if ((neighbor.tri == dummytri) || infected(neighbor)) {
|
|
if (neighborshelle.sh != dummysh) {
|
|
/* There is a shell edge separating the triangle from its */
|
|
/* neighbor, but both triangles are dying, so the shell */
|
|
/* edge dies too. */
|
|
shelledealloc(neighborshelle.sh);
|
|
if (neighbor.tri != dummytri) {
|
|
/* Make sure the shell edge doesn't get deallocated again */
|
|
/* later when the infected neighbor is visited. */
|
|
uninfect(neighbor);
|
|
tsdissolve(neighbor);
|
|
infect(neighbor);
|
|
}
|
|
}
|
|
} else { /* The neighbor exists and is not infected. */
|
|
if (neighborshelle.sh == dummysh) {
|
|
/* There is no shell edge protecting the neighbor, so */
|
|
/* the neighbor becomes infected. */
|
|
if (verbose > 2) {
|
|
org(neighbor, deadorg);
|
|
dest(neighbor, deaddest);
|
|
apex(neighbor, deadapex);
|
|
printf(
|
|
" Marking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
|
|
deadorg[0], deadorg[1], deaddest[0], deaddest[1],
|
|
deadapex[0], deadapex[1]);
|
|
}
|
|
infect(neighbor);
|
|
/* Ensure that the neighbor's neighbors will be infected. */
|
|
deadtri = (triangle **) poolalloc(&viri);
|
|
*deadtri = neighbor.tri;
|
|
} else { /* The neighbor is protected by a shell edge. */
|
|
/* Remove this triangle from the shell edge. */
|
|
stdissolve(neighborshelle);
|
|
/* The shell edge becomes a boundary. Set markers accordingly. */
|
|
if (mark(neighborshelle) == 0) {
|
|
setmark(neighborshelle, 1);
|
|
}
|
|
org(neighbor, norg);
|
|
dest(neighbor, ndest);
|
|
if (pointmark(norg) == 0) {
|
|
setpointmark(norg, 1);
|
|
}
|
|
if (pointmark(ndest) == 0) {
|
|
setpointmark(ndest, 1);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
/* Remark the triangle as infected, so it doesn't get added to the */
|
|
/* virus pool again. */
|
|
infect(testtri);
|
|
virusloop = (triangle **) traverse(&viri);
|
|
}
|
|
|
|
if (verbose) {
|
|
printf(" Deleting marked triangles.\n");
|
|
}
|
|
traversalinit(&viri);
|
|
virusloop = (triangle **) traverse(&viri);
|
|
while (virusloop != (triangle **) NULL) {
|
|
testtri.tri = *virusloop;
|
|
|
|
/* Check each of the three corners of the triangle for elimination. */
|
|
/* This is done by walking around each point, checking if it is */
|
|
/* still connected to at least one live triangle. */
|
|
for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
|
|
org(testtri, testpoint);
|
|
/* Check if the point has already been tested. */
|
|
if (testpoint != (point) NULL) {
|
|
killorg = 1;
|
|
/* Mark the corner of the triangle as having been tested. */
|
|
setorg(testtri, NULL);
|
|
/* Walk counterclockwise about the point. */
|
|
onext(testtri, neighbor);
|
|
/* Stop upon reaching a boundary or the starting triangle. */
|
|
while ((neighbor.tri != dummytri)
|
|
&& (!triedgeequal(neighbor, testtri))) {
|
|
if (infected(neighbor)) {
|
|
/* Mark the corner of this triangle as having been tested. */
|
|
setorg(neighbor, NULL);
|
|
} else {
|
|
/* A live triangle. The point survives. */
|
|
killorg = 0;
|
|
}
|
|
/* Walk counterclockwise about the point. */
|
|
onextself(neighbor);
|
|
}
|
|
/* If we reached a boundary, we must walk clockwise as well. */
|
|
if (neighbor.tri == dummytri) {
|
|
/* Walk clockwise about the point. */
|
|
oprev(testtri, neighbor);
|
|
/* Stop upon reaching a boundary. */
|
|
while (neighbor.tri != dummytri) {
|
|
if (infected(neighbor)) {
|
|
/* Mark the corner of this triangle as having been tested. */
|
|
setorg(neighbor, NULL);
|
|
} else {
|
|
/* A live triangle. The point survives. */
|
|
killorg = 0;
|
|
}
|
|
/* Walk clockwise about the point. */
|
|
oprevself(neighbor);
|
|
}
|
|
}
|
|
if (killorg) {
|
|
if (verbose > 1) {
|
|
printf(" Deleting point (%.12g, %.12g)\n",
|
|
testpoint[0], testpoint[1]);
|
|
}
|
|
pointdealloc(testpoint);
|
|
}
|
|
}
|
|
}
|
|
|
|
/* Record changes in the number of boundary edges, and disconnect */
|
|
/* dead triangles from their neighbors. */
|
|
for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
|
|
sym(testtri, neighbor);
|
|
if (neighbor.tri == dummytri) {
|
|
/* There is no neighboring triangle on this edge, so this edge */
|
|
/* is a boundary edge. This triangle is being deleted, so this */
|
|
/* boundary edge is deleted. */
|
|
hullsize--;
|
|
} else {
|
|
/* Disconnect the triangle from its neighbor. */
|
|
dissolve(neighbor);
|
|
/* There is a neighboring triangle on this edge, so this edge */
|
|
/* becomes a boundary edge when this triangle is deleted. */
|
|
hullsize++;
|
|
}
|
|
}
|
|
/* Return the dead triangle to the pool of triangles. */
|
|
triangledealloc(testtri.tri);
|
|
virusloop = (triangle **) traverse(&viri);
|
|
}
|
|
/* Empty the virus pool. */
|
|
poolrestart(&viri);
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* regionplague() Spread regional attributes and/or area constraints */
|
|
/* (from a .poly file) throughout the mesh. */
|
|
/* */
|
|
/* This procedure operates in two phases. The first phase spreads an */
|
|
/* attribute and/or an area constraint through a (segment-bounded) region. */
|
|
/* The triangles are marked to ensure that each triangle is added to the */
|
|
/* virus pool only once, so the procedure will terminate. */
|
|
/* */
|
|
/* The second phase uninfects all infected triangles, returning them to */
|
|
/* normal. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
void regionplague(attribute, area)
|
|
REAL attribute;
|
|
REAL area;
|
|
{
|
|
struct triedge testtri;
|
|
struct triedge neighbor;
|
|
triangle **virusloop;
|
|
triangle **regiontri;
|
|
struct edge neighborshelle;
|
|
point regionorg, regiondest, regionapex;
|
|
triangle ptr; /* Temporary variable used by sym() and onext(). */
|
|
shelle sptr; /* Temporary variable used by tspivot(). */
|
|
|
|
if (verbose > 1) {
|
|
printf(" Marking neighbors of marked triangles.\n");
|
|
}
|
|
/* Loop through all the infected triangles, spreading the attribute */
|
|
/* and/or area constraint to their neighbors, then to their neighbors' */
|
|
/* neighbors. */
|
|
traversalinit(&viri);
|
|
virusloop = (triangle **) traverse(&viri);
|
|
while (virusloop != (triangle **) NULL) {
|
|
testtri.tri = *virusloop;
|
|
/* A triangle is marked as infected by messing with one of its shell */
|
|
/* edges, setting it to an illegal value. Hence, we have to */
|
|
/* temporarily uninfect this triangle so that we can examine its */
|
|
/* adjacent shell edges. */
|
|
uninfect(testtri);
|
|
if (regionattrib) {
|
|
/* Set an attribute. */
|
|
setelemattribute(testtri, eextras, attribute);
|
|
}
|
|
if (vararea) {
|
|
/* Set an area constraint. */
|
|
setareabound(testtri, area);
|
|
}
|
|
if (verbose > 2) {
|
|
/* Assign the triangle an orientation for convenience in */
|
|
/* checking its points. */
|
|
testtri.orient = 0;
|
|
org(testtri, regionorg);
|
|
dest(testtri, regiondest);
|
|
apex(testtri, regionapex);
|
|
printf(" Checking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
|
|
regionorg[0], regionorg[1], regiondest[0], regiondest[1],
|
|
regionapex[0], regionapex[1]);
|
|
}
|
|
/* Check each of the triangle's three neighbors. */
|
|
for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) {
|
|
/* Find the neighbor. */
|
|
sym(testtri, neighbor);
|
|
/* Check for a shell between the triangle and its neighbor. */
|
|
tspivot(testtri, neighborshelle);
|
|
/* Make sure the neighbor exists, is not already infected, and */
|
|
/* isn't protected by a shell edge. */
|
|
if ((neighbor.tri != dummytri) && !infected(neighbor)
|
|
&& (neighborshelle.sh == dummysh)) {
|
|
if (verbose > 2) {
|
|
org(neighbor, regionorg);
|
|
dest(neighbor, regiondest);
|
|
apex(neighbor, regionapex);
|
|
printf(" Marking (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
|
|
regionorg[0], regionorg[1], regiondest[0], regiondest[1],
|
|
regionapex[0], regionapex[1]);
|
|
}
|
|
/* Infect the neighbor. */
|
|
infect(neighbor);
|
|
/* Ensure that the neighbor's neighbors will be infected. */
|
|
regiontri = (triangle **) poolalloc(&viri);
|
|
*regiontri = neighbor.tri;
|
|
}
|
|
}
|
|
/* Remark the triangle as infected, so it doesn't get added to the */
|
|
/* virus pool again. */
|
|
infect(testtri);
|
|
virusloop = (triangle **) traverse(&viri);
|
|
}
|
|
|
|
/* Uninfect all triangles. */
|
|
if (verbose > 1) {
|
|
printf(" Unmarking marked triangles.\n");
|
|
}
|
|
traversalinit(&viri);
|
|
virusloop = (triangle **) traverse(&viri);
|
|
while (virusloop != (triangle **) NULL) {
|
|
testtri.tri = *virusloop;
|
|
uninfect(testtri);
|
|
virusloop = (triangle **) traverse(&viri);
|
|
}
|
|
/* Empty the virus pool. */
|
|
poolrestart(&viri);
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* carveholes() Find the holes and infect them. Find the area */
|
|
/* constraints and infect them. Infect the convex hull. */
|
|
/* Spread the infection and kill triangles. Spread the */
|
|
/* area constraints. */
|
|
/* */
|
|
/* This routine mainly calls other routines to carry out all these */
|
|
/* functions. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
void carveholes(holelist, holes, regionlist, regions)
|
|
REAL *holelist;
|
|
int holes;
|
|
REAL *regionlist;
|
|
int regions;
|
|
{
|
|
struct triedge searchtri;
|
|
struct triedge triangleloop;
|
|
struct triedge *regiontris;
|
|
triangle **holetri;
|
|
triangle **regiontri;
|
|
point searchorg, searchdest;
|
|
enum locateresult intersect;
|
|
int i;
|
|
triangle ptr; /* Temporary variable used by sym(). */
|
|
|
|
if (!(quiet || (noholes && convex))) {
|
|
printf("Removing unwanted triangles.\n");
|
|
if (verbose && (holes > 0)) {
|
|
printf(" Marking holes for elimination.\n");
|
|
}
|
|
}
|
|
|
|
if (regions > 0) {
|
|
/* Allocate storage for the triangles in which region points fall. */
|
|
regiontris = (struct triedge *) malloc(regions * sizeof(struct triedge));
|
|
if (regiontris == (struct triedge *) NULL) {
|
|
printf("Error: Out of memory.\n");
|
|
exit(1);
|
|
}
|
|
}
|
|
|
|
if (((holes > 0) && !noholes) || !convex || (regions > 0)) {
|
|
/* Initialize a pool of viri to be used for holes, concavities, */
|
|
/* regional attributes, and/or regional area constraints. */
|
|
poolinit(&viri, sizeof(triangle *), VIRUSPERBLOCK, POINTER, 0);
|
|
}
|
|
|
|
if (!convex) {
|
|
/* Mark as infected any unprotected triangles on the boundary. */
|
|
/* This is one way by which concavities are created. */
|
|
infecthull();
|
|
}
|
|
|
|
if ((holes > 0) && !noholes) {
|
|
/* Infect each triangle in which a hole lies. */
|
|
for (i = 0; i < 2 * holes; i += 2) {
|
|
/* Ignore holes that aren't within the bounds of the mesh. */
|
|
if ((holelist[i] >= xmin) && (holelist[i] <= xmax)
|
|
&& (holelist[i + 1] >= ymin) && (holelist[i + 1] <= ymax)) {
|
|
/* Start searching from some triangle on the outer boundary. */
|
|
searchtri.tri = dummytri;
|
|
searchtri.orient = 0;
|
|
symself(searchtri);
|
|
/* Ensure that the hole is to the left of this boundary edge; */
|
|
/* otherwise, locate() will falsely report that the hole */
|
|
/* falls within the starting triangle. */
|
|
org(searchtri, searchorg);
|
|
dest(searchtri, searchdest);
|
|
if (counterclockwise(searchorg, searchdest, &holelist[i]) > 0.0) {
|
|
/* Find a triangle that contains the hole. */
|
|
intersect = locate(&holelist[i], &searchtri);
|
|
if ((intersect != OUTSIDE) && (!infected(searchtri))) {
|
|
/* Infect the triangle. This is done by marking the triangle */
|
|
/* as infect and including the triangle in the virus pool. */
|
|
infect(searchtri);
|
|
holetri = (triangle **) poolalloc(&viri);
|
|
*holetri = searchtri.tri;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
/* Now, we have to find all the regions BEFORE we carve the holes, because */
|
|
/* locate() won't work when the triangulation is no longer convex. */
|
|
/* (Incidentally, this is the reason why regional attributes and area */
|
|
/* constraints can't be used when refining a preexisting mesh, which */
|
|
/* might not be convex; they can only be used with a freshly */
|
|
/* triangulated PSLG.) */
|
|
if (regions > 0) {
|
|
/* Find the starting triangle for each region. */
|
|
for (i = 0; i < regions; i++) {
|
|
regiontris[i].tri = dummytri;
|
|
/* Ignore region points that aren't within the bounds of the mesh. */
|
|
if ((regionlist[4 * i] >= xmin) && (regionlist[4 * i] <= xmax) &&
|
|
(regionlist[4 * i + 1] >= ymin) && (regionlist[4 * i + 1] <= ymax)) {
|
|
/* Start searching from some triangle on the outer boundary. */
|
|
searchtri.tri = dummytri;
|
|
searchtri.orient = 0;
|
|
symself(searchtri);
|
|
/* Ensure that the region point is to the left of this boundary */
|
|
/* edge; otherwise, locate() will falsely report that the */
|
|
/* region point falls within the starting triangle. */
|
|
org(searchtri, searchorg);
|
|
dest(searchtri, searchdest);
|
|
if (counterclockwise(searchorg, searchdest, ®ionlist[4 * i]) >
|
|
0.0) {
|
|
/* Find a triangle that contains the region point. */
|
|
intersect = locate(®ionlist[4 * i], &searchtri);
|
|
if ((intersect != OUTSIDE) && (!infected(searchtri))) {
|
|
/* Record the triangle for processing after the */
|
|
/* holes have been carved. */
|
|
triedgecopy(searchtri, regiontris[i]);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
if (viri.items > 0) {
|
|
/* Carve the holes and concavities. */
|
|
plague();
|
|
}
|
|
/* The virus pool should be empty now. */
|
|
|
|
if (regions > 0) {
|
|
if (!quiet) {
|
|
if (regionattrib) {
|
|
if (vararea) {
|
|
printf("Spreading regional attributes and area constraints.\n");
|
|
} else {
|
|
printf("Spreading regional attributes.\n");
|
|
}
|
|
} else {
|
|
printf("Spreading regional area constraints.\n");
|
|
}
|
|
}
|
|
if (regionattrib && !refine) {
|
|
/* Assign every triangle a regional attribute of zero. */
|
|
traversalinit(&triangles);
|
|
triangleloop.orient = 0;
|
|
triangleloop.tri = triangletraverse();
|
|
while (triangleloop.tri != (triangle *) NULL) {
|
|
setelemattribute(triangleloop, eextras, 0.0);
|
|
triangleloop.tri = triangletraverse();
|
|
}
|
|
}
|
|
for (i = 0; i < regions; i++) {
|
|
if (regiontris[i].tri != dummytri) {
|
|
/* Make sure the triangle under consideration still exists. */
|
|
/* It may have been eaten by the virus. */
|
|
if (regiontris[i].tri[3] != (triangle) NULL) {
|
|
/* Put one triangle in the virus pool. */
|
|
infect(regiontris[i]);
|
|
regiontri = (triangle **) poolalloc(&viri);
|
|
*regiontri = regiontris[i].tri;
|
|
/* Apply one region's attribute and/or area constraint. */
|
|
regionplague(regionlist[4 * i + 2], regionlist[4 * i + 3]);
|
|
/* The virus pool should be empty now. */
|
|
}
|
|
}
|
|
}
|
|
if (regionattrib && !refine) {
|
|
/* Note the fact that each triangle has an additional attribute. */
|
|
eextras++;
|
|
}
|
|
}
|
|
|
|
/* Free up memory. */
|
|
if (((holes > 0) && !noholes) || !convex || (regions > 0)) {
|
|
pooldeinit(&viri);
|
|
}
|
|
if (regions > 0) {
|
|
free(regiontris);
|
|
}
|
|
}
|
|
|
|
/** **/
|
|
/** **/
|
|
/********* Carving out holes and concavities ends here *********/
|
|
|
|
/********* Mesh quality maintenance begins here *********/
|
|
/** **/
|
|
/** **/
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* tallyencs() Traverse the entire list of shell edges, check each edge */
|
|
/* to see if it is encroached. If so, add it to the list. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
#ifndef CDT_ONLY
|
|
|
|
void tallyencs()
|
|
{
|
|
struct edge edgeloop;
|
|
int dummy;
|
|
|
|
traversalinit(&shelles);
|
|
edgeloop.shorient = 0;
|
|
edgeloop.sh = shelletraverse();
|
|
while (edgeloop.sh != (shelle *) NULL) {
|
|
/* If the segment is encroached, add it to the list. */
|
|
dummy = checkedge4encroach(&edgeloop);
|
|
edgeloop.sh = shelletraverse();
|
|
}
|
|
}
|
|
|
|
#endif /* not CDT_ONLY */
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* precisionerror() Print an error message for precision problems. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
#ifndef CDT_ONLY
|
|
|
|
void precisionerror()
|
|
{
|
|
printf("Try increasing the area criterion and/or reducing the minimum\n");
|
|
printf(" allowable angle so that tiny triangles are not created.\n");
|
|
#ifdef SINGLE
|
|
printf("Alternatively, try recompiling me with double precision\n");
|
|
printf(" arithmetic (by removing \"#define SINGLE\" from the\n");
|
|
printf(" source file or \"-DSINGLE\" from the makefile).\n");
|
|
#endif /* SINGLE */
|
|
}
|
|
|
|
#endif /* not CDT_ONLY */
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* repairencs() Find and repair all the encroached segments. */
|
|
/* */
|
|
/* Encroached segments are repaired by splitting them by inserting a point */
|
|
/* at or near their centers. */
|
|
/* */
|
|
/* `flaws' is a flag that specifies whether one should take note of new */
|
|
/* encroached segments and bad triangles that result from inserting points */
|
|
/* to repair existing encroached segments. */
|
|
/* */
|
|
/* When a segment is split, the two resulting subsegments are always */
|
|
/* tested to see if they are encroached upon, regardless of the value */
|
|
/* of `flaws'. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
#ifndef CDT_ONLY
|
|
|
|
void repairencs(flaws)
|
|
int flaws;
|
|
{
|
|
struct triedge enctri;
|
|
struct triedge testtri;
|
|
struct edge *encloop;
|
|
struct edge testsh;
|
|
point eorg, edest;
|
|
point newpoint;
|
|
enum insertsiteresult success;
|
|
REAL segmentlength, nearestpoweroftwo;
|
|
REAL split;
|
|
int acuteorg, acutedest;
|
|
int dummy;
|
|
int i;
|
|
triangle ptr; /* Temporary variable used by stpivot(). */
|
|
shelle sptr; /* Temporary variable used by snext(). */
|
|
|
|
while ((badsegments.items > 0) && (steinerleft != 0)) {
|
|
traversalinit(&badsegments);
|
|
encloop = badsegmenttraverse();
|
|
while ((encloop != (struct edge *) NULL) && (steinerleft != 0)) {
|
|
/* To decide where to split a segment, we need to know if the */
|
|
/* segment shares an endpoint with an adjacent segment. */
|
|
/* The concern is that, if we simply split every encroached */
|
|
/* segment in its center, two adjacent segments with a small */
|
|
/* angle between them might lead to an infinite loop; each */
|
|
/* point added to split one segment will encroach upon the */
|
|
/* other segment, which must then be split with a point that */
|
|
/* will encroach upon the first segment, and so on forever. */
|
|
/* To avoid this, imagine a set of concentric circles, whose */
|
|
/* radii are powers of two, about each segment endpoint. */
|
|
/* These concentric circles determine where the segment is */
|
|
/* split. (If both endpoints are shared with adjacent */
|
|
/* segments, split the segment in the middle, and apply the */
|
|
/* concentric shells for later splittings.) */
|
|
|
|
/* Is the origin shared with another segment? */
|
|
stpivot(*encloop, enctri);
|
|
lnext(enctri, testtri);
|
|
tspivot(testtri, testsh);
|
|
acuteorg = testsh.sh != dummysh;
|
|
/* Is the destination shared with another segment? */
|
|
lnextself(testtri);
|
|
tspivot(testtri, testsh);
|
|
acutedest = testsh.sh != dummysh;
|
|
/* Now, check the other side of the segment, if there's a triangle */
|
|
/* there. */
|
|
sym(enctri, testtri);
|
|
if (testtri.tri != dummytri) {
|
|
/* Is the destination shared with another segment? */
|
|
lnextself(testtri);
|
|
tspivot(testtri, testsh);
|
|
acutedest = acutedest || (testsh.sh != dummysh);
|
|
/* Is the origin shared with another segment? */
|
|
lnextself(testtri);
|
|
tspivot(testtri, testsh);
|
|
acuteorg = acuteorg || (testsh.sh != dummysh);
|
|
}
|
|
|
|
sorg(*encloop, eorg);
|
|
sdest(*encloop, edest);
|
|
/* Use the concentric circles if exactly one endpoint is shared */
|
|
/* with another adjacent segment. */
|
|
if (acuteorg ^ acutedest) {
|
|
segmentlength = sqrt((edest[0] - eorg[0]) * (edest[0] - eorg[0])
|
|
+ (edest[1] - eorg[1]) * (edest[1] - eorg[1]));
|
|
/* Find the power of two nearest the segment's length. */
|
|
nearestpoweroftwo = 1.0;
|
|
while (segmentlength > SQUAREROOTTWO * nearestpoweroftwo) {
|
|
nearestpoweroftwo *= 2.0;
|
|
}
|
|
while (segmentlength < (0.5 * SQUAREROOTTWO) * nearestpoweroftwo) {
|
|
nearestpoweroftwo *= 0.5;
|
|
}
|
|
/* Where do we split the segment? */
|
|
split = 0.5 * nearestpoweroftwo / segmentlength;
|
|
if (acutedest) {
|
|
split = 1.0 - split;
|
|
}
|
|
} else {
|
|
/* If we're not worried about adjacent segments, split */
|
|
/* this segment in the middle. */
|
|
split = 0.5;
|
|
}
|
|
|
|
/* Create the new point. */
|
|
newpoint = (point) poolalloc(&points);
|
|
/* Interpolate its coordinate and attributes. */
|
|
for (i = 0; i < 2 + nextras; i++) {
|
|
newpoint[i] = (1.0 - split) * eorg[i] + split * edest[i];
|
|
}
|
|
setpointmark(newpoint, mark(*encloop));
|
|
if (verbose > 1) {
|
|
printf(
|
|
" Splitting edge (%.12g, %.12g) (%.12g, %.12g) at (%.12g, %.12g).\n",
|
|
eorg[0], eorg[1], edest[0], edest[1], newpoint[0], newpoint[1]);
|
|
}
|
|
/* Check whether the new point lies on an endpoint. */
|
|
if (((newpoint[0] == eorg[0]) && (newpoint[1] == eorg[1]))
|
|
|| ((newpoint[0] == edest[0]) && (newpoint[1] == edest[1]))) {
|
|
printf("Error: Ran out of precision at (%.12g, %.12g).\n",
|
|
newpoint[0], newpoint[1]);
|
|
printf("I attempted to split a segment to a smaller size than can\n");
|
|
printf(" be accommodated by the finite precision of floating point\n"
|
|
);
|
|
printf(" arithmetic.\n");
|
|
precisionerror();
|
|
exit(1);
|
|
}
|
|
/* Insert the splitting point. This should always succeed. */
|
|
success = insertsite(newpoint, &enctri, encloop, flaws, flaws);
|
|
if ((success != SUCCESSFULPOINT) && (success != ENCROACHINGPOINT)) {
|
|
printf("Internal error in repairencs():\n");
|
|
printf(" Failure to split a segment.\n");
|
|
internalerror();
|
|
}
|
|
if (steinerleft > 0) {
|
|
steinerleft--;
|
|
}
|
|
/* Check the two new subsegments to see if they're encroached. */
|
|
dummy = checkedge4encroach(encloop);
|
|
snextself(*encloop);
|
|
dummy = checkedge4encroach(encloop);
|
|
|
|
badsegmentdealloc(encloop);
|
|
encloop = badsegmenttraverse();
|
|
}
|
|
}
|
|
}
|
|
|
|
#endif /* not CDT_ONLY */
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* tallyfaces() Test every triangle in the mesh for quality measures. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
#ifndef CDT_ONLY
|
|
|
|
void tallyfaces()
|
|
{
|
|
struct triedge triangleloop;
|
|
|
|
if (verbose) {
|
|
printf(" Making a list of bad triangles.\n");
|
|
}
|
|
traversalinit(&triangles);
|
|
triangleloop.orient = 0;
|
|
triangleloop.tri = triangletraverse();
|
|
while (triangleloop.tri != (triangle *) NULL) {
|
|
/* If the triangle is bad, enqueue it. */
|
|
testtriangle(&triangleloop);
|
|
triangleloop.tri = triangletraverse();
|
|
}
|
|
}
|
|
|
|
#endif /* not CDT_ONLY */
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* findcircumcenter() Find the circumcenter of a triangle. */
|
|
/* */
|
|
/* The result is returned both in terms of x-y coordinates and xi-eta */
|
|
/* coordinates. The xi-eta coordinate system is defined in terms of the */
|
|
/* triangle: the origin of the triangle is the origin of the coordinate */
|
|
/* system; the destination of the triangle is one unit along the xi axis; */
|
|
/* and the apex of the triangle is one unit along the eta axis. */
|
|
/* */
|
|
/* The return value indicates which edge of the triangle is shortest. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
enum circumcenterresult findcircumcenter(torg, tdest, tapex, circumcenter,
|
|
xi, eta)
|
|
point torg;
|
|
point tdest;
|
|
point tapex;
|
|
point circumcenter;
|
|
REAL *xi;
|
|
REAL *eta;
|
|
{
|
|
REAL xdo, ydo, xao, yao, xad, yad;
|
|
REAL dodist, aodist, addist;
|
|
REAL denominator;
|
|
REAL dx, dy;
|
|
|
|
circumcentercount++;
|
|
|
|
/* Compute the circumcenter of the triangle. */
|
|
xdo = tdest[0] - torg[0];
|
|
ydo = tdest[1] - torg[1];
|
|
xao = tapex[0] - torg[0];
|
|
yao = tapex[1] - torg[1];
|
|
dodist = xdo * xdo + ydo * ydo;
|
|
aodist = xao * xao + yao * yao;
|
|
if (noexact) {
|
|
denominator = (REAL)(0.5 / (xdo * yao - xao * ydo));
|
|
} else {
|
|
/* Use the counterclockwise() routine to ensure a positive (and */
|
|
/* reasonably accurate) result, avoiding any possibility of */
|
|
/* division by zero. */
|
|
denominator = (REAL)(0.5 / counterclockwise(tdest, tapex, torg));
|
|
/* Don't count the above as an orientation test. */
|
|
counterclockcount--;
|
|
}
|
|
circumcenter[0] = torg[0] - (ydo * aodist - yao * dodist) * denominator;
|
|
circumcenter[1] = torg[1] + (xdo * aodist - xao * dodist) * denominator;
|
|
|
|
/* To interpolate point attributes for the new point inserted at */
|
|
/* the circumcenter, define a coordinate system with a xi-axis, */
|
|
/* directed from the triangle's origin to its destination, and */
|
|
/* an eta-axis, directed from its origin to its apex. */
|
|
/* Calculate the xi and eta coordinates of the circumcenter. */
|
|
dx = circumcenter[0] - torg[0];
|
|
dy = circumcenter[1] - torg[1];
|
|
*xi = (REAL)((dx * yao - xao * dy) * (2.0 * denominator));
|
|
*eta = (REAL)((xdo * dy - dx * ydo) * (2.0 * denominator));
|
|
|
|
xad = tapex[0] - tdest[0];
|
|
yad = tapex[1] - tdest[1];
|
|
addist = xad * xad + yad * yad;
|
|
if ((addist < dodist) && (addist < aodist)) {
|
|
return OPPOSITEORG;
|
|
} else if (dodist < aodist) {
|
|
return OPPOSITEAPEX;
|
|
} else {
|
|
return OPPOSITEDEST;
|
|
}
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* splittriangle() Inserts a point at the circumcenter of a triangle. */
|
|
/* Deletes the newly inserted point if it encroaches upon */
|
|
/* a segment. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
#ifndef CDT_ONLY
|
|
|
|
void splittriangle(badtri)
|
|
struct badface *badtri;
|
|
{
|
|
point borg, bdest, bapex;
|
|
point newpoint;
|
|
REAL xi, eta;
|
|
enum insertsiteresult success;
|
|
enum circumcenterresult shortedge;
|
|
int errorflag;
|
|
int i;
|
|
|
|
org(badtri->badfacetri, borg);
|
|
dest(badtri->badfacetri, bdest);
|
|
apex(badtri->badfacetri, bapex);
|
|
/* Make sure that this triangle is still the same triangle it was */
|
|
/* when it was tested and determined to be of bad quality. */
|
|
/* Subsequent transformations may have made it a different triangle. */
|
|
if ((borg == badtri->faceorg) && (bdest == badtri->facedest) &&
|
|
(bapex == badtri->faceapex)) {
|
|
if (verbose > 1) {
|
|
printf(" Splitting this triangle at its circumcenter:\n");
|
|
printf(" (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n", borg[0],
|
|
borg[1], bdest[0], bdest[1], bapex[0], bapex[1]);
|
|
}
|
|
errorflag = 0;
|
|
/* Create a new point at the triangle's circumcenter. */
|
|
newpoint = (point) poolalloc(&points);
|
|
shortedge = findcircumcenter(borg, bdest, bapex, newpoint, &xi, &eta);
|
|
/* Check whether the new point lies on a triangle vertex. */
|
|
if (((newpoint[0] == borg[0]) && (newpoint[1] == borg[1]))
|
|
|| ((newpoint[0] == bdest[0]) && (newpoint[1] == bdest[1]))
|
|
|| ((newpoint[0] == bapex[0]) && (newpoint[1] == bapex[1]))) {
|
|
if (!quiet) {
|
|
printf("Warning: New point (%.12g, %.12g) falls on existing vertex.\n"
|
|
, newpoint[0], newpoint[1]);
|
|
errorflag = 1;
|
|
}
|
|
pointdealloc(newpoint);
|
|
} else {
|
|
for (i = 2; i < 2 + nextras; i++) {
|
|
/* Interpolate the point attributes at the circumcenter. */
|
|
newpoint[i] = borg[i] + xi * (bdest[i] - borg[i])
|
|
+ eta * (bapex[i] - borg[i]);
|
|
}
|
|
/* The new point must be in the interior, and have a marker of zero. */
|
|
setpointmark(newpoint, 0);
|
|
/* Ensure that the handle `badtri->badfacetri' represents the shortest */
|
|
/* edge of the triangle. This ensures that the circumcenter must */
|
|
/* fall to the left of this edge, so point location will work. */
|
|
if (shortedge == OPPOSITEORG) {
|
|
lnextself(badtri->badfacetri);
|
|
} else if (shortedge == OPPOSITEDEST) {
|
|
lprevself(badtri->badfacetri);
|
|
}
|
|
/* Insert the circumcenter, searching from the edge of the triangle, */
|
|
/* and maintain the Delaunay property of the triangulation. */
|
|
success = insertsite(newpoint, &(badtri->badfacetri),
|
|
(struct edge *) NULL, 1, 1);
|
|
if (success == SUCCESSFULPOINT) {
|
|
if (steinerleft > 0) {
|
|
steinerleft--;
|
|
}
|
|
} else if (success == ENCROACHINGPOINT) {
|
|
/* If the newly inserted point encroaches upon a segment, delete it. */
|
|
deletesite(&(badtri->badfacetri));
|
|
} else if (success == VIOLATINGPOINT) {
|
|
/* Failed to insert the new point, but some segment was */
|
|
/* marked as being encroached. */
|
|
pointdealloc(newpoint);
|
|
} else { /* success == DUPLICATEPOINT */
|
|
/* Failed to insert the new point because a vertex is already there. */
|
|
if (!quiet) {
|
|
printf(
|
|
"Warning: New point (%.12g, %.12g) falls on existing vertex.\n"
|
|
, newpoint[0], newpoint[1]);
|
|
errorflag = 1;
|
|
}
|
|
pointdealloc(newpoint);
|
|
}
|
|
}
|
|
if (errorflag) {
|
|
if (verbose) {
|
|
printf(" The new point is at the circumcenter of triangle\n");
|
|
printf(" (%.12g, %.12g) (%.12g, %.12g) (%.12g, %.12g)\n",
|
|
borg[0], borg[1], bdest[0], bdest[1], bapex[0], bapex[1]);
|
|
}
|
|
printf("This probably means that I am trying to refine triangles\n");
|
|
printf(" to a smaller size than can be accommodated by the finite\n");
|
|
printf(" precision of floating point arithmetic. (You can be\n");
|
|
printf(" sure of this if I fail to terminate.)\n");
|
|
precisionerror();
|
|
}
|
|
}
|
|
/* Return the bad triangle to the pool. */
|
|
pooldealloc(&badtriangles, (VOID *) badtri);
|
|
}
|
|
|
|
#endif /* not CDT_ONLY */
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* enforcequality() Remove all the encroached edges and bad triangles */
|
|
/* from the triangulation. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
#ifndef CDT_ONLY
|
|
|
|
void enforcequality()
|
|
{
|
|
int i;
|
|
|
|
if (!quiet) {
|
|
printf("Adding Steiner points to enforce quality.\n");
|
|
}
|
|
/* Initialize the pool of encroached segments. */
|
|
poolinit(&badsegments, sizeof(struct edge), BADSEGMENTPERBLOCK, POINTER, 0);
|
|
if (verbose) {
|
|
printf(" Looking for encroached segments.\n");
|
|
}
|
|
/* Test all segments to see if they're encroached. */
|
|
tallyencs();
|
|
if (verbose && (badsegments.items > 0)) {
|
|
printf(" Splitting encroached segments.\n");
|
|
}
|
|
/* Note that steinerleft == -1 if an unlimited number */
|
|
/* of Steiner points is allowed. */
|
|
while ((badsegments.items > 0) && (steinerleft != 0)) {
|
|
/* Fix the segments without noting newly encroached segments or */
|
|
/* bad triangles. The reason we don't want to note newly */
|
|
/* encroached segments is because some encroached segments are */
|
|
/* likely to be noted multiple times, and would then be blindly */
|
|
/* split multiple times. I should fix that some time. */
|
|
repairencs(0);
|
|
/* Now, find all the segments that became encroached while adding */
|
|
/* points to split encroached segments. */
|
|
tallyencs();
|
|
}
|
|
/* At this point, if we haven't run out of Steiner points, the */
|
|
/* triangulation should be (conforming) Delaunay. */
|
|
|
|
/* Next, we worry about enforcing triangle quality. */
|
|
if ((minangle > 0.0) || vararea || fixedarea) {
|
|
/* Initialize the pool of bad triangles. */
|
|
poolinit(&badtriangles, sizeof(struct badface), BADTRIPERBLOCK, POINTER,
|
|
0);
|
|
/* Initialize the queues of bad triangles. */
|
|
for (i = 0; i < 64; i++) {
|
|
queuefront[i] = (struct badface *) NULL;
|
|
queuetail[i] = &queuefront[i];
|
|
}
|
|
/* Test all triangles to see if they're bad. */
|
|
tallyfaces();
|
|
if (verbose) {
|
|
printf(" Splitting bad triangles.\n");
|
|
}
|
|
while ((badtriangles.items > 0) && (steinerleft != 0)) {
|
|
/* Fix one bad triangle by inserting a point at its circumcenter. */
|
|
splittriangle(dequeuebadtri());
|
|
/* Fix any encroached segments that may have resulted. Record */
|
|
/* any new bad triangles or encroached segments that result. */
|
|
if (badsegments.items > 0) {
|
|
repairencs(1);
|
|
}
|
|
}
|
|
}
|
|
/* At this point, if we haven't run out of Steiner points, the */
|
|
/* triangulation should be (conforming) Delaunay and have no */
|
|
/* low-quality triangles. */
|
|
|
|
/* Might we have run out of Steiner points too soon? */
|
|
if (!quiet && (badsegments.items > 0) && (steinerleft == 0)) {
|
|
printf("\nWarning: I ran out of Steiner points, but the mesh has\n");
|
|
if (badsegments.items == 1) {
|
|
printf(" an encroached segment, and therefore might not be truly\n");
|
|
} else {
|
|
printf(" %ld encroached segments, and therefore might not be truly\n",
|
|
badsegments.items);
|
|
}
|
|
printf(" Delaunay. If the Delaunay property is important to you,\n");
|
|
printf(" try increasing the number of Steiner points (controlled by\n");
|
|
printf(" the -S switch) slightly and try again.\n\n");
|
|
}
|
|
}
|
|
|
|
#endif /* not CDT_ONLY */
|
|
|
|
/** **/
|
|
/** **/
|
|
/********* Mesh quality maintenance ends here *********/
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* highorder() Create extra nodes for quadratic subparametric elements. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
void highorder()
|
|
{
|
|
struct triedge triangleloop, trisym;
|
|
struct edge checkmark;
|
|
point newpoint;
|
|
point torg, tdest;
|
|
int i;
|
|
triangle ptr; /* Temporary variable used by sym(). */
|
|
shelle sptr; /* Temporary variable used by tspivot(). */
|
|
|
|
if (!quiet) {
|
|
printf("Adding vertices for second-order triangles.\n");
|
|
}
|
|
/* The following line ensures that dead items in the pool of nodes */
|
|
/* cannot be allocated for the extra nodes associated with high */
|
|
/* order elements. This ensures that the primary nodes (at the */
|
|
/* corners of elements) will occur earlier in the output files, and */
|
|
/* have lower indices, than the extra nodes. */
|
|
points.deaditemstack = (VOID *) NULL;
|
|
|
|
traversalinit(&triangles);
|
|
triangleloop.tri = triangletraverse();
|
|
/* To loop over the set of edges, loop over all triangles, and look at */
|
|
/* the three edges of each triangle. If there isn't another triangle */
|
|
/* adjacent to the edge, operate on the edge. If there is another */
|
|
/* adjacent triangle, operate on the edge only if the current triangle */
|
|
/* has a smaller pointer than its neighbor. This way, each edge is */
|
|
/* considered only once. */
|
|
while (triangleloop.tri != (triangle *) NULL) {
|
|
for (triangleloop.orient = 0; triangleloop.orient < 3;
|
|
triangleloop.orient++) {
|
|
sym(triangleloop, trisym);
|
|
if ((triangleloop.tri < trisym.tri) || (trisym.tri == dummytri)) {
|
|
org(triangleloop, torg);
|
|
dest(triangleloop, tdest);
|
|
/* Create a new node in the middle of the edge. Interpolate */
|
|
/* its attributes. */
|
|
newpoint = (point) poolalloc(&points);
|
|
for (i = 0; i < 2 + nextras; i++) {
|
|
newpoint[i] = (REAL)(0.5 * (torg[i] + tdest[i]));
|
|
}
|
|
/* Set the new node's marker to zero or one, depending on */
|
|
/* whether it lies on a boundary. */
|
|
setpointmark(newpoint, trisym.tri == dummytri);
|
|
if (useshelles) {
|
|
tspivot(triangleloop, checkmark);
|
|
/* If this edge is a segment, transfer the marker to the new node. */
|
|
if (checkmark.sh != dummysh) {
|
|
setpointmark(newpoint, mark(checkmark));
|
|
}
|
|
}
|
|
if (verbose > 1) {
|
|
printf(" Creating (%.12g, %.12g).\n", newpoint[0], newpoint[1]);
|
|
}
|
|
/* Record the new node in the (one or two) adjacent elements. */
|
|
triangleloop.tri[highorderindex + triangleloop.orient] =
|
|
(triangle) newpoint;
|
|
if (trisym.tri != dummytri) {
|
|
trisym.tri[highorderindex + trisym.orient] = (triangle) newpoint;
|
|
}
|
|
}
|
|
}
|
|
triangleloop.tri = triangletraverse();
|
|
}
|
|
}
|
|
|
|
/********* File I/O routines begin here *********/
|
|
/** **/
|
|
/** **/
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* readline() Read a nonempty line from a file. */
|
|
/* */
|
|
/* A line is considered "nonempty" if it contains something that looks like */
|
|
/* a number. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
#ifndef TRILIBRARY
|
|
|
|
char *readline(string, infile, infilename)
|
|
char *string;
|
|
FILE *infile;
|
|
char *infilename;
|
|
{
|
|
char *result;
|
|
|
|
/* Search for something that looks like a number. */
|
|
do {
|
|
result = fgets(string, INPUTLINESIZE, infile);
|
|
if (result == (char *) NULL) {
|
|
printf(" Error: Unexpected end of file in %s.\n", infilename);
|
|
exit(1);
|
|
}
|
|
/* Skip anything that doesn't look like a number, a comment, */
|
|
/* or the end of a line. */
|
|
while ((*result != '\0') && (*result != '#')
|
|
&& (*result != '.') && (*result != '+') && (*result != '-')
|
|
&& ((*result < '0') || (*result > '9'))) {
|
|
result++;
|
|
}
|
|
/* If it's a comment or end of line, read another line and try again. */
|
|
} while ((*result == '#') || (*result == '\0'));
|
|
return result;
|
|
}
|
|
|
|
#endif /* not TRILIBRARY */
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* findfield() Find the next field of a string. */
|
|
/* */
|
|
/* Jumps past the current field by searching for whitespace, then jumps */
|
|
/* past the whitespace to find the next field. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
#ifndef TRILIBRARY
|
|
|
|
char *findfield(string)
|
|
char *string;
|
|
{
|
|
char *result;
|
|
|
|
result = string;
|
|
/* Skip the current field. Stop upon reaching whitespace. */
|
|
while ((*result != '\0') && (*result != '#')
|
|
&& (*result != ' ') && (*result != '\t')) {
|
|
result++;
|
|
}
|
|
/* Now skip the whitespace and anything else that doesn't look like a */
|
|
/* number, a comment, or the end of a line. */
|
|
while ((*result != '\0') && (*result != '#')
|
|
&& (*result != '.') && (*result != '+') && (*result != '-')
|
|
&& ((*result < '0') || (*result > '9'))) {
|
|
result++;
|
|
}
|
|
/* Check for a comment (prefixed with `#'). */
|
|
if (*result == '#') {
|
|
*result = '\0';
|
|
}
|
|
return result;
|
|
}
|
|
|
|
#endif /* not TRILIBRARY */
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* readnodes() Read the points from a file, which may be a .node or .poly */
|
|
/* file. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
#ifndef TRILIBRARY
|
|
|
|
void readnodes(nodefilename, polyfilename, polyfile)
|
|
char *nodefilename;
|
|
char *polyfilename;
|
|
FILE **polyfile;
|
|
{
|
|
FILE *infile;
|
|
point pointloop;
|
|
char inputline[INPUTLINESIZE];
|
|
char *stringptr;
|
|
char *infilename;
|
|
REAL x, y;
|
|
int firstnode;
|
|
int nodemarkers;
|
|
int currentmarker;
|
|
int i, j;
|
|
|
|
if (poly) {
|
|
/* Read the points from a .poly file. */
|
|
if (!quiet) {
|
|
printf("Opening %s.\n", polyfilename);
|
|
}
|
|
*polyfile = fopen(polyfilename, "r");
|
|
if (*polyfile == (FILE *) NULL) {
|
|
printf(" Error: Cannot access file %s.\n", polyfilename);
|
|
exit(1);
|
|
}
|
|
/* Read number of points, number of dimensions, number of point */
|
|
/* attributes, and number of boundary markers. */
|
|
stringptr = readline(inputline, *polyfile, polyfilename);
|
|
inpoints = (int) strtol (stringptr, &stringptr, 0);
|
|
stringptr = findfield(stringptr);
|
|
if (*stringptr == '\0') {
|
|
mesh_dim = 2;
|
|
} else {
|
|
mesh_dim = (int) strtol (stringptr, &stringptr, 0);
|
|
}
|
|
stringptr = findfield(stringptr);
|
|
if (*stringptr == '\0') {
|
|
nextras = 0;
|
|
} else {
|
|
nextras = (int) strtol (stringptr, &stringptr, 0);
|
|
}
|
|
stringptr = findfield(stringptr);
|
|
if (*stringptr == '\0') {
|
|
nodemarkers = 0;
|
|
} else {
|
|
nodemarkers = (int) strtol (stringptr, &stringptr, 0);
|
|
}
|
|
if (inpoints > 0) {
|
|
infile = *polyfile;
|
|
infilename = polyfilename;
|
|
readnodefile = 0;
|
|
} else {
|
|
/* If the .poly file claims there are zero points, that means that */
|
|
/* the points should be read from a separate .node file. */
|
|
readnodefile = 1;
|
|
infilename = innodefilename;
|
|
}
|
|
} else {
|
|
readnodefile = 1;
|
|
infilename = innodefilename;
|
|
*polyfile = (FILE *) NULL;
|
|
}
|
|
|
|
if (readnodefile) {
|
|
/* Read the points from a .node file. */
|
|
if (!quiet) {
|
|
printf("Opening %s.\n", innodefilename);
|
|
}
|
|
infile = fopen(innodefilename, "r");
|
|
if (infile == (FILE *) NULL) {
|
|
printf(" Error: Cannot access file %s.\n", innodefilename);
|
|
exit(1);
|
|
}
|
|
/* Read number of points, number of dimensions, number of point */
|
|
/* attributes, and number of boundary markers. */
|
|
stringptr = readline(inputline, infile, innodefilename);
|
|
inpoints = (int) strtol (stringptr, &stringptr, 0);
|
|
stringptr = findfield(stringptr);
|
|
if (*stringptr == '\0') {
|
|
mesh_dim = 2;
|
|
} else {
|
|
mesh_dim = (int) strtol (stringptr, &stringptr, 0);
|
|
}
|
|
stringptr = findfield(stringptr);
|
|
if (*stringptr == '\0') {
|
|
nextras = 0;
|
|
} else {
|
|
nextras = (int) strtol (stringptr, &stringptr, 0);
|
|
}
|
|
stringptr = findfield(stringptr);
|
|
if (*stringptr == '\0') {
|
|
nodemarkers = 0;
|
|
} else {
|
|
nodemarkers = (int) strtol (stringptr, &stringptr, 0);
|
|
}
|
|
}
|
|
|
|
if (inpoints < 3) {
|
|
printf("Error: Input must have at least three input points.\n");
|
|
exit(1);
|
|
}
|
|
if (mesh_dim != 2) {
|
|
printf("Error: Triangle only works with two-dimensional meshes.\n");
|
|
exit(1);
|
|
}
|
|
|
|
initializepointpool();
|
|
|
|
/* Read the points. */
|
|
for (i = 0; i < inpoints; i++) {
|
|
pointloop = (point) poolalloc(&points);
|
|
stringptr = readline(inputline, infile, infilename);
|
|
if (i == 0) {
|
|
firstnode = (int) strtol (stringptr, &stringptr, 0);
|
|
if ((firstnode == 0) || (firstnode == 1)) {
|
|
firstnumber = firstnode;
|
|
}
|
|
}
|
|
stringptr = findfield(stringptr);
|
|
if (*stringptr == '\0') {
|
|
printf("Error: Point %d has no x coordinate.\n", firstnumber + i);
|
|
exit(1);
|
|
}
|
|
x = (REAL) strtod(stringptr, &stringptr);
|
|
stringptr = findfield(stringptr);
|
|
if (*stringptr == '\0') {
|
|
printf("Error: Point %d has no y coordinate.\n", firstnumber + i);
|
|
exit(1);
|
|
}
|
|
y = (REAL) strtod(stringptr, &stringptr);
|
|
pointloop[0] = x;
|
|
pointloop[1] = y;
|
|
/* Read the point attributes. */
|
|
for (j = 2; j < 2 + nextras; j++) {
|
|
stringptr = findfield(stringptr);
|
|
if (*stringptr == '\0') {
|
|
pointloop[j] = 0.0;
|
|
} else {
|
|
pointloop[j] = (REAL) strtod(stringptr, &stringptr);
|
|
}
|
|
}
|
|
if (nodemarkers) {
|
|
/* Read a point marker. */
|
|
stringptr = findfield(stringptr);
|
|
if (*stringptr == '\0') {
|
|
setpointmark(pointloop, 0);
|
|
} else {
|
|
currentmarker = (int) strtol (stringptr, &stringptr, 0);
|
|
setpointmark(pointloop, currentmarker);
|
|
}
|
|
} else {
|
|
/* If no markers are specified in the file, they default to zero. */
|
|
setpointmark(pointloop, 0);
|
|
}
|
|
/* Determine the smallest and largest x and y coordinates. */
|
|
if (i == 0) {
|
|
xmin = xmax = x;
|
|
ymin = ymax = y;
|
|
} else {
|
|
xmin = (x < xmin) ? x : xmin;
|
|
xmax = (x > xmax) ? x : xmax;
|
|
ymin = (y < ymin) ? y : ymin;
|
|
ymax = (y > ymax) ? y : ymax;
|
|
}
|
|
}
|
|
if (readnodefile) {
|
|
fclose(infile);
|
|
}
|
|
|
|
/* Nonexistent x value used as a flag to mark circle events in sweepline */
|
|
/* Delaunay algorithm. */
|
|
xminextreme = 10 * xmin - 9 * xmax;
|
|
}
|
|
|
|
#endif /* not TRILIBRARY */
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* transfernodes() Read the points from memory. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
#ifdef TRILIBRARY
|
|
|
|
void transfernodes(pointlist, pointattriblist, pointmarkerlist, numberofpoints,
|
|
numberofpointattribs)
|
|
REAL *pointlist;
|
|
REAL *pointattriblist;
|
|
int *pointmarkerlist;
|
|
int numberofpoints;
|
|
int numberofpointattribs;
|
|
{
|
|
point pointloop;
|
|
REAL x, y;
|
|
int i, j;
|
|
int coordindex;
|
|
int attribindex;
|
|
|
|
inpoints = numberofpoints;
|
|
mesh_dim = 2;
|
|
nextras = numberofpointattribs;
|
|
readnodefile = 0;
|
|
if (inpoints < 3) {
|
|
printf("Error: Input must have at least three input points.\n");
|
|
exit(1);
|
|
}
|
|
|
|
initializepointpool();
|
|
|
|
/* Read the points. */
|
|
coordindex = 0;
|
|
attribindex = 0;
|
|
for (i = 0; i < inpoints; i++) {
|
|
pointloop = (point) poolalloc(&points);
|
|
/* Read the point coordinates. */
|
|
x = pointloop[0] = pointlist[coordindex++];
|
|
y = pointloop[1] = pointlist[coordindex++];
|
|
/* Read the point attributes. */
|
|
for (j = 0; j < numberofpointattribs; j++) {
|
|
pointloop[2 + j] = pointattriblist[attribindex++];
|
|
}
|
|
if (pointmarkerlist != (int *) NULL) {
|
|
/* Read a point marker. */
|
|
setpointmark(pointloop, pointmarkerlist[i]);
|
|
} else {
|
|
/* If no markers are specified, they default to zero. */
|
|
setpointmark(pointloop, 0);
|
|
}
|
|
x = pointloop[0];
|
|
y = pointloop[1];
|
|
/* Determine the smallest and largest x and y coordinates. */
|
|
if (i == 0) {
|
|
xmin = xmax = x;
|
|
ymin = ymax = y;
|
|
} else {
|
|
xmin = (x < xmin) ? x : xmin;
|
|
xmax = (x > xmax) ? x : xmax;
|
|
ymin = (y < ymin) ? y : ymin;
|
|
ymax = (y > ymax) ? y : ymax;
|
|
}
|
|
}
|
|
|
|
/* Nonexistent x value used as a flag to mark circle events in sweepline */
|
|
/* Delaunay algorithm. */
|
|
xminextreme = 10 * xmin - 9 * xmax;
|
|
}
|
|
|
|
#endif /* TRILIBRARY */
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* readholes() Read the holes, and possibly regional attributes and area */
|
|
/* constraints, from a .poly file. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
#ifndef TRILIBRARY
|
|
|
|
void readholes(polyfile, polyfilename, hlist, holes, rlist, regions)
|
|
FILE *polyfile;
|
|
char *polyfilename;
|
|
REAL **hlist;
|
|
int *holes;
|
|
REAL **rlist;
|
|
int *regions;
|
|
{
|
|
REAL *holelist;
|
|
REAL *regionlist;
|
|
char inputline[INPUTLINESIZE];
|
|
char *stringptr;
|
|
int index;
|
|
int i;
|
|
|
|
/* Read the holes. */
|
|
stringptr = readline(inputline, polyfile, polyfilename);
|
|
*holes = (int) strtol (stringptr, &stringptr, 0);
|
|
if (*holes > 0) {
|
|
holelist = (REAL *) malloc(2 * *holes * sizeof(REAL));
|
|
*hlist = holelist;
|
|
if (holelist == (REAL *) NULL) {
|
|
printf("Error: Out of memory.\n");
|
|
exit(1);
|
|
}
|
|
for (i = 0; i < 2 * *holes; i += 2) {
|
|
stringptr = readline(inputline, polyfile, polyfilename);
|
|
stringptr = findfield(stringptr);
|
|
if (*stringptr == '\0') {
|
|
printf("Error: Hole %d has no x coordinate.\n",
|
|
firstnumber + (i >> 1));
|
|
exit(1);
|
|
} else {
|
|
holelist[i] = (REAL) strtod(stringptr, &stringptr);
|
|
}
|
|
stringptr = findfield(stringptr);
|
|
if (*stringptr == '\0') {
|
|
printf("Error: Hole %d has no y coordinate.\n",
|
|
firstnumber + (i >> 1));
|
|
exit(1);
|
|
} else {
|
|
holelist[i + 1] = (REAL) strtod(stringptr, &stringptr);
|
|
}
|
|
}
|
|
} else {
|
|
*hlist = (REAL *) NULL;
|
|
}
|
|
|
|
#ifndef CDT_ONLY
|
|
if ((regionattrib || vararea) && !refine) {
|
|
/* Read the area constraints. */
|
|
stringptr = readline(inputline, polyfile, polyfilename);
|
|
*regions = (int) strtol (stringptr, &stringptr, 0);
|
|
if (*regions > 0) {
|
|
regionlist = (REAL *) malloc(4 * *regions * sizeof(REAL));
|
|
*rlist = regionlist;
|
|
if (regionlist == (REAL *) NULL) {
|
|
printf("Error: Out of memory.\n");
|
|
exit(1);
|
|
}
|
|
index = 0;
|
|
for (i = 0; i < *regions; i++) {
|
|
stringptr = readline(inputline, polyfile, polyfilename);
|
|
stringptr = findfield(stringptr);
|
|
if (*stringptr == '\0') {
|
|
printf("Error: Region %d has no x coordinate.\n",
|
|
firstnumber + i);
|
|
exit(1);
|
|
} else {
|
|
regionlist[index++] = (REAL) strtod(stringptr, &stringptr);
|
|
}
|
|
stringptr = findfield(stringptr);
|
|
if (*stringptr == '\0') {
|
|
printf("Error: Region %d has no y coordinate.\n",
|
|
firstnumber + i);
|
|
exit(1);
|
|
} else {
|
|
regionlist[index++] = (REAL) strtod(stringptr, &stringptr);
|
|
}
|
|
stringptr = findfield(stringptr);
|
|
if (*stringptr == '\0') {
|
|
printf(
|
|
"Error: Region %d has no region attribute or area constraint.\n",
|
|
firstnumber + i);
|
|
exit(1);
|
|
} else {
|
|
regionlist[index++] = (REAL) strtod(stringptr, &stringptr);
|
|
}
|
|
stringptr = findfield(stringptr);
|
|
if (*stringptr == '\0') {
|
|
regionlist[index] = regionlist[index - 1];
|
|
} else {
|
|
regionlist[index] = (REAL) strtod(stringptr, &stringptr);
|
|
}
|
|
index++;
|
|
}
|
|
}
|
|
} else {
|
|
/* Set `*regions' to zero to avoid an accidental free() later. */
|
|
*regions = 0;
|
|
*rlist = (REAL *) NULL;
|
|
}
|
|
#endif /* not CDT_ONLY */
|
|
|
|
fclose(polyfile);
|
|
}
|
|
|
|
#endif /* not TRILIBRARY */
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* finishfile() Write the command line to the output file so the user */
|
|
/* can remember how the file was generated. Close the file. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
#ifndef TRILIBRARY
|
|
|
|
void finishfile(outfile, argc, argv)
|
|
FILE *outfile;
|
|
int argc;
|
|
char **argv;
|
|
{
|
|
int i;
|
|
|
|
fprintf(outfile, "# Generated by");
|
|
for (i = 0; i < argc; i++) {
|
|
fprintf(outfile, " ");
|
|
fputs(argv[i], outfile);
|
|
}
|
|
fprintf(outfile, "\n");
|
|
fclose(outfile);
|
|
}
|
|
|
|
#endif /* not TRILIBRARY */
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* writenodes() Number the points and write them to a .node file. */
|
|
/* */
|
|
/* To save memory, the point numbers are written over the shell markers */
|
|
/* after the points are written to a file. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
#ifdef TRILIBRARY
|
|
|
|
void writenodes(pointlist, pointattriblist, pointmarkerlist)
|
|
REAL **pointlist;
|
|
REAL **pointattriblist;
|
|
int **pointmarkerlist;
|
|
|
|
#else /* not TRILIBRARY */
|
|
|
|
void writenodes(nodefilename, argc, argv)
|
|
char *nodefilename;
|
|
int argc;
|
|
char **argv;
|
|
|
|
#endif /* not TRILIBRARY */
|
|
|
|
{
|
|
#ifdef TRILIBRARY
|
|
REAL *plist;
|
|
REAL *palist;
|
|
int *pmlist;
|
|
int coordindex;
|
|
int attribindex;
|
|
#else /* not TRILIBRARY */
|
|
FILE *outfile;
|
|
#endif /* not TRILIBRARY */
|
|
point pointloop;
|
|
int pointnumber;
|
|
int i;
|
|
|
|
#ifdef TRILIBRARY
|
|
if (!quiet) {
|
|
printf("Writing points.\n");
|
|
}
|
|
/* Allocate memory for output points if necessary. */
|
|
if (*pointlist == (REAL *) NULL) {
|
|
*pointlist = (REAL *) malloc(points.items * 2 * sizeof(REAL));
|
|
if (*pointlist == (REAL *) NULL) {
|
|
printf("Error: Out of memory.\n");
|
|
exit(1);
|
|
}
|
|
}
|
|
/* Allocate memory for output point attributes if necessary. */
|
|
if ((nextras > 0) && (*pointattriblist == (REAL *) NULL)) {
|
|
*pointattriblist = (REAL *) malloc(points.items * nextras * sizeof(REAL));
|
|
if (*pointattriblist == (REAL *) NULL) {
|
|
printf("Error: Out of memory.\n");
|
|
exit(1);
|
|
}
|
|
}
|
|
/* Allocate memory for output point markers if necessary. */
|
|
if (!nobound && (*pointmarkerlist == (int *) NULL)) {
|
|
*pointmarkerlist = (int *) malloc(points.items * sizeof(int));
|
|
if (*pointmarkerlist == (int *) NULL) {
|
|
printf("Error: Out of memory.\n");
|
|
exit(1);
|
|
}
|
|
}
|
|
plist = *pointlist;
|
|
palist = *pointattriblist;
|
|
pmlist = *pointmarkerlist;
|
|
coordindex = 0;
|
|
attribindex = 0;
|
|
#else /* not TRILIBRARY */
|
|
if (!quiet) {
|
|
printf("Writing %s.\n", nodefilename);
|
|
}
|
|
outfile = fopen(nodefilename, "w");
|
|
if (outfile == (FILE *) NULL) {
|
|
printf(" Error: Cannot create file %s.\n", nodefilename);
|
|
exit(1);
|
|
}
|
|
/* Number of points, number of dimensions, number of point attributes, */
|
|
/* and number of boundary markers (zero or one). */
|
|
fprintf(outfile, "%ld %d %d %d\n", points.items, mesh_dim, nextras,
|
|
1 - nobound);
|
|
#endif /* not TRILIBRARY */
|
|
|
|
traversalinit(&points);
|
|
pointloop = pointtraverse();
|
|
pointnumber = firstnumber;
|
|
while (pointloop != (point) NULL) {
|
|
#ifdef TRILIBRARY
|
|
/* X and y coordinates. */
|
|
plist[coordindex++] = pointloop[0];
|
|
plist[coordindex++] = pointloop[1];
|
|
/* Point attributes. */
|
|
for (i = 0; i < nextras; i++) {
|
|
palist[attribindex++] = pointloop[2 + i];
|
|
}
|
|
if (!nobound) {
|
|
/* Copy the boundary marker. */
|
|
pmlist[pointnumber - firstnumber] = pointmark(pointloop);
|
|
}
|
|
#else /* not TRILIBRARY */
|
|
/* Point number, x and y coordinates. */
|
|
fprintf(outfile, "%4d %.17g %.17g", pointnumber, pointloop[0],
|
|
pointloop[1]);
|
|
for (i = 0; i < nextras; i++) {
|
|
/* Write an attribute. */
|
|
fprintf(outfile, " %.17g", pointloop[i + 2]);
|
|
}
|
|
if (nobound) {
|
|
fprintf(outfile, "\n");
|
|
} else {
|
|
/* Write the boundary marker. */
|
|
fprintf(outfile, " %d\n", pointmark(pointloop));
|
|
}
|
|
#endif /* not TRILIBRARY */
|
|
|
|
setpointmark(pointloop, pointnumber);
|
|
pointloop = pointtraverse();
|
|
pointnumber++;
|
|
}
|
|
|
|
#ifndef TRILIBRARY
|
|
finishfile(outfile, argc, argv);
|
|
#endif /* not TRILIBRARY */
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* numbernodes() Number the points. */
|
|
/* */
|
|
/* Each point is assigned a marker equal to its number. */
|
|
/* */
|
|
/* Used when writenodes() is not called because no .node file is written. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
void numbernodes()
|
|
{
|
|
point pointloop;
|
|
int pointnumber;
|
|
|
|
traversalinit(&points);
|
|
pointloop = pointtraverse();
|
|
pointnumber = firstnumber;
|
|
while (pointloop != (point) NULL) {
|
|
setpointmark(pointloop, pointnumber);
|
|
pointloop = pointtraverse();
|
|
pointnumber++;
|
|
}
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* writeelements() Write the triangles to an .ele file. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
#ifdef TRILIBRARY
|
|
|
|
void writeelements(trianglelist, triangleattriblist)
|
|
int **trianglelist;
|
|
REAL **triangleattriblist;
|
|
|
|
#else /* not TRILIBRARY */
|
|
|
|
void writeelements(elefilename, argc, argv)
|
|
char *elefilename;
|
|
int argc;
|
|
char **argv;
|
|
|
|
#endif /* not TRILIBRARY */
|
|
|
|
{
|
|
#ifdef TRILIBRARY
|
|
int *tlist;
|
|
REAL *talist;
|
|
int pointindex;
|
|
int attribindex;
|
|
#else /* not TRILIBRARY */
|
|
FILE *outfile;
|
|
#endif /* not TRILIBRARY */
|
|
struct triedge triangleloop;
|
|
point p1, p2, p3;
|
|
point mid1, mid2, mid3;
|
|
int elementnumber;
|
|
int i;
|
|
|
|
#ifdef TRILIBRARY
|
|
if (!quiet) {
|
|
printf("Writing triangles.\n");
|
|
}
|
|
/* Allocate memory for output triangles if necessary. */
|
|
if (*trianglelist == (int *) NULL) {
|
|
*trianglelist = (int *) malloc(triangles.items *
|
|
((order + 1) * (order + 2) / 2) * sizeof(int));
|
|
if (*trianglelist == (int *) NULL) {
|
|
printf("Error: Out of memory.\n");
|
|
exit(1);
|
|
}
|
|
}
|
|
/* Allocate memory for output triangle attributes if necessary. */
|
|
if ((eextras > 0) && (*triangleattriblist == (REAL *) NULL)) {
|
|
*triangleattriblist = (REAL *) malloc(triangles.items * eextras *
|
|
sizeof(REAL));
|
|
if (*triangleattriblist == (REAL *) NULL) {
|
|
printf("Error: Out of memory.\n");
|
|
exit(1);
|
|
}
|
|
}
|
|
tlist = *trianglelist;
|
|
talist = *triangleattriblist;
|
|
pointindex = 0;
|
|
attribindex = 0;
|
|
#else /* not TRILIBRARY */
|
|
if (!quiet) {
|
|
printf("Writing %s.\n", elefilename);
|
|
}
|
|
outfile = fopen(elefilename, "w");
|
|
if (outfile == (FILE *) NULL) {
|
|
printf(" Error: Cannot create file %s.\n", elefilename);
|
|
exit(1);
|
|
}
|
|
/* Number of triangles, points per triangle, attributes per triangle. */
|
|
fprintf(outfile, "%ld %d %d\n", triangles.items,
|
|
(order + 1) * (order + 2) / 2, eextras);
|
|
#endif /* not TRILIBRARY */
|
|
|
|
traversalinit(&triangles);
|
|
triangleloop.tri = triangletraverse();
|
|
triangleloop.orient = 0;
|
|
elementnumber = firstnumber;
|
|
while (triangleloop.tri != (triangle *) NULL) {
|
|
org(triangleloop, p1);
|
|
dest(triangleloop, p2);
|
|
apex(triangleloop, p3);
|
|
if (order == 1) {
|
|
#ifdef TRILIBRARY
|
|
tlist[pointindex++] = pointmark(p1);
|
|
tlist[pointindex++] = pointmark(p2);
|
|
tlist[pointindex++] = pointmark(p3);
|
|
#else /* not TRILIBRARY */
|
|
/* Triangle number, indices for three points. */
|
|
fprintf(outfile, "%4d %4d %4d %4d", elementnumber,
|
|
pointmark(p1), pointmark(p2), pointmark(p3));
|
|
#endif /* not TRILIBRARY */
|
|
} else {
|
|
mid1 = (point) triangleloop.tri[highorderindex + 1];
|
|
mid2 = (point) triangleloop.tri[highorderindex + 2];
|
|
mid3 = (point) triangleloop.tri[highorderindex];
|
|
#ifdef TRILIBRARY
|
|
tlist[pointindex++] = pointmark(p1);
|
|
tlist[pointindex++] = pointmark(p2);
|
|
tlist[pointindex++] = pointmark(p3);
|
|
tlist[pointindex++] = pointmark(mid1);
|
|
tlist[pointindex++] = pointmark(mid2);
|
|
tlist[pointindex++] = pointmark(mid3);
|
|
#else /* not TRILIBRARY */
|
|
/* Triangle number, indices for six points. */
|
|
fprintf(outfile, "%4d %4d %4d %4d %4d %4d %4d", elementnumber,
|
|
pointmark(p1), pointmark(p2), pointmark(p3), pointmark(mid1),
|
|
pointmark(mid2), pointmark(mid3));
|
|
#endif /* not TRILIBRARY */
|
|
}
|
|
|
|
#ifdef TRILIBRARY
|
|
for (i = 0; i < eextras; i++) {
|
|
talist[attribindex++] = elemattribute(triangleloop, i);
|
|
}
|
|
#else /* not TRILIBRARY */
|
|
for (i = 0; i < eextras; i++) {
|
|
fprintf(outfile, " %.17g", elemattribute(triangleloop, i));
|
|
}
|
|
fprintf(outfile, "\n");
|
|
#endif /* not TRILIBRARY */
|
|
|
|
triangleloop.tri = triangletraverse();
|
|
elementnumber++;
|
|
}
|
|
|
|
#ifndef TRILIBRARY
|
|
finishfile(outfile, argc, argv);
|
|
#endif /* not TRILIBRARY */
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* writepoly() Write the segments and holes to a .poly file. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
#ifdef TRILIBRARY
|
|
|
|
void writepoly(segmentlist, segmentmarkerlist)
|
|
int **segmentlist;
|
|
int **segmentmarkerlist;
|
|
|
|
#else /* not TRILIBRARY */
|
|
|
|
void writepoly(polyfilename, holelist, holes, regionlist, regions, argc, argv)
|
|
char *polyfilename;
|
|
REAL *holelist;
|
|
int holes;
|
|
REAL *regionlist;
|
|
int regions;
|
|
int argc;
|
|
char **argv;
|
|
|
|
#endif /* not TRILIBRARY */
|
|
|
|
{
|
|
#ifdef TRILIBRARY
|
|
int *slist;
|
|
int *smlist;
|
|
int index;
|
|
#else /* not TRILIBRARY */
|
|
FILE *outfile;
|
|
int i;
|
|
#endif /* not TRILIBRARY */
|
|
struct edge shelleloop;
|
|
point endpoint1, endpoint2;
|
|
int shellenumber;
|
|
|
|
#ifdef TRILIBRARY
|
|
if (!quiet) {
|
|
printf("Writing segments.\n");
|
|
}
|
|
/* Allocate memory for output segments if necessary. */
|
|
if (*segmentlist == (int *) NULL) {
|
|
*segmentlist = (int *) malloc(shelles.items * 2 * sizeof(int));
|
|
if (*segmentlist == (int *) NULL) {
|
|
printf("Error: Out of memory.\n");
|
|
exit(1);
|
|
}
|
|
}
|
|
/* Allocate memory for output segment markers if necessary. */
|
|
if (!nobound && (*segmentmarkerlist == (int *) NULL)) {
|
|
*segmentmarkerlist = (int *) malloc(shelles.items * sizeof(int));
|
|
if (*segmentmarkerlist == (int *) NULL) {
|
|
printf("Error: Out of memory.\n");
|
|
exit(1);
|
|
}
|
|
}
|
|
slist = *segmentlist;
|
|
smlist = *segmentmarkerlist;
|
|
index = 0;
|
|
#else /* not TRILIBRARY */
|
|
if (!quiet) {
|
|
printf("Writing %s.\n", polyfilename);
|
|
}
|
|
outfile = fopen(polyfilename, "w");
|
|
if (outfile == (FILE *) NULL) {
|
|
printf(" Error: Cannot create file %s.\n", polyfilename);
|
|
exit(1);
|
|
}
|
|
/* The zero indicates that the points are in a separate .node file. */
|
|
/* Followed by number of dimensions, number of point attributes, */
|
|
/* and number of boundary markers (zero or one). */
|
|
fprintf(outfile, "%d %d %d %d\n", 0, mesh_dim, nextras, 1 - nobound);
|
|
/* Number of segments, number of boundary markers (zero or one). */
|
|
fprintf(outfile, "%ld %d\n", shelles.items, 1 - nobound);
|
|
#endif /* not TRILIBRARY */
|
|
|
|
traversalinit(&shelles);
|
|
shelleloop.sh = shelletraverse();
|
|
shelleloop.shorient = 0;
|
|
shellenumber = firstnumber;
|
|
while (shelleloop.sh != (shelle *) NULL) {
|
|
sorg(shelleloop, endpoint1);
|
|
sdest(shelleloop, endpoint2);
|
|
#ifdef TRILIBRARY
|
|
/* Copy indices of the segment's two endpoints. */
|
|
slist[index++] = pointmark(endpoint1);
|
|
slist[index++] = pointmark(endpoint2);
|
|
if (!nobound) {
|
|
/* Copy the boundary marker. */
|
|
smlist[shellenumber - firstnumber] = mark(shelleloop);
|
|
}
|
|
#else /* not TRILIBRARY */
|
|
/* Segment number, indices of its two endpoints, and possibly a marker. */
|
|
if (nobound) {
|
|
fprintf(outfile, "%4d %4d %4d\n", shellenumber,
|
|
pointmark(endpoint1), pointmark(endpoint2));
|
|
} else {
|
|
fprintf(outfile, "%4d %4d %4d %4d\n", shellenumber,
|
|
pointmark(endpoint1), pointmark(endpoint2), mark(shelleloop));
|
|
}
|
|
#endif /* not TRILIBRARY */
|
|
|
|
shelleloop.sh = shelletraverse();
|
|
shellenumber++;
|
|
}
|
|
|
|
#ifndef TRILIBRARY
|
|
#ifndef CDT_ONLY
|
|
fprintf(outfile, "%d\n", holes);
|
|
if (holes > 0) {
|
|
for (i = 0; i < holes; i++) {
|
|
/* Hole number, x and y coordinates. */
|
|
fprintf(outfile, "%4d %.17g %.17g\n", firstnumber + i,
|
|
holelist[2 * i], holelist[2 * i + 1]);
|
|
}
|
|
}
|
|
if (regions > 0) {
|
|
fprintf(outfile, "%d\n", regions);
|
|
for (i = 0; i < regions; i++) {
|
|
/* Region number, x and y coordinates, attribute, maximum area. */
|
|
fprintf(outfile, "%4d %.17g %.17g %.17g %.17g\n", firstnumber + i,
|
|
regionlist[4 * i], regionlist[4 * i + 1],
|
|
regionlist[4 * i + 2], regionlist[4 * i + 3]);
|
|
}
|
|
}
|
|
#endif /* not CDT_ONLY */
|
|
|
|
finishfile(outfile, argc, argv);
|
|
#endif /* not TRILIBRARY */
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* writeedges() Write the edges to a .edge file. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
#ifdef TRILIBRARY
|
|
|
|
void writeedges(edgelist, edgemarkerlist)
|
|
int **edgelist;
|
|
int **edgemarkerlist;
|
|
|
|
#else /* not TRILIBRARY */
|
|
|
|
void writeedges(edgefilename, argc, argv)
|
|
char *edgefilename;
|
|
int argc;
|
|
char **argv;
|
|
|
|
#endif /* not TRILIBRARY */
|
|
|
|
{
|
|
#ifdef TRILIBRARY
|
|
int *elist;
|
|
int *emlist;
|
|
int index;
|
|
#else /* not TRILIBRARY */
|
|
FILE *outfile;
|
|
#endif /* not TRILIBRARY */
|
|
struct triedge triangleloop, trisym;
|
|
struct edge checkmark;
|
|
point p1, p2;
|
|
int edgenumber;
|
|
triangle ptr; /* Temporary variable used by sym(). */
|
|
shelle sptr; /* Temporary variable used by tspivot(). */
|
|
|
|
#ifdef TRILIBRARY
|
|
if (!quiet) {
|
|
printf("Writing edges.\n");
|
|
}
|
|
/* Allocate memory for edges if necessary. */
|
|
if (*edgelist == (int *) NULL) {
|
|
*edgelist = (int *) malloc(edges * 2 * sizeof(int));
|
|
if (*edgelist == (int *) NULL) {
|
|
printf("Error: Out of memory.\n");
|
|
exit(1);
|
|
}
|
|
}
|
|
/* Allocate memory for edge markers if necessary. */
|
|
if (!nobound && (*edgemarkerlist == (int *) NULL)) {
|
|
*edgemarkerlist = (int *) malloc(edges * sizeof(int));
|
|
if (*edgemarkerlist == (int *) NULL) {
|
|
printf("Error: Out of memory.\n");
|
|
exit(1);
|
|
}
|
|
}
|
|
elist = *edgelist;
|
|
emlist = *edgemarkerlist;
|
|
index = 0;
|
|
#else /* not TRILIBRARY */
|
|
if (!quiet) {
|
|
printf("Writing %s.\n", edgefilename);
|
|
}
|
|
outfile = fopen(edgefilename, "w");
|
|
if (outfile == (FILE *) NULL) {
|
|
printf(" Error: Cannot create file %s.\n", edgefilename);
|
|
exit(1);
|
|
}
|
|
/* Number of edges, number of boundary markers (zero or one). */
|
|
fprintf(outfile, "%ld %d\n", edges, 1 - nobound);
|
|
#endif /* not TRILIBRARY */
|
|
|
|
traversalinit(&triangles);
|
|
triangleloop.tri = triangletraverse();
|
|
edgenumber = firstnumber;
|
|
/* To loop over the set of edges, loop over all triangles, and look at */
|
|
/* the three edges of each triangle. If there isn't another triangle */
|
|
/* adjacent to the edge, operate on the edge. If there is another */
|
|
/* adjacent triangle, operate on the edge only if the current triangle */
|
|
/* has a smaller pointer than its neighbor. This way, each edge is */
|
|
/* considered only once. */
|
|
while (triangleloop.tri != (triangle *) NULL) {
|
|
for (triangleloop.orient = 0; triangleloop.orient < 3;
|
|
triangleloop.orient++) {
|
|
sym(triangleloop, trisym);
|
|
if ((triangleloop.tri < trisym.tri) || (trisym.tri == dummytri)) {
|
|
org(triangleloop, p1);
|
|
dest(triangleloop, p2);
|
|
#ifdef TRILIBRARY
|
|
elist[index++] = pointmark(p1);
|
|
elist[index++] = pointmark(p2);
|
|
#endif /* TRILIBRARY */
|
|
if (nobound) {
|
|
#ifndef TRILIBRARY
|
|
/* Edge number, indices of two endpoints. */
|
|
fprintf(outfile, "%4d %d %d\n", edgenumber,
|
|
pointmark(p1), pointmark(p2));
|
|
#endif /* not TRILIBRARY */
|
|
} else {
|
|
/* Edge number, indices of two endpoints, and a boundary marker. */
|
|
/* If there's no shell edge, the boundary marker is zero. */
|
|
if (useshelles) {
|
|
tspivot(triangleloop, checkmark);
|
|
if (checkmark.sh == dummysh) {
|
|
#ifdef TRILIBRARY
|
|
emlist[edgenumber - firstnumber] = 0;
|
|
#else /* not TRILIBRARY */
|
|
fprintf(outfile, "%4d %d %d %d\n", edgenumber,
|
|
pointmark(p1), pointmark(p2), 0);
|
|
#endif /* not TRILIBRARY */
|
|
} else {
|
|
#ifdef TRILIBRARY
|
|
emlist[edgenumber - firstnumber] = mark(checkmark);
|
|
#else /* not TRILIBRARY */
|
|
fprintf(outfile, "%4d %d %d %d\n", edgenumber,
|
|
pointmark(p1), pointmark(p2), mark(checkmark));
|
|
#endif /* not TRILIBRARY */
|
|
}
|
|
} else {
|
|
#ifdef TRILIBRARY
|
|
emlist[edgenumber - firstnumber] = trisym.tri == dummytri;
|
|
#else /* not TRILIBRARY */
|
|
fprintf(outfile, "%4d %d %d %d\n", edgenumber,
|
|
pointmark(p1), pointmark(p2), trisym.tri == dummytri);
|
|
#endif /* not TRILIBRARY */
|
|
}
|
|
}
|
|
edgenumber++;
|
|
}
|
|
}
|
|
triangleloop.tri = triangletraverse();
|
|
}
|
|
|
|
#ifndef TRILIBRARY
|
|
finishfile(outfile, argc, argv);
|
|
#endif /* not TRILIBRARY */
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* writevoronoi() Write the Voronoi diagram to a .v.node and .v.edge */
|
|
/* file. */
|
|
/* */
|
|
/* The Voronoi diagram is the geometric dual of the Delaunay triangulation. */
|
|
/* Hence, the Voronoi vertices are listed by traversing the Delaunay */
|
|
/* triangles, and the Voronoi edges are listed by traversing the Delaunay */
|
|
/* edges. */
|
|
/* */
|
|
/* WARNING: In order to assign numbers to the Voronoi vertices, this */
|
|
/* procedure messes up the shell edges or the extra nodes of every */
|
|
/* element. Hence, you should call this procedure last. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
#ifdef TRILIBRARY
|
|
|
|
void writevoronoi(vpointlist, vpointattriblist, vpointmarkerlist, vedgelist,
|
|
vedgemarkerlist, vnormlist)
|
|
REAL **vpointlist;
|
|
REAL **vpointattriblist;
|
|
int **vpointmarkerlist;
|
|
int **vedgelist;
|
|
int **vedgemarkerlist;
|
|
REAL **vnormlist;
|
|
|
|
#else /* not TRILIBRARY */
|
|
|
|
void writevoronoi(vnodefilename, vedgefilename, argc, argv)
|
|
char *vnodefilename;
|
|
char *vedgefilename;
|
|
int argc;
|
|
char **argv;
|
|
|
|
#endif /* not TRILIBRARY */
|
|
|
|
{
|
|
#ifdef TRILIBRARY
|
|
REAL *plist;
|
|
REAL *palist;
|
|
int *elist;
|
|
REAL *normlist;
|
|
int coordindex;
|
|
int attribindex;
|
|
#else /* not TRILIBRARY */
|
|
FILE *outfile;
|
|
#endif /* not TRILIBRARY */
|
|
struct triedge triangleloop, trisym;
|
|
point torg, tdest, tapex;
|
|
REAL circumcenter[2];
|
|
REAL xi, eta;
|
|
int vnodenumber, vedgenumber;
|
|
int p1, p2;
|
|
int i;
|
|
triangle ptr; /* Temporary variable used by sym(). */
|
|
|
|
#ifdef TRILIBRARY
|
|
if (!quiet) {
|
|
printf("Writing Voronoi vertices.\n");
|
|
}
|
|
/* Allocate memory for Voronoi vertices if necessary. */
|
|
if (*vpointlist == (REAL *) NULL) {
|
|
*vpointlist = (REAL *) malloc(triangles.items * 2 * sizeof(REAL));
|
|
if (*vpointlist == (REAL *) NULL) {
|
|
printf("Error: Out of memory.\n");
|
|
exit(1);
|
|
}
|
|
}
|
|
/* Allocate memory for Voronoi vertex attributes if necessary. */
|
|
if (*vpointattriblist == (REAL *) NULL) {
|
|
*vpointattriblist = (REAL *) malloc(triangles.items * nextras *
|
|
sizeof(REAL));
|
|
if (*vpointattriblist == (REAL *) NULL) {
|
|
printf("Error: Out of memory.\n");
|
|
exit(1);
|
|
}
|
|
}
|
|
*vpointmarkerlist = (int *) NULL;
|
|
plist = *vpointlist;
|
|
palist = *vpointattriblist;
|
|
coordindex = 0;
|
|
attribindex = 0;
|
|
#else /* not TRILIBRARY */
|
|
if (!quiet) {
|
|
printf("Writing %s.\n", vnodefilename);
|
|
}
|
|
outfile = fopen(vnodefilename, "w");
|
|
if (outfile == (FILE *) NULL) {
|
|
printf(" Error: Cannot create file %s.\n", vnodefilename);
|
|
exit(1);
|
|
}
|
|
/* Number of triangles, two dimensions, number of point attributes, */
|
|
/* zero markers. */
|
|
fprintf(outfile, "%ld %d %d %d\n", triangles.items, 2, nextras, 0);
|
|
#endif /* not TRILIBRARY */
|
|
|
|
traversalinit(&triangles);
|
|
triangleloop.tri = triangletraverse();
|
|
triangleloop.orient = 0;
|
|
vnodenumber = firstnumber;
|
|
while (triangleloop.tri != (triangle *) NULL) {
|
|
org(triangleloop, torg);
|
|
dest(triangleloop, tdest);
|
|
apex(triangleloop, tapex);
|
|
findcircumcenter(torg, tdest, tapex, circumcenter, &xi, &eta);
|
|
#ifdef TRILIBRARY
|
|
/* X and y coordinates. */
|
|
plist[coordindex++] = circumcenter[0];
|
|
plist[coordindex++] = circumcenter[1];
|
|
for (i = 2; i < 2 + nextras; i++) {
|
|
/* Interpolate the point attributes at the circumcenter. */
|
|
palist[attribindex++] = torg[i] + xi * (tdest[i] - torg[i])
|
|
+ eta * (tapex[i] - torg[i]);
|
|
}
|
|
#else /* not TRILIBRARY */
|
|
/* Voronoi vertex number, x and y coordinates. */
|
|
fprintf(outfile, "%4d %.17g %.17g", vnodenumber, circumcenter[0],
|
|
circumcenter[1]);
|
|
for (i = 2; i < 2 + nextras; i++) {
|
|
/* Interpolate the point attributes at the circumcenter. */
|
|
fprintf(outfile, " %.17g", torg[i] + xi * (tdest[i] - torg[i])
|
|
+ eta * (tapex[i] - torg[i]));
|
|
}
|
|
fprintf(outfile, "\n");
|
|
#endif /* not TRILIBRARY */
|
|
|
|
* (int *) (triangleloop.tri + 6) = vnodenumber;
|
|
triangleloop.tri = triangletraverse();
|
|
vnodenumber++;
|
|
}
|
|
|
|
#ifndef TRILIBRARY
|
|
finishfile(outfile, argc, argv);
|
|
#endif /* not TRILIBRARY */
|
|
|
|
#ifdef TRILIBRARY
|
|
if (!quiet) {
|
|
printf("Writing Voronoi edges.\n");
|
|
}
|
|
/* Allocate memory for output Voronoi edges if necessary. */
|
|
if (*vedgelist == (int *) NULL) {
|
|
*vedgelist = (int *) malloc(edges * 2 * sizeof(int));
|
|
if (*vedgelist == (int *) NULL) {
|
|
printf("Error: Out of memory.\n");
|
|
exit(1);
|
|
}
|
|
}
|
|
*vedgemarkerlist = (int *) NULL;
|
|
/* Allocate memory for output Voronoi norms if necessary. */
|
|
if (*vnormlist == (REAL *) NULL) {
|
|
*vnormlist = (REAL *) malloc(edges * 2 * sizeof(REAL));
|
|
if (*vnormlist == (REAL *) NULL) {
|
|
printf("Error: Out of memory.\n");
|
|
exit(1);
|
|
}
|
|
}
|
|
elist = *vedgelist;
|
|
normlist = *vnormlist;
|
|
coordindex = 0;
|
|
#else /* not TRILIBRARY */
|
|
if (!quiet) {
|
|
printf("Writing %s.\n", vedgefilename);
|
|
}
|
|
outfile = fopen(vedgefilename, "w");
|
|
if (outfile == (FILE *) NULL) {
|
|
printf(" Error: Cannot create file %s.\n", vedgefilename);
|
|
exit(1);
|
|
}
|
|
/* Number of edges, zero boundary markers. */
|
|
fprintf(outfile, "%ld %d\n", edges, 0);
|
|
#endif /* not TRILIBRARY */
|
|
|
|
traversalinit(&triangles);
|
|
triangleloop.tri = triangletraverse();
|
|
vedgenumber = firstnumber;
|
|
/* To loop over the set of edges, loop over all triangles, and look at */
|
|
/* the three edges of each triangle. If there isn't another triangle */
|
|
/* adjacent to the edge, operate on the edge. If there is another */
|
|
/* adjacent triangle, operate on the edge only if the current triangle */
|
|
/* has a smaller pointer than its neighbor. This way, each edge is */
|
|
/* considered only once. */
|
|
while (triangleloop.tri != (triangle *) NULL) {
|
|
for (triangleloop.orient = 0; triangleloop.orient < 3;
|
|
triangleloop.orient++) {
|
|
sym(triangleloop, trisym);
|
|
if ((triangleloop.tri < trisym.tri) || (trisym.tri == dummytri)) {
|
|
/* Find the number of this triangle (and Voronoi vertex). */
|
|
p1 = * (int *) (triangleloop.tri + 6);
|
|
if (trisym.tri == dummytri) {
|
|
org(triangleloop, torg);
|
|
dest(triangleloop, tdest);
|
|
#ifdef TRILIBRARY
|
|
/* Copy an infinite ray. Index of one endpoint, and -1. */
|
|
elist[coordindex] = p1;
|
|
normlist[coordindex++] = tdest[1] - torg[1];
|
|
elist[coordindex] = -1;
|
|
normlist[coordindex++] = torg[0] - tdest[0];
|
|
#else /* not TRILIBRARY */
|
|
/* Write an infinite ray. Edge number, index of one endpoint, -1, */
|
|
/* and x and y coordinates of a vector representing the */
|
|
/* direction of the ray. */
|
|
fprintf(outfile, "%4d %d %d %.17g %.17g\n", vedgenumber,
|
|
p1, -1, tdest[1] - torg[1], torg[0] - tdest[0]);
|
|
#endif /* not TRILIBRARY */
|
|
} else {
|
|
/* Find the number of the adjacent triangle (and Voronoi vertex). */
|
|
p2 = * (int *) (trisym.tri + 6);
|
|
/* Finite edge. Write indices of two endpoints. */
|
|
#ifdef TRILIBRARY
|
|
elist[coordindex] = p1;
|
|
normlist[coordindex++] = 0.0;
|
|
elist[coordindex] = p2;
|
|
normlist[coordindex++] = 0.0;
|
|
#else /* not TRILIBRARY */
|
|
fprintf(outfile, "%4d %d %d\n", vedgenumber, p1, p2);
|
|
#endif /* not TRILIBRARY */
|
|
}
|
|
vedgenumber++;
|
|
}
|
|
}
|
|
triangleloop.tri = triangletraverse();
|
|
}
|
|
|
|
#ifndef TRILIBRARY
|
|
finishfile(outfile, argc, argv);
|
|
#endif /* not TRILIBRARY */
|
|
}
|
|
|
|
#ifdef TRILIBRARY
|
|
|
|
void writeneighbors(neighborlist)
|
|
int **neighborlist;
|
|
|
|
#else /* not TRILIBRARY */
|
|
|
|
void writeneighbors(neighborfilename, argc, argv)
|
|
char *neighborfilename;
|
|
int argc;
|
|
char **argv;
|
|
|
|
#endif /* not TRILIBRARY */
|
|
|
|
{
|
|
#ifdef TRILIBRARY
|
|
int *nlist;
|
|
int index;
|
|
#else /* not TRILIBRARY */
|
|
FILE *outfile;
|
|
#endif /* not TRILIBRARY */
|
|
struct triedge triangleloop, trisym;
|
|
int elementnumber;
|
|
int neighbor1, neighbor2, neighbor3;
|
|
triangle ptr; /* Temporary variable used by sym(). */
|
|
|
|
#ifdef TRILIBRARY
|
|
if (!quiet) {
|
|
printf("Writing neighbors.\n");
|
|
}
|
|
/* Allocate memory for neighbors if necessary. */
|
|
if (*neighborlist == (int *) NULL) {
|
|
*neighborlist = (int *) malloc(triangles.items * 3 * sizeof(int));
|
|
if (*neighborlist == (int *) NULL) {
|
|
printf("Error: Out of memory.\n");
|
|
exit(1);
|
|
}
|
|
}
|
|
nlist = *neighborlist;
|
|
index = 0;
|
|
#else /* not TRILIBRARY */
|
|
if (!quiet) {
|
|
printf("Writing %s.\n", neighborfilename);
|
|
}
|
|
outfile = fopen(neighborfilename, "w");
|
|
if (outfile == (FILE *) NULL) {
|
|
printf(" Error: Cannot create file %s.\n", neighborfilename);
|
|
exit(1);
|
|
}
|
|
/* Number of triangles, three edges per triangle. */
|
|
fprintf(outfile, "%ld %d\n", triangles.items, 3);
|
|
#endif /* not TRILIBRARY */
|
|
|
|
traversalinit(&triangles);
|
|
triangleloop.tri = triangletraverse();
|
|
triangleloop.orient = 0;
|
|
elementnumber = firstnumber;
|
|
while (triangleloop.tri != (triangle *) NULL) {
|
|
* (int *) (triangleloop.tri + 6) = elementnumber;
|
|
triangleloop.tri = triangletraverse();
|
|
elementnumber++;
|
|
}
|
|
* (int *) (dummytri + 6) = -1;
|
|
|
|
traversalinit(&triangles);
|
|
triangleloop.tri = triangletraverse();
|
|
elementnumber = firstnumber;
|
|
while (triangleloop.tri != (triangle *) NULL) {
|
|
triangleloop.orient = 1;
|
|
sym(triangleloop, trisym);
|
|
neighbor1 = * (int *) (trisym.tri + 6);
|
|
triangleloop.orient = 2;
|
|
sym(triangleloop, trisym);
|
|
neighbor2 = * (int *) (trisym.tri + 6);
|
|
triangleloop.orient = 0;
|
|
sym(triangleloop, trisym);
|
|
neighbor3 = * (int *) (trisym.tri + 6);
|
|
#ifdef TRILIBRARY
|
|
nlist[index++] = neighbor1;
|
|
nlist[index++] = neighbor2;
|
|
nlist[index++] = neighbor3;
|
|
#else /* not TRILIBRARY */
|
|
/* Triangle number, neighboring triangle numbers. */
|
|
fprintf(outfile, "%4d %d %d %d\n", elementnumber,
|
|
neighbor1, neighbor2, neighbor3);
|
|
#endif /* not TRILIBRARY */
|
|
|
|
triangleloop.tri = triangletraverse();
|
|
elementnumber++;
|
|
}
|
|
|
|
#ifndef TRILIBRARY
|
|
finishfile(outfile, argc, argv);
|
|
#endif /* TRILIBRARY */
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* writeoff() Write the triangulation to an .off file. */
|
|
/* */
|
|
/* OFF stands for the Object File Format, a format used by the Geometry */
|
|
/* Center's Geomview package. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
#ifndef TRILIBRARY
|
|
|
|
void writeoff(offfilename, argc, argv)
|
|
char *offfilename;
|
|
int argc;
|
|
char **argv;
|
|
{
|
|
FILE *outfile;
|
|
struct triedge triangleloop;
|
|
point pointloop;
|
|
point p1, p2, p3;
|
|
|
|
if (!quiet) {
|
|
printf("Writing %s.\n", offfilename);
|
|
}
|
|
outfile = fopen(offfilename, "w");
|
|
if (outfile == (FILE *) NULL) {
|
|
printf(" Error: Cannot create file %s.\n", offfilename);
|
|
exit(1);
|
|
}
|
|
/* Number of points, triangles, and edges. */
|
|
fprintf(outfile, "OFF\n%ld %ld %ld\n", points.items, triangles.items,
|
|
edges);
|
|
|
|
/* Write the points. */
|
|
traversalinit(&points);
|
|
pointloop = pointtraverse();
|
|
while (pointloop != (point) NULL) {
|
|
/* The "0.0" is here because the OFF format uses 3D coordinates. */
|
|
fprintf(outfile, " %.17g %.17g %.17g\n", pointloop[0],
|
|
pointloop[1], 0.0);
|
|
pointloop = pointtraverse();
|
|
}
|
|
|
|
/* Write the triangles. */
|
|
traversalinit(&triangles);
|
|
triangleloop.tri = triangletraverse();
|
|
triangleloop.orient = 0;
|
|
while (triangleloop.tri != (triangle *) NULL) {
|
|
org(triangleloop, p1);
|
|
dest(triangleloop, p2);
|
|
apex(triangleloop, p3);
|
|
/* The "3" means a three-vertex polygon. */
|
|
fprintf(outfile, " 3 %4d %4d %4d\n", pointmark(p1) - 1,
|
|
pointmark(p2) - 1, pointmark(p3) - 1);
|
|
triangleloop.tri = triangletraverse();
|
|
}
|
|
finishfile(outfile, argc, argv);
|
|
}
|
|
|
|
#endif /* not TRILIBRARY */
|
|
|
|
/** **/
|
|
/** **/
|
|
/********* File I/O routines end here *********/
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* quality_statistics() Print statistics about the quality of the mesh. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
void quality_statistics()
|
|
{
|
|
struct triedge triangleloop;
|
|
point p[3];
|
|
REAL cossquaretable[8];
|
|
REAL ratiotable[16];
|
|
REAL dx[3], dy[3];
|
|
REAL edgelength[3];
|
|
REAL dotproduct;
|
|
REAL cossquare;
|
|
REAL triarea;
|
|
REAL shortest, longest;
|
|
REAL trilongest2;
|
|
REAL smallestarea, biggestarea;
|
|
REAL triminaltitude2;
|
|
REAL minaltitude;
|
|
REAL triaspect2;
|
|
REAL worstaspect;
|
|
REAL smallestangle, biggestangle;
|
|
REAL radconst, degconst;
|
|
int angletable[18];
|
|
int aspecttable[16];
|
|
int aspectindex;
|
|
int tendegree;
|
|
int acutebiggest;
|
|
int i, ii, j, k;
|
|
|
|
printf("Mesh quality statistics:\n\n");
|
|
radconst = (REAL)(PI / 18.0);
|
|
degconst = (REAL)(180.0 / PI);
|
|
for (i = 0; i < 8; i++) {
|
|
cossquaretable[i] = (REAL)(cos(radconst * (REAL) (i + 1)));
|
|
cossquaretable[i] = cossquaretable[i] * cossquaretable[i];
|
|
}
|
|
for (i = 0; i < 18; i++) {
|
|
angletable[i] = 0;
|
|
}
|
|
|
|
ratiotable[0] = 1.5; ratiotable[1] = 2.0;
|
|
ratiotable[2] = 2.5; ratiotable[3] = 3.0;
|
|
ratiotable[4] = 4.0; ratiotable[5] = 6.0;
|
|
ratiotable[6] = 10.0; ratiotable[7] = 15.0;
|
|
ratiotable[8] = 25.0; ratiotable[9] = 50.0;
|
|
ratiotable[10] = 100.0; ratiotable[11] = 300.0;
|
|
ratiotable[12] = 1000.0; ratiotable[13] = 10000.0;
|
|
ratiotable[14] = 100000.0; ratiotable[15] = 0.0;
|
|
for (i = 0; i < 16; i++) {
|
|
aspecttable[i] = 0;
|
|
}
|
|
|
|
worstaspect = 0.0;
|
|
minaltitude = xmax - xmin + ymax - ymin;
|
|
minaltitude = minaltitude * minaltitude;
|
|
shortest = minaltitude;
|
|
longest = 0.0;
|
|
smallestarea = minaltitude;
|
|
biggestarea = 0.0;
|
|
worstaspect = 0.0;
|
|
smallestangle = 0.0;
|
|
biggestangle = 2.0;
|
|
acutebiggest = 1;
|
|
|
|
traversalinit(&triangles);
|
|
triangleloop.tri = triangletraverse();
|
|
triangleloop.orient = 0;
|
|
while (triangleloop.tri != (triangle *) NULL) {
|
|
org(triangleloop, p[0]);
|
|
dest(triangleloop, p[1]);
|
|
apex(triangleloop, p[2]);
|
|
trilongest2 = 0.0;
|
|
|
|
for (i = 0; i < 3; i++) {
|
|
j = plus1mod3[i];
|
|
k = minus1mod3[i];
|
|
dx[i] = p[j][0] - p[k][0];
|
|
dy[i] = p[j][1] - p[k][1];
|
|
edgelength[i] = dx[i] * dx[i] + dy[i] * dy[i];
|
|
if (edgelength[i] > trilongest2) {
|
|
trilongest2 = edgelength[i];
|
|
}
|
|
if (edgelength[i] > longest) {
|
|
longest = edgelength[i];
|
|
}
|
|
if (edgelength[i] < shortest) {
|
|
shortest = edgelength[i];
|
|
}
|
|
}
|
|
|
|
triarea = counterclockwise(p[0], p[1], p[2]);
|
|
if (triarea < smallestarea) {
|
|
smallestarea = triarea;
|
|
}
|
|
if (triarea > biggestarea) {
|
|
biggestarea = triarea;
|
|
}
|
|
triminaltitude2 = triarea * triarea / trilongest2;
|
|
if (triminaltitude2 < minaltitude) {
|
|
minaltitude = triminaltitude2;
|
|
}
|
|
triaspect2 = trilongest2 / triminaltitude2;
|
|
if (triaspect2 > worstaspect) {
|
|
worstaspect = triaspect2;
|
|
}
|
|
aspectindex = 0;
|
|
while ((triaspect2 > ratiotable[aspectindex] * ratiotable[aspectindex])
|
|
&& (aspectindex < 15)) {
|
|
aspectindex++;
|
|
}
|
|
aspecttable[aspectindex]++;
|
|
|
|
for (i = 0; i < 3; i++) {
|
|
j = plus1mod3[i];
|
|
k = minus1mod3[i];
|
|
dotproduct = dx[j] * dx[k] + dy[j] * dy[k];
|
|
cossquare = dotproduct * dotproduct / (edgelength[j] * edgelength[k]);
|
|
tendegree = 8;
|
|
for (ii = 7; ii >= 0; ii--) {
|
|
if (cossquare > cossquaretable[ii]) {
|
|
tendegree = ii;
|
|
}
|
|
}
|
|
if (dotproduct <= 0.0) {
|
|
angletable[tendegree]++;
|
|
if (cossquare > smallestangle) {
|
|
smallestangle = cossquare;
|
|
}
|
|
if (acutebiggest && (cossquare < biggestangle)) {
|
|
biggestangle = cossquare;
|
|
}
|
|
} else {
|
|
angletable[17 - tendegree]++;
|
|
if (acutebiggest || (cossquare > biggestangle)) {
|
|
biggestangle = cossquare;
|
|
acutebiggest = 0;
|
|
}
|
|
}
|
|
}
|
|
triangleloop.tri = triangletraverse();
|
|
}
|
|
|
|
shortest = (REAL)sqrt(shortest);
|
|
longest = (REAL)sqrt(longest);
|
|
minaltitude = (REAL)sqrt(minaltitude);
|
|
worstaspect = (REAL)sqrt(worstaspect);
|
|
smallestarea *= 2.0;
|
|
biggestarea *= 2.0;
|
|
if (smallestangle >= 1.0) {
|
|
smallestangle = 0.0;
|
|
} else {
|
|
smallestangle = (REAL)(degconst * acos(sqrt(smallestangle)));
|
|
}
|
|
if (biggestangle >= 1.0) {
|
|
biggestangle = 180.0;
|
|
} else {
|
|
if (acutebiggest) {
|
|
biggestangle = (REAL)(degconst * acos(sqrt(biggestangle)));
|
|
} else {
|
|
biggestangle = (REAL)(180.0 - degconst * acos(sqrt(biggestangle)));
|
|
}
|
|
}
|
|
|
|
printf(" Smallest area: %16.5g | Largest area: %16.5g\n",
|
|
smallestarea, biggestarea);
|
|
printf(" Shortest edge: %16.5g | Longest edge: %16.5g\n",
|
|
shortest, longest);
|
|
printf(" Shortest altitude: %12.5g | Largest aspect ratio: %8.5g\n\n",
|
|
minaltitude, worstaspect);
|
|
printf(" Aspect ratio histogram:\n");
|
|
printf(" 1.1547 - %-6.6g : %8d | %6.6g - %-6.6g : %8d\n",
|
|
ratiotable[0], aspecttable[0], ratiotable[7], ratiotable[8],
|
|
aspecttable[8]);
|
|
for (i = 1; i < 7; i++) {
|
|
printf(" %6.6g - %-6.6g : %8d | %6.6g - %-6.6g : %8d\n",
|
|
ratiotable[i - 1], ratiotable[i], aspecttable[i],
|
|
ratiotable[i + 7], ratiotable[i + 8], aspecttable[i + 8]);
|
|
}
|
|
printf(" %6.6g - %-6.6g : %8d | %6.6g - : %8d\n",
|
|
ratiotable[6], ratiotable[7], aspecttable[7], ratiotable[14],
|
|
aspecttable[15]);
|
|
printf(
|
|
" (Triangle aspect ratio is longest edge divided by shortest altitude)\n\n");
|
|
printf(" Smallest angle: %15.5g | Largest angle: %15.5g\n\n",
|
|
smallestangle, biggestangle);
|
|
printf(" Angle histogram:\n");
|
|
for (i = 0; i < 9; i++) {
|
|
printf(" %3d - %3d degrees: %8d | %3d - %3d degrees: %8d\n",
|
|
i * 10, i * 10 + 10, angletable[i],
|
|
i * 10 + 90, i * 10 + 100, angletable[i + 9]);
|
|
}
|
|
printf("\n");
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* statistics() Print all sorts of cool facts. */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
void statistics()
|
|
{
|
|
printf("\nStatistics:\n\n");
|
|
printf(" Input points: %d\n", inpoints);
|
|
if (refine) {
|
|
printf(" Input triangles: %d\n", inelements);
|
|
}
|
|
if (poly) {
|
|
printf(" Input segments: %d\n", insegments);
|
|
if (!refine) {
|
|
printf(" Input holes: %d\n", holes);
|
|
}
|
|
}
|
|
|
|
printf("\n Mesh points: %ld\n", points.items);
|
|
printf(" Mesh triangles: %ld\n", triangles.items);
|
|
printf(" Mesh edges: %ld\n", edges);
|
|
if (poly || refine) {
|
|
printf(" Mesh boundary edges: %ld\n", hullsize);
|
|
printf(" Mesh segments: %ld\n\n", shelles.items);
|
|
} else {
|
|
printf(" Mesh convex hull edges: %ld\n\n", hullsize);
|
|
}
|
|
if (verbose) {
|
|
quality_statistics();
|
|
printf("Memory allocation statistics:\n\n");
|
|
printf(" Maximum number of points: %ld\n", points.maxitems);
|
|
printf(" Maximum number of triangles: %ld\n", triangles.maxitems);
|
|
if (shelles.maxitems > 0) {
|
|
printf(" Maximum number of segments: %ld\n", shelles.maxitems);
|
|
}
|
|
if (viri.maxitems > 0) {
|
|
printf(" Maximum number of viri: %ld\n", viri.maxitems);
|
|
}
|
|
if (badsegments.maxitems > 0) {
|
|
printf(" Maximum number of encroached segments: %ld\n",
|
|
badsegments.maxitems);
|
|
}
|
|
if (badtriangles.maxitems > 0) {
|
|
printf(" Maximum number of bad triangles: %ld\n",
|
|
badtriangles.maxitems);
|
|
}
|
|
if (splaynodes.maxitems > 0) {
|
|
printf(" Maximum number of splay tree nodes: %ld\n",
|
|
splaynodes.maxitems);
|
|
}
|
|
printf(" Approximate heap memory use (bytes): %ld\n\n",
|
|
points.maxitems * points.itembytes
|
|
+ triangles.maxitems * triangles.itembytes
|
|
+ shelles.maxitems * shelles.itembytes
|
|
+ viri.maxitems * viri.itembytes
|
|
+ badsegments.maxitems * badsegments.itembytes
|
|
+ badtriangles.maxitems * badtriangles.itembytes
|
|
+ splaynodes.maxitems * splaynodes.itembytes);
|
|
|
|
printf("Algorithmic statistics:\n\n");
|
|
printf(" Number of incircle tests: %ld\n", incirclecount);
|
|
printf(" Number of orientation tests: %ld\n", counterclockcount);
|
|
if (hyperbolacount > 0) {
|
|
printf(" Number of right-of-hyperbola tests: %ld\n",
|
|
hyperbolacount);
|
|
}
|
|
if (circumcentercount > 0) {
|
|
printf(" Number of circumcenter computations: %ld\n",
|
|
circumcentercount);
|
|
}
|
|
if (circletopcount > 0) {
|
|
printf(" Number of circle top computations: %ld\n",
|
|
circletopcount);
|
|
}
|
|
printf("\n");
|
|
}
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/* */
|
|
/* main() or triangulate() Gosh, do everything. */
|
|
/* */
|
|
/* The sequence is roughly as follows. Many of these steps can be skipped, */
|
|
/* depending on the command line switches. */
|
|
/* */
|
|
/* - Initialize constants and parse the command line. */
|
|
/* - Read the points from a file and either */
|
|
/* - triangulate them (no -r), or */
|
|
/* - read an old mesh from files and reconstruct it (-r). */
|
|
/* - Insert the PSLG segments (-p), and possibly segments on the convex */
|
|
/* hull (-c). */
|
|
/* - Read the holes (-p), regional attributes (-pA), and regional area */
|
|
/* constraints (-pa). Carve the holes and concavities, and spread the */
|
|
/* regional attributes and area constraints. */
|
|
/* - Enforce the constraints on minimum angle (-q) and maximum area (-a). */
|
|
/* Also enforce the conforming Delaunay property (-q and -a). */
|
|
/* - Compute the number of edges in the resulting mesh. */
|
|
/* - Promote the mesh's linear triangles to higher order elements (-o). */
|
|
/* - Write the output files and print the statistics. */
|
|
/* - Check the consistency and Delaunay property of the mesh (-C). */
|
|
/* */
|
|
/*****************************************************************************/
|
|
|
|
#ifdef TRILIBRARY
|
|
|
|
void triangulate(triswitches, in, out, vorout)
|
|
char *triswitches;
|
|
struct triangulateio *in;
|
|
struct triangulateio *out;
|
|
struct triangulateio *vorout;
|
|
|
|
#else /* not TRILIBRARY */
|
|
|
|
int main(argc, argv)
|
|
int argc;
|
|
char **argv;
|
|
|
|
#endif /* not TRILIBRARY */
|
|
|
|
{
|
|
REAL *holearray; /* Array of holes. */
|
|
REAL *regionarray; /* Array of regional attributes and area constraints. */
|
|
#ifndef TRILIBRARY
|
|
FILE *polyfile;
|
|
#endif /* not TRILIBRARY */
|
|
#ifndef NO_TIMER
|
|
/* Variables for timing the performance of Triangle. The types are */
|
|
/* defined in sys/time.h. */
|
|
struct timeval tv0, tv1, tv2, tv3, tv4, tv5, tv6;
|
|
struct timezone tz;
|
|
#endif /* NO_TIMER */
|
|
|
|
#ifndef NO_TIMER
|
|
gettimeofday(&tv0, &tz);
|
|
#endif /* NO_TIMER */
|
|
|
|
triangleinit();
|
|
#ifdef TRILIBRARY
|
|
parsecommandline(1, &triswitches);
|
|
#else /* not TRILIBRARY */
|
|
parsecommandline(argc, argv);
|
|
#endif /* not TRILIBRARY */
|
|
|
|
#ifdef TRILIBRARY
|
|
transfernodes(in->pointlist, in->pointattributelist, in->pointmarkerlist,
|
|
in->numberofpoints, in->numberofpointattributes);
|
|
#else /* not TRILIBRARY */
|
|
readnodes(innodefilename, inpolyfilename, &polyfile);
|
|
#endif /* not TRILIBRARY */
|
|
|
|
#ifndef NO_TIMER
|
|
if (!quiet) {
|
|
gettimeofday(&tv1, &tz);
|
|
}
|
|
#endif /* NO_TIMER */
|
|
|
|
#ifdef CDT_ONLY
|
|
hullsize = delaunay(); /* Triangulate the points. */
|
|
#else /* not CDT_ONLY */
|
|
if (refine) {
|
|
/* Read and reconstruct a mesh. */
|
|
#ifdef TRILIBRARY
|
|
hullsize = reconstruct(in->trianglelist, in->triangleattributelist,
|
|
in->trianglearealist, in->numberoftriangles,
|
|
in->numberofcorners, in->numberoftriangleattributes,
|
|
in->segmentlist, in->segmentmarkerlist,
|
|
in->numberofsegments);
|
|
#else /* not TRILIBRARY */
|
|
hullsize = reconstruct(inelefilename, areafilename, inpolyfilename,
|
|
polyfile);
|
|
#endif /* not TRILIBRARY */
|
|
} else {
|
|
hullsize = delaunay(); /* Triangulate the points. */
|
|
}
|
|
#endif /* not CDT_ONLY */
|
|
|
|
#ifndef NO_TIMER
|
|
if (!quiet) {
|
|
gettimeofday(&tv2, &tz);
|
|
if (refine) {
|
|
printf("Mesh reconstruction");
|
|
} else {
|
|
printf("Delaunay");
|
|
}
|
|
printf(" milliseconds: %ld\n", 1000l * (tv2.tv_sec - tv1.tv_sec)
|
|
+ (tv2.tv_usec - tv1.tv_usec) / 1000l);
|
|
}
|
|
#endif /* NO_TIMER */
|
|
|
|
/* Ensure that no point can be mistaken for a triangular bounding */
|
|
/* box point in insertsite(). */
|
|
infpoint1 = (point) NULL;
|
|
infpoint2 = (point) NULL;
|
|
infpoint3 = (point) NULL;
|
|
|
|
if (useshelles) {
|
|
checksegments = 1; /* Segments will be introduced next. */
|
|
if (!refine) {
|
|
/* Insert PSLG segments and/or convex hull segments. */
|
|
#ifdef TRILIBRARY
|
|
insegments = formskeleton(in->segmentlist, in->segmentmarkerlist,
|
|
in->numberofsegments);
|
|
#else /* not TRILIBRARY */
|
|
insegments = formskeleton(polyfile, inpolyfilename);
|
|
#endif /* not TRILIBRARY */
|
|
}
|
|
}
|
|
|
|
#ifndef NO_TIMER
|
|
if (!quiet) {
|
|
gettimeofday(&tv3, &tz);
|
|
if (useshelles && !refine) {
|
|
printf("Segment milliseconds: %ld\n",
|
|
1000l * (tv3.tv_sec - tv2.tv_sec)
|
|
+ (tv3.tv_usec - tv2.tv_usec) / 1000l);
|
|
}
|
|
}
|
|
#endif /* NO_TIMER */
|
|
|
|
if (poly) {
|
|
#ifdef TRILIBRARY
|
|
holearray = in->holelist;
|
|
holes = in->numberofholes;
|
|
regionarray = in->regionlist;
|
|
regions = in->numberofregions;
|
|
#else /* not TRILIBRARY */
|
|
readholes(polyfile, inpolyfilename, &holearray, &holes,
|
|
®ionarray, ®ions);
|
|
#endif /* not TRILIBRARY */
|
|
if (!refine) {
|
|
/* Carve out holes and concavities. */
|
|
carveholes(holearray, holes, regionarray, regions);
|
|
}
|
|
} else {
|
|
/* Without a PSLG, there can be no holes or regional attributes */
|
|
/* or area constraints. The following are set to zero to avoid */
|
|
/* an accidental free() later. */
|
|
holes = 0;
|
|
regions = 0;
|
|
}
|
|
|
|
#ifndef NO_TIMER
|
|
if (!quiet) {
|
|
gettimeofday(&tv4, &tz);
|
|
if (poly && !refine) {
|
|
printf("Hole milliseconds: %ld\n", 1000l * (tv4.tv_sec - tv3.tv_sec)
|
|
+ (tv4.tv_usec - tv3.tv_usec) / 1000l);
|
|
}
|
|
}
|
|
#endif /* NO_TIMER */
|
|
|
|
#ifndef CDT_ONLY
|
|
if (quality) {
|
|
enforcequality(); /* Enforce angle and area constraints. */
|
|
}
|
|
#endif /* not CDT_ONLY */
|
|
|
|
#ifndef NO_TIMER
|
|
if (!quiet) {
|
|
gettimeofday(&tv5, &tz);
|
|
#ifndef CDT_ONLY
|
|
if (quality) {
|
|
printf("Quality milliseconds: %ld\n",
|
|
1000l * (tv5.tv_sec - tv4.tv_sec)
|
|
+ (tv5.tv_usec - tv4.tv_usec) / 1000l);
|
|
}
|
|
#endif /* not CDT_ONLY */
|
|
}
|
|
#endif /* NO_TIMER */
|
|
|
|
/* Compute the number of edges. */
|
|
edges = (3l * triangles.items + hullsize) / 2l;
|
|
|
|
if (order > 1) {
|
|
highorder(); /* Promote elements to higher polynomial order. */
|
|
}
|
|
if (!quiet) {
|
|
printf("\n");
|
|
}
|
|
|
|
#ifdef TRILIBRARY
|
|
out->numberofpoints = points.items;
|
|
out->numberofpointattributes = nextras;
|
|
out->numberoftriangles = triangles.items;
|
|
out->numberofcorners = (order + 1) * (order + 2) / 2;
|
|
out->numberoftriangleattributes = eextras;
|
|
out->numberofedges = edges;
|
|
if (useshelles) {
|
|
out->numberofsegments = shelles.items;
|
|
} else {
|
|
out->numberofsegments = hullsize;
|
|
}
|
|
if (vorout != (struct triangulateio *) NULL) {
|
|
vorout->numberofpoints = triangles.items;
|
|
vorout->numberofpointattributes = nextras;
|
|
vorout->numberofedges = edges;
|
|
}
|
|
#endif /* TRILIBRARY */
|
|
/* If not using iteration numbers, don't write a .node file if one was */
|
|
/* read, because the original one would be overwritten! */
|
|
if (nonodewritten || (noiterationnum && readnodefile)) {
|
|
if (!quiet) {
|
|
#ifdef TRILIBRARY
|
|
printf("NOT writing points.\n");
|
|
#else /* not TRILIBRARY */
|
|
printf("NOT writing a .node file.\n");
|
|
#endif /* not TRILIBRARY */
|
|
}
|
|
numbernodes(); /* We must remember to number the points. */
|
|
} else {
|
|
#ifdef TRILIBRARY
|
|
writenodes(&out->pointlist, &out->pointattributelist,
|
|
&out->pointmarkerlist);
|
|
#else /* not TRILIBRARY */
|
|
writenodes(outnodefilename, argc, argv); /* Numbers the points too. */
|
|
#endif /* TRILIBRARY */
|
|
}
|
|
if (noelewritten) {
|
|
if (!quiet) {
|
|
#ifdef TRILIBRARY
|
|
printf("NOT writing triangles.\n");
|
|
#else /* not TRILIBRARY */
|
|
printf("NOT writing an .ele file.\n");
|
|
#endif /* not TRILIBRARY */
|
|
}
|
|
} else {
|
|
#ifdef TRILIBRARY
|
|
writeelements(&out->trianglelist, &out->triangleattributelist);
|
|
#else /* not TRILIBRARY */
|
|
writeelements(outelefilename, argc, argv);
|
|
#endif /* not TRILIBRARY */
|
|
}
|
|
/* The -c switch (convex switch) causes a PSLG to be written */
|
|
/* even if none was read. */
|
|
if (poly || convex) {
|
|
/* If not using iteration numbers, don't overwrite the .poly file. */
|
|
if (nopolywritten || noiterationnum) {
|
|
if (!quiet) {
|
|
#ifdef TRILIBRARY
|
|
printf("NOT writing segments.\n");
|
|
#else /* not TRILIBRARY */
|
|
printf("NOT writing a .poly file.\n");
|
|
#endif /* not TRILIBRARY */
|
|
}
|
|
} else {
|
|
#ifdef TRILIBRARY
|
|
writepoly(&out->segmentlist, &out->segmentmarkerlist);
|
|
out->numberofholes = holes;
|
|
out->numberofregions = regions;
|
|
if (poly) {
|
|
out->holelist = in->holelist;
|
|
out->regionlist = in->regionlist;
|
|
} else {
|
|
out->holelist = (REAL *) NULL;
|
|
out->regionlist = (REAL *) NULL;
|
|
}
|
|
#else /* not TRILIBRARY */
|
|
writepoly(outpolyfilename, holearray, holes, regionarray, regions,
|
|
argc, argv);
|
|
#endif /* not TRILIBRARY */
|
|
}
|
|
}
|
|
#ifndef TRILIBRARY
|
|
#ifndef CDT_ONLY
|
|
if (regions > 0) {
|
|
free(regionarray);
|
|
}
|
|
#endif /* not CDT_ONLY */
|
|
if (holes > 0) {
|
|
free(holearray);
|
|
}
|
|
if (geomview) {
|
|
writeoff(offfilename, argc, argv);
|
|
}
|
|
#endif /* not TRILIBRARY */
|
|
if (edgesout) {
|
|
#ifdef TRILIBRARY
|
|
writeedges(&out->edgelist, &out->edgemarkerlist);
|
|
#else /* not TRILIBRARY */
|
|
writeedges(edgefilename, argc, argv);
|
|
#endif /* not TRILIBRARY */
|
|
}
|
|
if (voronoi) {
|
|
#ifdef TRILIBRARY
|
|
writevoronoi(&vorout->pointlist, &vorout->pointattributelist,
|
|
&vorout->pointmarkerlist, &vorout->edgelist,
|
|
&vorout->edgemarkerlist, &vorout->normlist);
|
|
#else /* not TRILIBRARY */
|
|
writevoronoi(vnodefilename, vedgefilename, argc, argv);
|
|
#endif /* not TRILIBRARY */
|
|
}
|
|
if (neighbors) {
|
|
#ifdef TRILIBRARY
|
|
writeneighbors(&out->neighborlist);
|
|
#else /* not TRILIBRARY */
|
|
writeneighbors(neighborfilename, argc, argv);
|
|
#endif /* not TRILIBRARY */
|
|
}
|
|
|
|
if (!quiet) {
|
|
#ifndef NO_TIMER
|
|
gettimeofday(&tv6, &tz);
|
|
printf("\nOutput milliseconds: %ld\n",
|
|
1000l * (tv6.tv_sec - tv5.tv_sec)
|
|
+ (tv6.tv_usec - tv5.tv_usec) / 1000l);
|
|
printf("Total running milliseconds: %ld\n",
|
|
1000l * (tv6.tv_sec - tv0.tv_sec)
|
|
+ (tv6.tv_usec - tv0.tv_usec) / 1000l);
|
|
#endif /* NO_TIMER */
|
|
|
|
statistics();
|
|
}
|
|
|
|
#ifndef REDUCED
|
|
if (docheck) {
|
|
checkmesh();
|
|
checkdelaunay();
|
|
}
|
|
#endif /* not REDUCED */
|
|
|
|
triangledeinit();
|
|
#ifndef TRILIBRARY
|
|
return 0;
|
|
#endif /* not TRILIBRARY */
|
|
}
|