triangle三角剖分

/*****************************************************************************/ /* */ /* 888888888 ,o, / 888 */ /* 888 88o88o " o8888o 88o8888o o88888o 888 o88888o */ /* 888 888 888 88b 888 888 888 888 888 d888 88b */ /* 888 888 888 o88^o888 888 888 "88888" 888 8888oo888 */ /* 888 888 888 C888 888 888 888 / 888 q888 */ /* 888 888 888 "88o^888 888 888 Cb 888 "88oooo" */ /* "8oo8D */ /* */ /* A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator. */ /* (triangle.c) */ /* */ /* Version 1.6 */ /* July 28, 2005 */ /* */ /* Copyright 1993, 1995, 1997, 1998, 2002, 2005 */ /* Jonathan Richard Shewchuk */ /* 2360 Woolsey #H */ /* Berkeley, California 94705-1927 */ /* [email protected] */ /* */ /* This program may be freely redistributed under the condition that the */ /* copyright notices (including this entire header and the copyright */ /* notice printed when the `-h' switch is selected) are not removed, and */ /* no compensation is received. Private, research, and institutional */ /* use is free. You may distribute modified versions of this code UNDER */ /* THE CONDITION THAT THIS CODE AND ANY MODIFICATIONS MADE TO IT IN THE */ /* SAME FILE REMAIN UNDER COPYRIGHT OF THE ORIGINAL AUTHOR, BOTH SOURCE */ /* AND OBJECT CODE ARE MADE FREELY AVAILABLE WITHOUT CHARGE, AND CLEAR */ /* NOTICE IS GIVEN OF THE MODIFICATIONS. Distribution of this code as */ /* part of a commercial system is permissible ONLY BY DIRECT ARRANGEMENT */ /* WITH THE AUTHOR. (If you are not directly supplying this code to a */ /* customer, and you are instead telling them how they can obtain it for */ /* free, then you are not required to make any arrangement with me.) */ /* */ /* Hypertext instructions for Triangle are available on the Web at */ /* */ /* http://www.cs.cmu.edu/~quake/triangle.html */ /* */ /* Disclaimer: Neither I nor Carnegie Mellon warrant this code in any way */ /* whatsoever. This code is provided "as-is". Use at your own risk. */ /* */ /* Some of the references listed below are marked with an asterisk. [*] */ /* These references are available for downloading from the Web page */ /* */ /* http://www.cs.cmu.edu/~quake/triangle.research.html */ /* */ /* Three papers discussing aspects of Triangle are available. A short */ /* overview appears in "Triangle: Engineering a 2D Quality Mesh */ /* Generator and Delaunay Triangulator," in Applied Computational */ /* Geometry: Towards Geometric Engineering, Ming C. Lin and Dinesh */ /* Manocha, editors, Lecture Notes in Computer Science volume 1148, */ /* pages 203-222, Springer-Verlag, Berlin, May 1996 (from the First ACM */ /* Workshop on Applied Computational Geometry). [*] */ /* */ /* The algorithms are discussed in the greatest detail in "Delaunay */ /* Refinement Algorithms for Triangular Mesh Generation," Computational */ /* Geometry: Theory and Applications 22(1-3):21-74, May 2002. [*] */ /* */ /* More detail about the data structures may be found in my dissertation: */ /* "Delaunay Refinement Mesh Generation," Ph.D. thesis, Technical Report */ /* CMU-CS-97-137, School of Computer Science, Carnegie Mellon University, */ /* Pittsburgh, Pennsylvania, 18 May 1997. [*] */ /* */ /* Triangle was created as part of the Quake Project in the School of */ /* Computer Science at Carnegie Mellon University. For further */ /* information, see Hesheng Bao, Jacobo Bielak, Omar Ghattas, Loukas F. */ /* Kallivokas, David R. O'Hallaron, Jonathan R. Shewchuk, and Jifeng Xu, */ /* "Large-scale Simulation of Elastic Wave Propagation in Heterogeneous */ /* Media on Parallel Computers," Computer Methods in Applied Mechanics */ /* and Engineering 152(1-2):85-102, 22 January 1998. */ /* */ /* Triangle's Delaunay refinement algorithm for quality mesh generation is */ /* a hybrid of one due to Jim Ruppert, "A Delaunay Refinement Algorithm */ /* for Quality 2-Dimensional Mesh Generation," Journal of Algorithms */ /* 18(3):548-585, May 1995 [*], and one due to L. Paul Chew, "Guaranteed- */ /* Quality Mesh Generation for Curved Surfaces," Proceedings of the Ninth */ /* Annual Symposium on Computational Geometry (San Diego, California), */ /* pages 274-280, Association for Computing Machinery, May 1993, */ /* http://portal.acm.org/citation.cfm?id=161150 . */ /* */ /* The Delaunay refinement algorithm has been modified so that it meshes */ /* domains with small input angles well, as described in Gary L. Miller, */ /* Steven E. Pav, and Noel J. Walkington, "When and Why Ruppert's */ /* Algorithm Works," Twelfth International Meshing Roundtable, pages */ /* 91-102, Sandia National Laboratories, September 2003. [*] */ /* */ /* My implementation of the divide-and-conquer and incremental Delaunay */ /* triangulation algorithms follows closely the presentation of Guibas */ /* and Stolfi, even though I use a triangle-based data structure instead */ /* of their quad-edge data structure. (In fact, I originally implemented */ /* Triangle using the quad-edge data structure, but the switch to a */ /* triangle-based data structure sped Triangle by a factor of two.) The */ /* mesh manipulation primitives and the two aforementioned Delaunay */ /* triangulation algorithms are described by Leonidas J. Guibas and Jorge */ /* Stolfi, "Primitives for the Manipulation of General Subdivisions and */ /* the Computation of Voronoi Diagrams," ACM Transactions on Graphics */ /* 4(2):74-123, April 1985, http://portal.acm.org/citation.c