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Abstract: We present a simple new algorithm for triangulating polygons and planar straightline graphs. It provides "shape" and "size" guarantees: ffl All triangles have a bounded aspect ratio. ffl The number of triangles is within a constant factor of optimal. Such "quality" triangulations are desirable as meshes for the finite element method, in which the running time generally increases with the number of triangles, and where the convergence and stability may be hurt by very skinny triangles. The... (Update)
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.... Delaunay refinement algorithms typically bound the sizes of the elements they create in terms of this or a similar definition oflfs [17, 21].lfs is a continuous function that is positive everywhere and suggests a rough upper bound on how large high quality elements can be. It...
.... to the traditional setting, where appropriate measures of quality and algorithms to compute highquality meshes are well known [1, 2, 4, 13, 15]. Acknowledgments The authors thank David Bunde, Michael Garland, Shripad Thite, and especially Bob Haber for several helpful...
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9: Guaranteed-quality triangular meshes (context) - Chew - 1989
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BibTeX entry: (Update)
Jim Ruppert. A Delaunay Refinement Algorithm for Quality 2-Dimensional Mesh Generation. Journal of Algorithms 18(3):548--585, May 1995. http://citeseer.nj.nec.com/article/ruppert94delaunay.html More
@article{ ruppert95delaunay,
author = "Jim Ruppert",
title = "A Delaunay Refinement Algorithm for Quality 2-Dimensional Mesh Generation",
journal = "J. Algorithms",
volume = "18",
number = "3",
pages = "548-585",
year = "1995",
url = "citeseer.nj.nec.com/article/ruppert94delaunay.html" }
Citations (may not include all citations):1084 Computational Geometry -- an Introduction (context) - Preparata, Shamos - 1985
216 Primitives for the manipulation of general subdivisions and .. (context) - Guibas, Stolfi - 1985
119 A sweepline algorithm for Voronoi diagrams (context) - Fortune - 1987
100 Mesh generation and optimal triangulation - Bern, Eppstein - 1992
93 Provably good mesh generation - Bern, Eppstein et al. - 1990
66 Constrained Delaunay triangulation (context) - Chew - 1989
57 Quality mesh generation in three dimensions - Mitchell, Vavasis - 1992
42 Guaranteed-quality triangular meshes (context) - Chew - 1989
42 Guaranteed-quality mesh generation for curved surfaces (context) - Chew - 1993
34 A new and simple algorithm for quality 2-dimensional mesh ge.. (context) - Ruppert - 1992
34 A new and simple algorithm for quality 2-dimensional mesh ge.. (context) - Ruppert - 1993
27 Generalized Delaunay triangulation for planar graphs (context) - Lee, Lin - 1986
21 Nonobtuse triangulation of polygons (context) - Baker, Grosse et al. - 1988
15 Coping with inconsistencies: A new approach to produce quali.. (context) - Melissaratos, Souvaine - 1992
15 On good triangulations in three dimensions (context) - Dey, Bajaj et al. - 1991
9 Implementing Watson's algorithm in three dimensions (context) - Field - 1986
7 Constrained Delaunay triangulations and Voronoi diagrams wit.. (context) - Seidel - 1988
6 Results on Triangulation and High Quality Mesh Generation (context) - Ruppert - 1992
2 Three-dimensional unstructured grid generation based on Dela.. (context) - Meshkat, Ruppert et al. - 1991
1 Delaunay edge refinements (context) - Saalfield - 1991
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