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Abstract: Scott A. Mitchell Stephen A. Vavasis y Abstract We show how to triangulate a three dimensional polyhedral region with holes. Our triangulation is optimal in the following two senses. First, our triangulation achieves the best possible aspect ratio up to a constant. Second, for any other triangulation of the same region into m triangles with bounded aspect ratio, our triangulation has size n = O(m). Such a triangulation is desired as an initial mesh for a finite element mesh refinement... (Update)
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BibTeX entry: (Update)
S. A. Mitchell and S. A. Vavasis. Quality mesh generation in three dimensions. Proc. ACM Symposium on Computational Geometry, pp 212-221, 1992. http://citeseer.ist.psu.edu/mitchell92quality.html More
@inproceedings{ mitchell92quality,
author = "Scott A. Mitchell and Stephen A. Vavasis",
title = "Quality Mesh Generation in Three Dimensions",
booktitle = "Symposium on Computational Geometry",
pages = "212-221",
year = "1992",
url = "citeseer.ist.psu.edu/mitchell92quality.html" }
Citations (may not include all citations):481 Algorithms in combinatorial geometry (context) - Edelsbrunner - 1987
117 Mesh Generation and Optimal Triangulation - Bern, Eppstein - 1991
88 the angle condition in the finite element method (context) - Babuska, Aziz - 1976
86 Constrained Delaunay Triangulation (context) - Chew
67 A Unified Geometric Approach to Graph Separators (context) - Miller, Teng et al. - 1991
48 Guaranteed-Quality Triangular Meshes (context) - Chew
46 A Comparison of Adaptive Refinement Techniques for Elliptic .. (context) - Mitchell - 1987
31 Separators in Two and Three Dimensions (context) - Miller, Thurston - 1990
22 Edge-insertion for optimal triangulations - Bern, Edelsbrunner et al. - 1991
20 Triangulating polygons without large angles - Bern, Dobkin et al. - 1991
14 Unified Multilevel Adaptive Finite Element Methods for Ellip.. (context) - Mitchell - 1988
5 Numerical Grid Generation in Computational Fluid Dynamics (context) - Hauser, Taylor - 1986
5 Xerox Palo Alto Research Center (context) - Bern, Eppstein et al. - 1990
4 A Class of Data Structures for 2-D and 3-D adaptive mesh ref.. (context) - Carey, Sharna et al. - 1988
2 th ACM Symposium on Computational Geometry (context) - Chazelle, Palios et al. - 1989
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Documents on the same site (http://endo.sandia.gov/~samitch/csstuff/csguide.html): More
Cardinality Bounds for Triangulations with Bounded Minimum Angle - Mitchell (1994) (Correct)
Linear-size Nonobtuse Triangulation of Polygons - Bern, Mitchell, Ruppert (1994) (Correct)
Edge Insertion for Optimal Triangulations - Bern, Edelsbrunner, Eppstein.. (1993) (Correct)
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