Delaunay Refinement for Piecewise Smooth Complexes

We present a Delaunay refinement algorithm for meshing a piecewise smooth complex in three dimensions. The algorithm protects edges with weighted points to avoid the difficulty posed by small angles between adjacent input elements. These weights are chosen to mimic the local feature size and to sati...

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Bibliographic Details
Published in:Discrete & computational geometry 2010, Vol.43 (1), p.121-166
Main Authors: Cheng, Siu-Wing, Dey, Tamal K., Ramos, Edgar A.
Format: Article
Language:English
Subjects:
Algorithms
Combinatorics
Computational Mathematics and Numerical Analysis
Mathematics
Mathematics and Statistics
Topology
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Summary:We present a Delaunay refinement algorithm for meshing a piecewise smooth complex in three dimensions. The algorithm protects edges with weighted points to avoid the difficulty posed by small angles between adjacent input elements. These weights are chosen to mimic the local feature size and to satisfy a Lipschitz-like property. A Delaunay refinement algorithm using the weighted Voronoi diagram is shown to terminate with the recovery of the topology of the input. Guaranteed bounds on the aspect ratios, normal variation, and dihedral angles are also provided. To this end, we present new concepts and results including a new definition of local feature size and a proof for a generalized topological ball property.
ISSN:0179-5376
1432-0444
DOI:10.1007/s00454-008-9109-3