Sliver-free perturbation for the Delaunay tetrahedrization

Authors:
Kokichi Sugihara
Affiliations:
Department of Mathematical Informatics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
Venue:
Computer-Aided Design
Year:
2007

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Abstract

This paper studies symbolic perturbation schemes in the context of Delaunay meshing in the three-dimensional space. Symbolic perturbation is a general and powerful technique for removing geometric degeneracy. However, a straightforward application of this technique to Delaunay meshing does not work well, because the perturbation generates volume-zero tetrahedra, called slivers, which should not appear in meshes for the finite element method. First we characterize the set of directions in which a point can be perturbed without generating slivers. Next, as an application of this characterization, we construct a graph-theoretic method for finding a sliver-free perturbation. We also show that an ordinary symbolic perturbation cannot avoid slivers for integer-grid points, and point out that there is a generalized type of perturbation that can avoid slivers completely.