Anisotropic Diagrams: Labelle Shewchuk approach revisitedReport as inadecuate

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* Corresponding author 1 GEOMETRICA - Geometric computing CRISAM - Inria Sophia Antipolis - Méditerranée 2 GEOMETRICA - Geometric computing INRIA Futurs, CRISAM - Inria Sophia Antipolis - Méditerranée

Abstract : F. Labelle and J. Shewchuk have proposed a discrete definition of anisotropic Voronoi diagrams. These diagrams are parametrized by a metric field. Under mild hypotheses on the metric field, such Voronoi diagrams can be refined so that their dual is a triangulation, with elements shaped according to the specified anisotropic metric field. We propose an alternative view of the construction of these diagrams and a variant of Labelle and Shewchuk-s meshing algorithm. This variant computes the Voronoi vertices using a higher dimensional power diagram and refines the diagram as long as dual triangles overlap. We see this variant as a first step toward a 3-dimensional anisotropic meshing algorithm.

keyword : anisotropic Voronoi diagram anisotropic meshing

Author: Jean-Daniel Boissonnat - Camille Wormser - Mariette Yvinec -



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