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Anisotropic Diagrams: Labelle Shewchuk approach revisited

Jean-Daniel Boissonnat 1 Camille Wormser 1 Mariette yvinec 1 
1 GEOMETRICA - Geometric computing
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.
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Submitted on : Friday, May 19, 2006 - 7:50:47 PM
Last modification on : Friday, February 4, 2022 - 3:16:25 AM
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  • HAL Id : inria-00070277, version 1



Jean-Daniel Boissonnat, Camille Wormser, Mariette yvinec. Anisotropic Diagrams: Labelle Shewchuk approach revisited. [Research Report] RR-5741, INRIA. 2006, pp.23. ⟨inria-00070277⟩



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