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Anisotropic Diagrams: Labelle Shewchuk approach revisited

Jean-Daniel Boissonnat 1, 2 Camille Wormser 1, * Mariette Yvinec 1
* 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.
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Submitted on : Wednesday, November 5, 2008 - 10:29:20 AM
Last modification on : Friday, April 12, 2019 - 10:18:03 AM
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Jean-Daniel Boissonnat, Camille Wormser, Mariette Yvinec. Anisotropic Diagrams: Labelle Shewchuk approach revisited. Theoretical Computer Science, Elsevier, 2008, pp.163-173. ⟨10.1016/j.tcs.2008.08.006⟩. ⟨inria-00336798⟩

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