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.
https://hal.inria.fr/inria-00336798
Contributor : Mariette Yvinec
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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
Long-term archiving on: Monday, June 7, 2010 - 8:26:16 PM
