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Reports (Research Report) Year : 2006

Anisotropic Diagrams: Labelle Shewchuk approach revisited

Jean-Daniel Boissonnat
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Mariette Yvinec


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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Dates and versions

inria-00070277 , version 1 (19-05-2006)


  • 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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