Anisotropic diagrams: Labelle Shewchuk approach revisited

F. Labelle and J. Shewchuk [3] 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 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.

• Type: Journal
• Year: 2008
• Where: TCS
• Authors: Jean-Daniel Boissonnat, Camille Wormser, Mariette Yvinec
• Keywords: Anisotropic Voronoi Diagrams, Metric Field, TCS 2008, Theoretical Computer Science, Voronoi Diagrams