Anisotropic diagrams: Labelle Shewchuk approach revisited

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.