Anisotropic voronoi diagrams and guaranteed-quality anisotropic mesh generation

We introduce anisotropic Voronoi diagrams, a generalization of multiplicatively weighted Voronoi diagrams suitable for generating guaranteed-quality meshes of domains in which long, skinny triangles are required, and where the desired anisotropy varies over the domain. We discuss properties of anisotropic Voronoi diagrams of arbitrary dimensionality—most notably circumstances in which a site can see its entire Voronoi cell. In two dimensions, the anisotropic Voronoi diagram dualizes to a triangulation under these same circumstances. We use these properties to develop an algorithm for anisotropic triangular mesh generation in which no triangle has an angle smaller than 20◦ , as measured from the skewed perspective of any point in the triangle. Categories and Subject Descriptors F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems General Terms Algorithms, Theory Keywords Anisotropic Voronoi diagram, anisotropic mesh generation

• Type: Conference
• Year: 2003
• Where: COMPGEOM
• Authors: François Labelle, Jonathan Richard Shewchuk
• Keywords: Anisotropic Voronoi Diagram, COMPGEOM 2003, Entire Voronoi Cell, Keywords Anisotropic Voronoi