Locally uniform anisotropic meshing

  • Authors:
  • Jean-Daniel Boissonnat;Camille Wormser;Mariette Yvinec

  • Affiliations:
  • INRIA Sophia Antipolis, Sophia Antipolis, France;INRIA Sophia Antipolis, Sophia Antipolis, France;INRIA Sophia Antipolis, Sophia Antipolis, France

  • Venue:
  • Proceedings of the twenty-fourth annual symposium on Computational geometry
  • Year:
  • 2008

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Abstract

Various definitions of so called anisotropic Voronoi diagrams have been proposed. These diagrams are typically parameterized 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 approach to anisotropic mesh generation, relying on the notion of locally uniform anisotropic mesh. A locally uniform anisotropic mesh is a mesh such that the star around each vertex v coincides with the star that v would have if the metric on the domain was uniform and equal to the metric at v. This definition allows to define a simple refinement algorithm which relies on elementary predicates, and provides, after completion, an anisotropic mesh in dimensions 2 and 3. A practical implementation has been done in the 2D case.