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A Level Set Method for the Construction of Anisotropic Boundary-Conforming Voronoi Regions and Delaunay Triangulations

Keskin, Umit and Joaquim Peiro

Research Notes, 20th International Meshing Roundtable, Springer-Verlag, pp.Research Note, October 23-26 2011


20th International Meshing Roundtable
Paris, France
October 23-26, 2011

Department of Aeronautics, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom

We interpret a Voronoi region as the shape achieved by a crystal that grows from a seed and stops growing when it reaches either the domain boundary or another crystal. Using this analogy we devise a method for generating anisotropic boundary-conforming Voronoi regions and their dual Delaunay triangulation for a set of points. The method simulates the propagation of crystals as evolving fronts modelled by a level set method. The generation of anisotropic Voronoi regions is achieved by re-interpreting the user-specificied Riemmanian metric in terms of the propagation speed normal to the boundary of the crystal.

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