Efficient Computation of 3D Clipped Voronoi Diagram

Dong-Ming Yan 1, 2 Wenping Wang 2 Bruno Lévy 1 Yang Liu 1
1 ALICE - Geometry and Lighting
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : The Voronoi diagram is a fundamental geometry structure widely used in various fields, especially in computer graphics and geometry computing. For a set of points in a compact 3D domain (i.e. a finite 3D volume), some Voronoi cells of their Voronoi diagram are infinite, but in practice only the parts of the cells inside the domain are needed, as when computing the centroidal Voronoi tessellation. Such a Voronoi diagram confined to a compact domain is called a clipped Voronoi diagram. We present an efficient algorithm for computing the clipped Voronoi diagram for a set of sites with respect to a compact 3D volume, assuming that the volume is represented as a tetrahedral mesh. We also describe an application of the proposed method to implementing a fast method for optimal tetrahedral mesh generation based on the centroidal Voronoi tessellation.
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Dong-Ming Yan, Wenping Wang, Bruno Lévy, Yang Liu. Efficient Computation of 3D Clipped Voronoi Diagram. Geometric Modeling and Processing, University of Cantabria, Jun 2010, Castro Urdiales, Spain. pp.269-282, ⟨10.1007/978-3-642-13411-1_18⟩. ⟨inria-00547794⟩

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