Efficient Computation of 3D Clipped Voronoi Diagram

  • Dong-Ming Yan
  • Wenping Wang
  • Bruno Lévy
  • Yang Liu
Conference paper

DOI: 10.1007/978-3-642-13411-1_18

Volume 6130 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Yan DM., Wang W., Lévy B., Liu Y. (2010) Efficient Computation of 3D Clipped Voronoi Diagram. In: Mourrain B., Schaefer S., Xu G. (eds) Advances in Geometric Modeling and Processing. GMP 2010. Lecture Notes in Computer Science, vol 6130. Springer, Berlin, Heidelberg

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.

Keywords

Voronoi diagram Delaunay triangulation centroidal Voronoi tessellation tetrahedral meshing 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Dong-Ming Yan
    • 1
    • 2
  • Wenping Wang
    • 1
    • 2
  • Bruno Lévy
    • 1
    • 2
  • Yang Liu
    • 1
    • 2
  1. 1.The University of Hong KongHong KongChina
  2. 2.Project Alice, INRIANancyFrance