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“Efficient Computation of 3D Clipped Voronoi Diagram”

Dong-Ming Yan, Wenping Wang, Bruno Lévy and Yang Liu

GMP 2010 Conference Proceedings

Abstract: The Voronoi diagram is a fundamental geometry structure widely used in various fields, especially in computer graphics and geom- etry 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 dia- gram confined to a compact domain is called a clipped Voronoi diagram. We present an efficient algorithm for computing the clipped Voronoi di- agram 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.

## BibTex reference

@INPROCEEDINGS{Yan:ECC:2010,
AUTHOR = "Dong-Ming Yan and Wenping Wang and Bruno Lévy and Yang Liu",
TITLE = "Efficient Computation of 3D Clipped Voronoi Diagram",
BOOKTITLE = "GMP 2010 Conference Proceedings",
}