Efficient Computation of 3D Clipped Voronoi Diagram
Identifieur interne : 002C34 ( Main/Exploration ); précédent : 002C33; suivant : 002C35Efficient Computation of 3D Clipped Voronoi Diagram
Auteurs : Dong-Ming Yan [France] ; Wenping Wang [Hong Kong] ; Bruno Lévy [France] ; Yang Liu [France]Source :
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.
Url:
DOI: 10.1007/978-3-642-13411-1_18
Affiliations:
- France, Hong Kong
- Grand Est, Lorraine (région)
- Nancy
- Institut national polytechnique de Lorraine, Université Nancy 2, Université de Lorraine
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Le document en format XML
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<front><div type="abstract" xml:lang="en">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.</div>
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<tree><country name="France"><region name="Grand Est"><name sortKey="Yan, Dong Ming" sort="Yan, Dong Ming" uniqKey="Yan D" first="Dong-Ming" last="Yan">Dong-Ming Yan</name>
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