Efficient computation of clipped Voronoi diagram for mesh generation
KAUST DepartmentVisual Computing Center (VCC)
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AbstractThe Voronoi diagram is a fundamental geometric structure widely used in various fields, especially in computer graphics and geometry computing. For a set of points in a compact domain (i.e. a bounded and closed 2D region or a 3D volume), some Voronoi cells of their Voronoi diagram are infinite or partially outside of the domain, 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 to compute the clipped Voronoi diagram for a set of sites with respect to a compact 2D region or a 3D volume. We also apply the proposed method to optimal mesh generation based on the centroidal Voronoi tessellation. Crown Copyright © 2011 Published by Elsevier Ltd. All rights reserved.
SponsorsWe would like to thank anonymous reviewers for their detailed comments and suggestions which greatly improve the manuscript. We also thank one reviewer who pointed out the Ref. . This work is partially supported by the Research Grant Council of Hong Kong (project no.: 718209 and 718010), the State Key Program of NSFC project (60933008), European Research Council (GOODSHAPE FP7-ERC-StG-205693), and ANR/NSFC (60625202, 60911130368) Program (SHAN Project).
JournalCAD Computer Aided Design