Efficient computation of clipped Voronoi diagram for mesh generation

• DOI: 10.1016/j.cad.2011.09.004
• Publication Date: 2011-09-16T17:30:14Z
• Authors: Dong-Ming Yan; Wenping Wang; Bruno Lévy; Yang Liu
• Keywords: Clipped Voronoi diagram; Mesh generation; [INFO.INFO-GR] Computer Science [cs]/Graphics [cs.GR]; Centroidal Voronoi Tessellation; Delaunay triangulation; 02 engineering and technology; Delaunay Triangulation; Clipped Voronoi diagram Delaunay triangulation Centroidal Voronoi tessellation Mesh generation; [INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR]; 004; Clipped Voronoi Diagram; Centroidal Voronoi tessellation; Mesh Generation; 0202 electrical engineering, electronic engineering, information engineering

The 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.