Lp Centroidal Voronoi Tesselation and its applications

Bruno Lévy 1 Yang Liu 1
1 ALICE - Geometry and Lighting
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : This paper introduces Lp -Centroidal Voronoi Tessellation (Lp -CVT), a generalization of CVT that minimizes a higher-order moment of the coordinates on the Voronoi cells. This generalization allows for aligning the axes of the Voronoi cells with a predefined background tensor field (anisotropy). Lp -CVT is computed by a quasi-Newton optimization framework, based on closed-form derivations of the objective function and its gradient. The derivations are given for both surface meshing (Ω is a triangulated mesh with per-facet anisotropy) and volume meshing (Ω is the interior of a closed triangulated mesh with a 3D anisotropy field). Applications to anisotropic, quad-dominant surface remeshing and to hex-dominant volume meshing are presented. Unlike previous work, Lp -CVT captures sharp features and intersections without requiring any pre-tagging.
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Bruno Lévy, Yang Liu. Lp Centroidal Voronoi Tesselation and its applications. ACM Transactions on Graphics, Association for Computing Machinery, 2010, Proceedings of ACM SIGGRAPH 2010, 29 (4), ⟨10.1145/1833349.1778856⟩. ⟨inria-00600251⟩

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