Lp Centroidal Voronoi Tessellation and its applications

نویسندگان

Bruno Lévy

Yang Liu

چکیده

This paper introduces Lp-Centroidal Voronoi Tessellation (LpCVT), 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 hexdominant volume meshing are presented. Unlike previous work, Lp-CVT captures sharp features and intersections without requiring any pre-tagging. CR Categories: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Geometric algorithms, languages, and systems; Algorithms

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