Mesh clustering by approximating centroidal Voronoi tessellation

Abstract

An elegant and efficient mesh clustering algorithm is presented. The faces of a polygonal mesh are divided into different clusters for mesh coarsening purpose by approximating the Centroidal Voronoi Tessellation of the mesh. The mesh coarsening process after clustering can be done in an isotropic or anisotropic fashion. The presented algorithm improves previous techniques in local geometric operations and parallel updates. The new algorithm is very simple but is guaranteed to converge, and generates better approximating meshes with the same computation cost. Moreover, the new algorithm is suitable for the variational shape approximation problem with L2, 1 distortion error metric and the convergence is guaranteed. Examples demonstrating efficiency of the new algorithm are also included in the paper.