Mesh Coarsening based upon Multiplicatively Weighted Centroidal Voronoi Diagrams

An approximated Centroidal Voronoi Diagram (CVD) construction provides an efficient and fast way for coarsening polygonal meshes. In this article a new generalization of the CVD for 3D meshes is presented a Multiplicatively Weighted Centroidal Voronoi Diagram. Based on this concept we propose a mesh coarsening algorithm which is intended to capture the mesh features as good as possible. To achieve this, we propose three different types of cluster’s weights. The mesh clusters are obtained by minimization of the underlying energy functional. To guarantee cluster connectivity, a specific vertex-boundary-count approach is introduced. The final coarse mesh is obtained by triangulating the optimized clustered model. Along with that, we present a new and fast algorithm for initial seeds generation that can also be used for various types of applications which require an approximatively uniformly distributed initial set of seeds.