Generalized edge-weighted centroidal Voronoi tessellations for geometry processing

Abstract

In this paper, we propose a generalized edge-weighted centroidal Voronoi tessellation (GEWCVT) model and corresponding solution algorithms, then apply them for geometry processing such as curve/surface smoothing and reconstruction. The main idea of the method is to seek a good way to discretize the similarity and regularity measures of the objective functional in the context of centroidal Voronoi tessellation methodology, so that its minimization can be done by clustering-type algorithms. Through various numerical examples, the proposed GEWCVT-based method is shown to be an effective and robust tool for such applications.