Most existing applications of centroidal Voronoi tessellations (CVTs) lack consideration of the length of the cluster boundaries. In this paper we propose a new model and algorithms to produce segmentations which would minimize the total energy — a sum of the classic CVT energy and the weighted length of cluster boundaries. To distinguish it with the classic CVTs, we call it an Edge-Weighted CV...

This paper describes a dynamic and adaptive scheme for three-dimensional mesh morphing. Using several control maps, the connectivity of intermediate meshes is dynamically changing and the mesh vertices are adaptively modified. The 2D control maps in parametric space that include curvature map, area deformation map and distance map, are used to schedule the inserting and deleting vertices in eac...

Centroidal Voronoi tessellations (CVTs) are Voronoi tessellations of a bounded geometric domain such that the generating points of the tessellations are also the centroids (mass centers) of the corresponding Voronoi regions with respect to a given density function. Centroidal Voronoi tessellations may also be defined in more abstract and more general settings. Due to the natural optimization pr...

There are many new applications of the centroidal Voronoi tessellations that come to life in recent years, along with more mathematical understandings and new algorithmic advances in their efficient computation. Some examples are presented in this paper as an illustration with an emphasis on the construction of ideal point distributions, best mode selections and optimal spatial partitions.