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 achi...

We present a 2D mesh improvement technique that optimizes Voronoi diagrams for their use in polygonal finite element computations. Starting from a centroidal Voronoi tessellation of the simulation domain we optimize the mesh by minimizing a carefully designed energy functional that effectively removes the major reason for numerical instabilities—short edges in the Voronoi diagram. We evaluate o...

One of the most important pieces of information for health resources planning is the definition of catchment areas for health units. Voronoi Diagrams are a potential technique for this purpose. They are polygons with the property whereby adjacent polygons have their borders located within the same distance of the respective generator points. One possible adjustment to the catchment areas thus d...

AVNEESH SUD: Efficient Computation of Discrete Voronoi Diagram and Homotopy-Preserving Simplified Medial Axis of a 3D Polyhedron. (Under the direction of Dinesh Manocha.) The Voronoi diagram is a fundamental geometric data structure and has been well studied in computational geometry and related areas. A Voronoi diagram defined using the Euclidean distance metric is also closely related to the ...

Proper orthogonal decompositons (POD) have been used to systematically extract the most energetic modes while centroidal Voronoi tessellations has been used to systematically extract best representatives. We combine the ideas of CVT and POD into a hybird method for model reduction. The optimality of such an approach and various practical implementation strategies are discussed.

We present a C++ open-source implementation of an incremental algorithm for the computation of the Voronoi diagram of ellipses in the Euclidean plane. This is the first complete implementation, under the exact computation paradigm; it also computes the approximate diagram with any given precision. It is based on the cgal package for the Apollonius diagram. The ellipses are given in parametric r...

Presented in this paper are algorithms to compute the positions of vertices and equations of edges of the Voronoi diagram of a circle set on a plane, where the radii of the circles are not necessarily equal and the circles are not necessarily disjoint. The algorithms correctly and efficiently work in conjunction with the first paper of the series dealing with the construction of the correct top...

This paper introduces the notion of Voronoi diagrams and Delaunay triangulations generated by the vertices of a piecewise #at, triangulated surface. Based on properties of such structures, a generalized #ip algorithm to construct the Delaunay triangulation and Voronoi diagram is presented. An application to biological membrane growth modeling is then given. A Voronoi partition of the membrane i...

We introduce a weighting scheme for Voronoi diagrams that has preferred directions. This generalizes the concept of weighted Delaunay triangulations and overcomes some of the difficulties of using multiplicative anisotropic weight systems. We discuss properties that make these weighting schemes attractive.