Wenping Wang, The University of Hong Kong

Wenping Wang is Associate Professor of Computer Science at University of Hong Kong (HKU). His research covers computer graphics, geometric computing and visualization, and has published over 100 papers in these fields. He got his B.Sc. (1983) and M.Eng. (1986) at Shandong University, China, and Ph.D. (1992) at University of Alberta, Canada, all in computer science. He is associate editor of the Springer journal Computer Aided Geometric Design, and has been program chair of several international conferences, including Geometric Modeling and Processing (GMP 2000), Pacific Graphics (PG 2000 and PG 2003), ACM Symposium on Virtual Reality Software and Technology (VRST 2001), and ACM Symposium on Physical and Solid Modeling (SPM 2006).

Title: Computation and Properties of Centroidal Voronoi Diagram

Abstract:
Centroidal Voronoi Diagram (also called Centroidal Voronoi Tessellation, or CVT) is a variational framework of computing an optimal geometric structure based on the Voronoi Diagram, and is used in many applications of computer graphics and geometric processing. I shall present several recent results on CVT. First it will be shown that the objective function of the CVT problem in Euclidean space of dimension two or higher is almost always C2, contrary to the common belief that it is a nonsmooth piecewise function. Based on the C2 smoothness of its objective function, a Newton-like method for computing CVT is presented that is one order of magnitude faster than the prevailing Lloyd method. Then from an empirical point of view, I shall discuss the extremal properties of the CVT problem and the associated challenges in computing acceptable local minimum points. Finally, several extensions and applications of the CVT problem relevant to shape modeling will be presented, including CVT-based triangulation on surfaces and variational computation with Power Diagrams.

This talk is based on a collection of joined works with Yang Liu, Bruno Levy, Feng Sun, Dongming Yan, Lu Lin.