Speaker: Dr. Ying He

Host: Prof. Changhe Tu

Time: 10:00am-11:00am, Dec. 16, 2015

Venue: Room 111, High Performance Building

Title: Intrinsic Delaunay Triangulations and Discrete Laplace-Beltrami Operator

Abstract: Delaunay triangulation is a fundamental data structure and has tremendous applications in many engineering fields. Although Delaunay triangulations in Euclidean spaces are well studied and understood, computing intrinsic Delaunay triangulations on polyhedral surfaces has received much less attention. In this talk, I will introduce new methods for constructing IDTs on manifold triangle meshes. Based on the duality of geodesic Voronoi diagrams, our method can guarantee the resultant IDTs are strongly regular. Our method is non-iterative so that its runtime performance is independent to the number of non-Delaunay edges.  As a by-product, the regular Delaunay triangulations naturally induce discrete Laplace-Beltrami operator (LBO), which is intrinsic to the geometry and guaranteed to have non-negative weights. Computational results show that the IDT-induced LBO is ideal for applications which solve the linear system and eigensystem of the discrete Laplacian. This is a joint work with Y.-J. Liu, C. Xu and D. Fan. 

Biography: Ying He is currently an associate professor at School of Computer Engineering, Nanyang Technological University, Singapore. He received the BS and MS degrees in electrical engineering from Tsinghua University, China, and the PhD degree in computer science from Stony Brook University, USA. His research interests fall into the general areas of visual computing and he is particularly interested in the problems which require geometric analysis and computation.

For more information, please visit http://www.ntu.edu.sg/home/yhe