题目：Geometric Methods for VR/AR Applications
内容简介：Virtual Reality and Augmented Reality are developing rapidly, which have raised many fundamental technical problems. In order to tackle these challenges, profound geometric theories need to be applied.
In this talk, several challenges and their solutions will be discussed, such as geometric compression based on optimal mass transportation and normal cycle theory; human expression capture based on Riemann surface and Teichmuller theory; mesh generation based on surface foliation theory and so on.
题目：On 3d Irreducible and Indecomposable Polyhedra and the Number of Interior Steiner Points
简介：The topic of this talk is mainly motivated by the boundary recovery problem in tetrahedral mesh generation, in which a given set of constraints, edges and faces, is required to be represented by the generated tetrahedral mesh.
A theoretical difficulty in this problem is the existence of 3d (non-convex) indecomposable polyhedra, whose interior cannot be decomposed into a set of tetrahedra with its own vertices, such as the well-known Sch\“onhardt polyhedron.
Although it is known that any indecomposable polyhedra can be tetrahedralised by inserting a certain number of additional points, so-called Steiner points, it remains a challenging problem, when the Steiner points can only be placed in the interior.
We call a 3d (non-convex) polyhedron irreducible if it cannot be cut into smaller regions without introducing additional vertices.
In this talk, we focus on a class of 3d polyhedron which are both irreducible and indecomposable. We present new class of such polyhedra obtained by studying some well-known examples, namely the Sch\“onhardt and Bagemihl polyhedra, and the Chazelle polyhedron. Optimal number of Steiner points and efficient algorithm are presented to tetrahedralize these polyhedra.
报告人简介：Dr. Hang Si is a senior researcher in Weierstrass Institute (WIAS) in Berlin. His main research interest is mesh generation and the discrete and computational geometry problems behind it. The goal is to develop efficient algorithms for automatically generating meshes suitable for numerical methods such as finite element and finite volume methods. He is the developer of the software, TetGen -- a Delaunay-based tetrahedral mesh generator. It is freely available for academic use at http://www.tetgen.org.
Hang Si received his B.S. in Electrical Engineering from Hangzhou University (now merged in Zhejiang University) in 1994, and his M.S. in Computer Science from Zhejiang University in 2002. He joined the research group Numerical Mathematics and Scientific Computing of WIAS in 2002. He received his Ph.D from the Institute of Mathematics of Technische Universitaet Berlin in 2008.
For more recent work of Dr. Hang Si, please visit his website at: http://www.wias-berlin.de/people/si