Ronald Lui, CUHK, Hong Kong

Computational Conformal/Quasi-conformal Geometry and its applications

Abstract

Conformal (C)/Quasi-conformal (QC) geometry has a long history in pure mathematics, and is an active field in both modern geometry and modern physics. Recently, with the rapid development of 3D digital scanning technology, the demand for effective geometric processing techniques is ever increasing. Computational conformal/quasi-conformal geometry plays an important role for this purpose, and has found important applications in different areas such as medical imaging and computer graphics.

In practice, geometric structures are usually represented discretely by triangulation meshes. In this talk, I will firstly describe how C/QC theories can be discretized onto discrete meshes. This gives a discrete analogue of C/QC geometry on meshes. Then, I will talk about how computational C/QC geometry can be practically applied to different applications such as computer graphics and medical imaging for disease analysis.