北京雁栖湖应用数学研究院

This course introduces the algorithms and philosophy of Computational Discrete Global Geometric Structures. There are six components in this course: 1) the mathematical theory of global geometric structures on smooth manifolds; 2) their discrete counterparts; 3) the algorithms to compute them; 4) the programming and coding techniques for the implementaitons of the algorithms; 5) the visualization techniques to demonstrate these geometry structures; 6) besides computer graphcis, the possible discussion of their potential applications in other inter-discipline fields, and so on. Computational discrete global geometric structures(CDGGS) is pioneered by Prof. Shing-Tung Yau and Prof Xianfeng Gu with the classic Gu-Yau algorithm to compute discrete harmonic one-form around 2000. After twenty year's research by mathematicians and computer scientists, currently, CDGGS can handle many other discrete global geometric structures, such as holomorphic one-form, foliation, holomorphic quadratic differentials, conformal structures, and so on, and play an important role in the application of geometry modeling and meshing.