Level: Graduate & Undergraduate
Differentials Geometry, Linear Algebra, Topology
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.
Hui Zhao is an assistant research fellow in Yanxi Lake Beijing institute of mathematical sciences and applications, he had been a visiting scholar in Harvard university and YMSC, Tsinghua university. His research focuses on the theory and algorithms of computational conformal geometry, computational discrete global geometric structures, computer graphics, geometry modeling and their applications in medical images, materials, CAD, virtual reality, Metaverse, and so on. He published fives computer graphics books and dozens of papers in related journals.
Lecturer Email: email@example.com
TA: Dr. Shuo Yang, firstname.lastname@example.org