Program
Computational Conformal Geometry
Student No.:50
Time:4:00-5:30 pm every Tuesday and Thursday
Instructor:Jian Sun  [Tsinghua University]
Place:Conference Room 3, Floor 2, Jin Chun Yuan West Building
Starting Date:2012-2-21
Ending Date:2012-5-31

Course description:

In this course, we study basic concepts in conformal geometry and algorithms for computing conformal maps. Conformal geometry is more flexible than Riemannian geometry and more rigid than topology, whence arises in many areas of science and engineering. In the last decade or so, there has been a huge development of computational methods for computing conformal maps and conformal invariants, and has been many successful examples in applying such methods in various fields, including computer graphics and computer vision, sensor network and geometric modeling. At the same time, this area of research remains active and has many unsolved problems. This course focuses on the algorithms of computing conformal maps for surfaces in 3D space and covers the following topics: basic concenpts in conformal geometry, algorithms for computing canonical polygonal schema, harmonic map, harmonic 1-form, holomorphic 1-form, Ricci flow.

 

Textbook: Computational Conformal Geometry, by Xianfeng David Gu and Shing-Tung Yau, International Press, 2008.

 

Course Format:
The purpose of this course is not only to introduce basic concepts in conformal geometry and algorithms for computing conformal maps but also to teach how to develop algorithms and apply them to different applications. To fillful this purpose, the course is devided into two parts: lectures and labs. Two thirds of the course is for lectures and the remaining one third is for labs. Be prepared to get your hands dirty :).

For more information about the specific course schedule, please visit the Course Webpage http://www.geomtop.org/teaching/conformal_2012Spring/.

 

Prerequisite:

Mathematics: calculus and linear algebra
Computer Science: c/c++ programming and basic data structures

 

Reference for the course:

[GY08] Computational Conformal Geometry, by Xianfeng David Gu and Shing-Tung Yau, International Press, 2008.
[LGD08] Variational Principles for Discrete Surfaces: Theory and Algorithm by Feng Luo, Xianfeng David Gu and Junfei Dai, International Press, 2008.
[BS08] Discrete Differential Geometry: Integrable Structure by Alexander I. Bobenko, Yuri B. Suris, American Mathematical Society, 2008.