How is Ricci flow related to computer graphics?

Question

I recently came across the book Ricci Flow for Shape Analysis and Surface Registration: Theories, Algorithms and Applications by Wei Zeng and Xianfeng David Gu. Because, I just saw the book on the passing and then read a bit about it in Amazon, I still don't exactly know how Ricci flow is related to computer graphics and especially to 3D modelling in computer science. If someone can give me a comprehensive answer or point me to one, I would be glad.

On the other hand, I also would like to learn whether the Poincaré conjecture has some applications in computer graphics and 3D modelling.

Lastly, I want to learn what are some mathematical research topics in these areas that have (or may have) direct applications in computer graphics and 3D modelling.

Answer 1

Perhaps this—and its references both past & future ("cited by 152" subsequent papers)—will help...?

Jin, Miao, Junho Kim, Feng Luo, and Xianfeng Gu. "Discrete surface Ricci flow." IEEE Transactions on Visualization and Computer Graphics, no. 5 (2008): 1030-1043. (DOI).

         

---

David (Xianfeng) Gu's work was cited by Deane Yang in the comments.

Here is one among the (many) later papers, coauthored by David Gu:

Wang, Yalin, Jie Shi, Xiaotian Yin, Xianfeng Gu, Tony F. Chan, Shing-Tung Yau, Arthur W. Toga, and Paul M. Thompson. "Brain surface conformal parameterization with the Ricci flow." IEEE Transactions on Medical Imaging. 31, no. 2 (2012): 251-264. (Journal link.)