Variational Principles for Discrete Surfaces (volume 4 of the Advanced Lectures in Mathematics series): Theories and Algorithms

This volume introduces readers to some of the current topics of research in the geometry of polyhedral surfaces, with applications to computer graphics. The main feature of the volume is a systematic introduction to the geometry of polyhedral surfaces based on the variational principle. The authors focus on using analytic methods in the study of some of the fundamental results and problems of polyhedral geometry: for instance, the Cauchy rigidity theorem, Thurston's circle packing theorem, rigidity of circle packing theorems, and Colin de Verdiere's variational principle. This is the first complete treatment of the vast, and expansively developed, field of polyhedral geometry.

Junfei Dai

Junfei Dai is a post-doctoral researcher at the Center of Mathematical Sciences at Zhejiang University in China. He received his Ph.D. degree in Applied Mathematics from Zhejiang University in 2007. His research interests include digital geometry processing, geometric modeling, and related topics.

Xianfeng David Gu

Xianfeng David Gu received his PhD from Harvard University in 2003, having studied under Shing-Tung Yau and Steven Gortler. He is the recipient of a National Science Foundation Career Award (2004-2009), has held teaching posts at the University of Florida (2003-2004), and is currently an Assistant Professor at the State University of New York at Stony Brook. His research interests include differential geometry, algebraic topology, and especially computational conformal geometry -- with applications to computer graphics, computer vision, medical imaging, geometric modeling, and visualization.

Feng Luo

Feng Luo received his B.S. degree in mathematics from Peking University in 1983, and his Ph.D. from the University of California at San Diego in 1989. He is a professor of Mathematics at Rutgers University. His research interests include geometry and topology of surfaces and 3-manifolds, and computer graphics.