Advanced Lectures in Mathematics (ALM 4): Variational Principles for Discrete Surfaces


Price: $25.00


Author: Feng Luo
Language: English
ISBN/ISSN: 7040231946
Published on: 2008-01

This book intends to lead its 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 book is a systematic introduction to 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 on polyhedral geometry, e. g., the Cauchy rigidity theorem, Thurston's circle packing theorem, rigidity of circle packing theorems and Colin de Verdiere's variational principle. With the vast development of the mathematics subject of polyhedral geometry, the present book is the first complete treatment of the subject.

1 Introduction
2 Spherical Geometry and Cauchy Rigidity Theorem
3 A Brief Introduction to Hyperbolic Geometry
4 The Cosine Law and Polyhedral Surfaces
5 Spherical Polyhedral Surfaces and Legendre Transformation
6 Rigidity of Euclidean Polyhedral Surfaces
7 Polyhedral Surfaces of Circle Packing Type
8 Non-negative Curvature metrics and Delaunay Polytopes
9 A Brief Introduction to Teichmiiller Space
10 Parameterizatios of Teichmuller spaces
11 Surface Ricci Flow
12 Geometric Structure
13 Shape Acquisition and Representation
14 Discrete Ricci Flow
15 Hyperbolic Ricci Flow

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