内容简介

《离散曲面的变分原理(英文版)》主要内容：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

目录

1 Introduction

1.1 Variational Principle and Isoperimetric Problems

1.2 Polyhedral Metrics and Polyhedral Surfaces

1.3 A Brief History on Geometry of Polyhedral Surface

1.4 Recent Works on Polyhedral Surfaces

1.5 Some of Our Results

1.6 The Method of Proofs and Related Works

2 Spherical Geometry and Cauchy Rigidity Theorem

2.1 Spherical Geometry and Spherical Triangles

2.2 The Cosine law and the Spherical Dual

2.3 The Cauchy Rigidity Theorem

3 A Brief Introduction to Hyperbolic Geometry

3.1 The Hyperboloid Model of the Hyperbolic Geometry

3.2 The Klein Model of Hn

3.3 The Upper Half Space Model of Hn

3.4 The Poincar6 Disc Model Bn of Hn