Variational Principles for Discrete SurfacesJunfei Dai, Xianfeng David Gu, Feng Luo International Press, 2008 - 146 Seiten "This new 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. The present book is the first complete treatment of the vast, and expansively developed, field of polyhedral geometry."--Back cover. |
Inhalt
Introduction | 1 |
Spherical Geometry and Cauchy Rigidity Theorem | 11 |
A Brief Introduction to Hyperbolic Geometry | 19 |
Urheberrecht | |
15 weitere Abschnitte werden nicht angezeigt.
Häufige Begriffe und Wortgruppen
adjacent algorithm angle structure angles facing B-arcs circle packing metric closed surface Compute conformal mappings converges convex polytope convex set cosh cosine law deck transformation defined Delaunay denoted discrete curvature discrete Ricci flow edge lengths energy function Euclidean polyhedral metrics Euclidean polyhedral surface Euclidean triangles Euler characteristic Əli Əyi facing the edge follows forall Furthermore Gauss-Bonnet theorem Gaussian curvature genus geodesic boundary geometry half-edge Hessian matrix hyperbolic angle hyperbolic circle Hyperbolic embedding hyperbolic metric hyperbolic polyhedral hyperbolic triangle inner angles intersection isometry Legendre transformation Leibon Lemma limm metrics on S,T Möbius transformation parameterization plane Poincaré disk Proof Ricci flow Riemannian metric rigidity theorem sin² sinh smooth strictly concave strictly convex Suppose surface Ricci flow tangent target curvature Teichmüller space triangular mesh universal covering space vertex vertices