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 | |
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Häufige Begriffe und Wortgruppen
2-dimensional A₁ adjacent algorithm angle structure angles facing B-arcs circle packing metric closed surface Compute conformal mappings convex polytope corner cosh cosx cosxi defined Delaunay denoted dihedral angles discrete curvature edge lengths energy function Euclidean polyhedral metric Euclidean polyhedral surface Euclidean triangles Euler Euler characteristic facing the edge follows Furthermore Gauss Gauss-Bonnet theorem Gaussian curvature geodesic boundary geometry half-edge Hessian matrix hexagon hyperbolic circle Hyperbolic embedding hyperbolic metric hyperbolic polyhedral hyperbolic triangle inner angles intersection isometry Legendre transformation Leibon Lemma limm limml(m metrics on S,T Möbius transformation parameterization plane Poincaré disk projective structure Proof Ricci flow Riemannian metric rigidity theorem sinh tdt smooth spherical triangle strictly concave strictly convex Suppose surface Ricci flow tangent Teichmüller space totally geodesic u₁ universal covering space variational principle vertex vertices дө дхі