Polyhedral Surfaces of Constant Mean Curvature
Konrad Polthier · 2002
Contents Preface vii 1 Introduction to Polyhedral Meshes 1 1.1 SimplicialComplexes................... 2 1.2 TopologicalProperties.................. 6 1.3 DistanceandMetric ................... 8 1.4 DiscreteGauCurvature................. 9 1.5 GridsinNumericsandGraphics ............ 15 1.5.1 DelaunayTriangulation ............. 18 1.5.2 VoronoiDiagrams ................ 20 1.5.3 ##Shapes..................... 21 1.6 FiniteElementSpaces .................. 22 1.6.1 Non-ConformingFiniteElements........ 23 2 Discrete Geodesics on Polyhedral Surfaces 25 2.1 ReviewofSmoothGeodesics .............. 27 2.2 DiscreteStraightestGeodesics.............. 29 2.3 DiscreteGeodesicCurvature............... 34 2.4 ParallelTranslationofVectors ............. 37 2.4.1 GeodesicRungeKutta.............. 39 2.5 GeodesicFlow ...................... 42 2.5.1 Circles on Surfaces and the Geodesic Flow . . . 44 2.5.2 Computing Discrete Distance Circles . . . . . . 47 2.5.3 Dynamic Computation of a Wave Text