Discrete Differential Geometry (Paperback)

Discretization of Surfaces: Special Classes and Parametrizations.- Surfaces from Circles.- Minimal Surfaces from Circle Patterns: Boundary Value Problems, Examples.- Designing Cylinders with Constant Negative Curvature.- On the Integrability of Infinitesimal and Finite Deformations of Polyhedral Surfaces.- Discrete Hashimoto Surfaces and a Doubly Discrete Smoke-Ring Flow.- The Discrete Green's Function.- Curvatures of Discrete Curves and Surfaces.- Curves of Finite Total Curvature.- Convergence and Isotopy Type for Graphs of Finite Total Curvature.- Curvatures of Smooth and Discrete Surfaces.- Geometric Realizations of Combinatorial Surfaces.- Polyhedral Surfaces of High Genus.- Necessary Conditions for Geometric Realizability of Simplicial Complexes.- Enumeration and Random Realization of Triangulated Surfaces.- On Heuristic Methods for Finding Realizations of Surfaces.- Geometry Processing and Modeling with Discrete Differential Geometry.- What Can We Measure?.- Convergence of the Cotangent Formula: An Overview.- Discrete Differential Forms for Computational Modeling.- A Discrete Model of Thin Shells.