Discrete Differential Geometry

by Bobenko, Alexander I.; Schroder, Peter; Sullivan, John M.; Ziegler, Gunter M.

• ISBN13: 9783764386207
• ISBN10: 3764386207
• Format: Paperback
• Copyright: 2008-03-30
• Publisher: Birkhauser

Summary

This is the first book on a newly emerging field of discrete differential geometry providing an excellent way to access this exciting area. It provides discrete equivalents of the geometric notions and methods of differential geometry, such as notions of curvature and integrability for polyhedral surfaces. The carefully edited collection of essays gives a lively, multi-facetted introduction to this emerging field.

Table of Contents

Preface	p. v
Discretization of Surfaces: Special Classes and Parametrizations	p. 1
Surfaces from Circles	p. 3
Minimal Surfaces from Circle Patterns: Boundary Value Problems, Examples	p. 37
Designing Cylinders with Constant Negative Curvature	p. 57
On the Integrability of Infinitesimal and Finite Deformations of Polyhedral Surfaces	p. 67
Discrete Hashimoto Surfaces and a Doubly Discrete Smoke-Ring Flow	p. 95
The Discrete Green's Function	p. 117
Curvatures of Discrete Curves and Surfaces	p. 135
Curves of Finite Total Curvature	p. 137
Convergence and Isotopy Type for Graphs of Finite Total Curvature	p. 163
Curvatures of Smooth and Discrete Surfaces	p. 175
Geometric Realizations of Combinatorial Surfaces	p. 189
Polyhedral Surfaces of High Genus	p. 191
Necessary Conditions for Geometric Realizability of Simplicial Complexes	p. 215
Enumeration and Random Realization of Triangulated Surfaces	p. 235
On Heuristic Methods for Finding Realizations of Surfaces	p. 255
Geometry Processing and Modeling with Discrete Differential Geometry	p. 261
What Can We Measure?	p. 263
Convergence of the Cotangent Formula: An Overview	p. 275
Discrete Differential Forms for Computational Modeling	p. 287
A Discrete Model of Thin Shells	p. 325
Index	p. 339
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