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Discrete Differential Geometry : Discrete Differential Geometry Preliminary Entry 38 - Alexander I. Bobenko

Discrete Differential Geometry

Discrete Differential Geometry Preliminary Entry 38

By: Alexander I. Bobenko (Editor), Peter Schroder (Editor), John M. Sullivan (Editor), Gunter M. Ziegler (Editor)


Published: 17th January 2008
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Discrete differential geometry is an active mathematical terrain where differential geometry and discrete geometry meet and interact. It provides discrete equivalents of the geometric notions and methods of differential geometry, such as notions of curvature and integrability for polyhedral surfaces. Current progress in this field is to a large extent stimulated by its relevance for computer graphics and mathematical physics. This collection of essays, which documents the main lectures of the 2004 Oberwolfach Seminar on the topic, as well as a number of additional contributions by key participants, gives a lively, multi-facetted introduction to this emerging field.

Prefacep. v
Discretization of Surfaces: Special Classes and Parametrizationsp. 1
Surfaces from Circlesp. 3
Minimal Surfaces from Circle Patterns: Boundary Value Problems, Examplesp. 37
Designing Cylinders with Constant Negative Curvaturep. 57
On the Integrability of Infinitesimal and Finite Deformations of Polyhedral Surfacesp. 67
Discrete Hashimoto Surfaces and a Doubly Discrete Smoke-Ring Flowp. 95
The Discrete Green's Functionp. 117
Curvatures of Discrete Curves and Surfacesp. 135
Curves of Finite Total Curvaturep. 137
Convergence and Isotopy Type for Graphs of Finite Total Curvaturep. 163
Curvatures of Smooth and Discrete Surfacesp. 175
Geometric Realizations of Combinatorial Surfacesp. 189
Polyhedral Surfaces of High Genusp. 191
Necessary Conditions for Geometric Realizability of Simplicial Complexesp. 215
Enumeration and Random Realization of Triangulated Surfacesp. 235
On Heuristic Methods for Finding Realizations of Surfacesp. 255
Geometry Processing and Modeling with Discrete Differential Geometryp. 261
What Can We Measure?p. 263
Convergence of the Cotangent Formula: An Overviewp. 275
Discrete Differential Forms for Computational Modelingp. 287
A Discrete Model of Thin Shellsp. 325
Indexp. 339
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9783764386207
ISBN-10: 3764386207
Series: Oberwolfach Seminars
Audience: General
Format: Paperback
Language: English
Number Of Pages: 341
Published: 17th January 2008
Publisher: Birkhauser Verlag AG
Country of Publication: CH
Dimensions (cm): 23.8 x 17.17  x 2.44
Weight (kg): 0.65