Preface.......................................................... v
Part I:
Discretization of Surfaces: Special Classes and
Parametrizations ................................................ 1
Surfaces from Circles
by Alexander I. Bobenko ...................................... 3
Minimal Surfaces from Circle Patterns: Boundary Value Problems,
Examples
by Ulrike Bucking ........................................... 37
Designing Cylinders with Constant Negative Curvature
by Ulrich Pinkall ........................................... 57
On the Integrability of Infinitesimal and Finite Deformations
of Polyhedral Surfaces
by Wolfgang K. Schief, Alexander I. Bobenko and
Jim Hoffmann................................................. 67
Discrete Hashimoto Surfaces and a Doubly Discrete Smoke-Ring Flow
by Tim Hoffmann ............................................. 95
The Discrete Green's Function
by Yuri B. Suris ........................................... 117
Part II:
Curvatures of Discrete Curves and Surfaces..................... 135
Curves of Finite Total Curvature
by John M. Sullivan ........................................ 137
Convergence and Isotopy Type for Graphs of Finite Total Curvature
by Elizabeth Denne and John M. Sullivan .................... 163
Curvatures of Smooth and Discrete Surfaces
by John M. Sullivan ........................................ 175
Part III:
Geometric Realizations of Combinatorial Surfaces .............. 189
Polyhedral Surfaces of High Genus
by Giinter M. Ziegler ...................................... 191
Necessary Conditions for Geometric Realizability of Simplicial
Complexes by Dagmar Timmreck ............................... 215
Enumeration and Random Realization of Triangulated Surfaces
by Frank H. Lutz ........................................... 235
On Heuristic Methods for Finding Realizations of Surfaces
by Jiirgen Bokowski ........................................ 255
Part IV:
Geometry Processing and Modeling with Discrete Differential
Geometry ...................................................... 261
What Can We Measure?
by Peter Schroder .......................................... 263
Convergence of the Cotangent Formula: An Overview
by Max Wardetzky ........................................... 275
Discrete Differential Forms for Computational Modeling
by Mathieu Desbrun, Eva Kanso and Yiying Tong .............. 287
A Discrete Model of Thin Shells
by Eitan Grinspun .......................................... 325
Index ......................................................... 339
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