Discrete Differential Geometry

Part I.Discretization of Surfaces: Special Classes and Parametrizations

1. Surfaces from Circles
Alexander I. Bobenko

2. Minimal Surfaces from Circle Patterns: Boundary Value Problems, Examples
Ulrike Bücking

3. Designing Cylinders with Constant Negative Curvature
Ulrich Pinkall

4. On the Integrability of Infinitesimal and Finite Deformations of Polyhedral Surfaces
Wolfgang K. Schief, Alexander I. Bobenko, Tim Hoffmann

5. Discrete Hashimoto Surfaces and a Doubly Discrete Smoke-Ring Flow
Tim Hoffmann

6. The Discrete Green’s Function
Yuri B. Suris

Part II.Curvatures of Discrete Curves and Surfaces

7. Curves of Finite Total Curvature
John M. Sullivan

8. Convergence and Isotopy Type for Graphs of Finite Total Curvature
Elizabeth Denne, John M. Sullivan

9. Curvatures of Smooth and Discrete Surfaces
John M. Sullivan

Part III.Geometric Realizations of Combinatorial Surfaces

10. Polyhedral Surfaces of High Genus
Günter M. Ziegler

11. Necessary Conditions for Geometric Realizability of Simplicial Complexes
Dagmar Timmreck

12. Enumeration and Random Realization of Triangulated Surfaces
Frank H. Lutz

13. On Heuristic Methods for Finding Realizations of Surfaces
Jürgen Bokowski

Part IV.Geometry Processing and Modeling with Discrete Differential Geometry

14. What Can We Measure?
Peter Schröder

15. Convergence of the Cotangent Formula: An Overview
Max Wardetzky

16. Discrete Differential Forms for Computational Modeling
Mathieu Desbrun, Eva Kanso, Yiying Tong

17. A Discrete Model of Thin Shells
Eitan Grinspun

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Keywords: MATHEMATICS / General MAT000000