Advances in Discrete Differential Geometry

Editors: Bobenko, Alexander I. (Ed.)
One of the first books on a newly emerging field of discrete differential geometry
Excellent way to access this new exciting area
Topics survey fascinating connections of discrete models in differential geometry to complex analysis, integrable systems, and to applications in computer graphics

This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics.

The authors take a closer look at discrete models in differential
geometry and dynamical systems. Their curves are polygonal, surfaces
are made from triangles and quadrilaterals, and time is discrete.
Nevertheless, the difference between the corresponding smooth curves,
surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, and on pure mathematics and its practical applications. The interaction of these facets is demonstrated by concrete examples, including discrete conformal mappings, discrete complex analysis, discrete curvatures and special surfaces, discrete integrable systems, conformal texture mappings in computer graphics, and free-form architecture.

This richly illustrated book will convince readers that this new branch of mathematics is both beautiful and useful. It will appeal to graduate students and researchers in differential geometry, complex analysis, mathematical physics, numerical methods, discrete geometry, as well as computer graphics and geometry processing.

About the authors
Alexander I. Bobenko is a professor at the Technische Universität Berlin. He is an author with Yuri Suris of the book „Discrete Differential Geometry“, editor of several books on this topic and a co-organizer of the regular conference „Discrete Differential Geometry“ in Oberwolfach. He is the Coordinator of the DFG Collaboration Research Center „Discretization in Geometry and Dynamics“.

Number of Illustrations and Tables
47 b/w illustrations, 67 illustrations in colour
Topics
Differential Geometry
Functions of a Complex Variable
Dynamical Systems and Ergodic Theory
Computer Graphics
Numerical and Computational Physics



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