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Advances in discrete differential geometry

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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.

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Detail Information

Series Title

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Call Number

516.36 ADV a

Publisher

Berlin, Germany : Springer Open., 2016

Collation

x, 439p. : ill.

Language

English

ISBN/ISSN

9783662504475

Classification

516.36

Content Type

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Media Type

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Carrier Type

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Edition

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Subject(s)

Mathematics
Computer graphics
physics
Geometry, Differential
Discrete geometry
Functions of complex variables
Dynamics
Ergodic theory

Specific Detail Info

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Statement of Responsibility

edited by Alexander I. Bobenko

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