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Advances in Discrete Differential Geometry

Editors: Bobenko, Alexander I. (Ed.)

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  • 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
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Buy this book

eBook  
  • ISBN 978-3-662-50447-5
  • This book is an open access book, you can download it for free on link.springer.com
Hardcover $59.99
price for USA in USD
  • ISBN 978-3-662-50446-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $59.99
price for USA in USD
  • ISBN 978-3-662-57061-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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“.

Table of contents (14 chapters)

Table of contents (14 chapters)
  • Discrete Conformal Maps: Boundary Value Problems, Circle Domains, Fuchsian and Schottky Uniformization

    Pages 1-56

    Bobenko, Alexander I. (et al.)

  • Discrete Complex Analysis on Planar Quad-Graphs

    Pages 57-132

    Bobenko, Alexander I. (et al.)

  • Approximation of Conformal Mappings Using Conformally Equivalent Triangular Lattices

    Pages 133-149

    Bücking, Ulrike

  • Numerical Methods for the Discrete Map $$Z^a$$

    Pages 151-176

    Bornemann, Folkmar (et al.)

  • A Variational Principle for Cyclic Polygons with Prescribed Edge Lengths

    Pages 177-195

    Kouřimská, Hana (et al.)

Buy this book

eBook  
  • ISBN 978-3-662-50447-5
  • This book is an open access book, you can download it for free on link.springer.com
Hardcover $59.99
price for USA in USD
  • ISBN 978-3-662-50446-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $59.99
price for USA in USD
  • ISBN 978-3-662-57061-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Advances in Discrete Differential Geometry
Editors
  • Alexander I. Bobenko
Copyright
2016
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
The Editor(s) (if applicable) and The Author(s)
eBook ISBN
978-3-662-50447-5
DOI
10.1007/978-3-662-50447-5
Hardcover ISBN
978-3-662-50446-8
Softcover ISBN
978-3-662-57061-6
Edition Number
1
Number of Pages
X, 439
Number of Illustrations
47 b/w illustrations, 67 illustrations in colour
Topics