Table of contents

  1. Front Matter
    Pages i-x
  2. Alexander I. Bobenko, Stefan Sechelmann, Boris Springborn
    Pages 1-56 Open Access
  3. Alexander I. Bobenko, Felix Günther
    Pages 57-132 Open Access
  4. Folkmar Bornemann, Alexander Its, Sheehan Olver, Georg Wechslberger
    Pages 151-176 Open Access
  5. Hana Kouřimská, Lara Skuppin, Boris Springborn
    Pages 177-195 Open Access
  6. Felix Knöppel, Ulrich Pinkall
    Pages 197-239 Open Access
  7. Wai Yeung Lam, Ulrich Pinkall
    Pages 241-265 Open Access
  8. Xiang Sun, Caigui Jiang, Johannes Wallner, Helmut Pottmann
    Pages 267-286 Open Access
  9. Yuri B. Suris, Mats Vermeeren
    Pages 347-378 Open Access
  10. Raphael Boll, Matteo Petrera, Yuri B. Suris
    Pages 379-405 Open Access
  11. Arnau Padrol, Günter M. Ziegler
    Pages 407-419 Open Access
  12. Michael Joswig, Milan Mehner, Stefan Sechelmann, Jan Techter, Alexander I. Bobenko
    Pages 421-439 Open Access

About this book

Introduction

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.

Keywords

discrete conformal maps discrete curvature integrable systems discrete complex analysis triangle meshes polyhedral surfaces

Editors and affiliations

  • Alexander I. Bobenko
    • 1
  1. 1.Technical University of BerlinBerlinGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-50447-5
  • Copyright Information The Editor(s) (if applicable) and The Author(s) 2016
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-662-50446-8
  • Online ISBN 978-3-662-50447-5
  • About this book