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Visualization and Mathematics

Experiments, Simulations and Environments

  • Book
  • © 1997

Overview

Editors:
  1. Hans-Christian Hege

    1. Wissenschaftliche Visualisierung, Konrad-Zuse-Zentrum für Informationstechnik Berlin, Berlin, Germany

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  2. Konrad Polthier

    1. Fachbereich 3, Mathematik, Technische Universität Berlin, Berlin, Germany

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    You can also search for this editor in PubMed   Google Scholar

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Table of contents (22 chapters)

  1. Front Matter

    Pages I-XIX
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  2. Visualizing Mathematics

    1. Front Matter

      Pages 1-1
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    2. The Minimax Sphere Eversion

      • George Francis, John M. Sullivan, Rob B. Kusner, Ken A. Brakke, Chris Hartman, Glenn Chappell
      Pages 3-20

    3. Exploring Plane Hyperbolic Geometry

      • Barbara Hausmann, Britta Slopianka, Hans-Peter Seidel
      Pages 21-36

    4. Visualizing Nonlinear Electrodynamics

      • Geoffrey Martin, Ivan Sterling
      Pages 37-51

    5. The Use of Computer Graphics for Solving Problems in Singularity Theory

      • Richard J. Morris
      Pages 53-66

    6. What Should a Surface in 4-Space Look Like?

      • Dennis Roseman
      Pages 67-82

    7. Animation of Algebraic Surfaces

      • Dietmar Saupe, Matthias Ruhl
      Pages 83-92

  3. Geometric Algorithms and Experiments

    1. Front Matter

      Pages 93-93
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    2. Using Symmetry Features of the Surface Evolver to Study Foams

      • Ken A. Brakke, John M. Sullivan
      Pages 95-117

    3. Constant Mean Curvature Surfaces Derived from Delaunay’s and Wente’s Examples

      • Karsten Große-Brauckmann, Konrad Polthier
      Pages 119-134

    4. Visualization of Periodic Tilings

      • Daniel H. Huson
      Pages 135-139

    5. An Algorithm for Discrete Constant Mean Curvature Surfaces

      • Bernd Oberknapp, Konrad Polthier
      Pages 141-161

  4. Visualization Algorithms and Data Structures

    1. Front Matter

      Pages 163-163
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    2. Efficient Calculation of Subdivision Surfaces for Visualization

      • Markus Kohler, Heinrich Müller
      Pages 165-179

    3. Fast Line Integral Convolution for Arbitrary Surfaces in 3D

      • Henrik Battke, Detlev Stalling, Hans-Christian Hege
      Pages 181-195

    4. Visualization of Parallel Data based on Procedural Access

      • Martin Rumpf, Bernhard Schupp
      Pages 197-208

  5. Visualization Environments

    1. Front Matter

      Pages 209-209
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    2. A new 3D Graphics Library: Concepts, Implementation, and Examples

      • Markus Alefeld, Jörg Haber, Alexander Heim
      Pages 211-225

    3. A Generic Approach to Computer Graphics

      • Ekkehard Beier
      Pages 227-238
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Keywords

About this book

Visualization and mathematics have begun a fruitful relationship, establishing links between problems and solutions of both fields. In some areas of mathematics, like differential geometry and numerical mathematics, visualization techniques are applied with great success. However, visualization methods are relying heavily on mathematical concepts.
Applications of visualization in mathematical research and the use of mathematical methods in visualization have been topic of an international workshop in Berlin in June 1995. Selected contributions treat topics of particular interest in current research. Experts are reporting on their latest work, giving an overview on this fascinating new area. The reader will get insight to state-of-the-art techniques for solving visualization problems and mathematical questions.

Editors and Affiliations

  • Wissenschaftliche Visualisierung, Konrad-Zuse-Zentrum für Informationstechnik Berlin, Berlin, Germany

    Hans-Christian Hege

  • Fachbereich 3, Mathematik, Technische Universität Berlin, Berlin, Germany

    Konrad Polthier

Bibliographic Information

  • Book Title: Visualization and Mathematics

  • Book Subtitle: Experiments, Simulations and Environments

  • Editors: Hans-Christian Hege, Konrad Polthier

  • DOI: https://doi.org/10.1007/978-3-642-59195-2

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1997

  • Hardcover ISBN: 978-3-540-61269-8Published: 25 July 1997

  • Softcover ISBN: 978-3-642-63891-6Published: 28 October 2012

  • eBook ISBN: 978-3-642-59195-2Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: XIX, 388

  • Number of Illustrations: 154 b/w illustrations, 45 illustrations in colour

  • Topics: Visualization, Differential Geometry, Computer Graphics, Global Analysis and Analysis on Manifolds, Topology

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