Visualization and Mathematics

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

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.

• Computergraphik
• Differentialgeometrie
• Wissenschaftliche Visualisierung
• algorithms
• computer graphics
• differential geometry
• graphics
• numerical analysis
• numerical mathematics
• numerische Mathematik
• scientific computing
• scientific visualization
• simulation
• visualization
• wissenschaftliches Rechnen

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

  Hans-Christian Hege

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

  Konrad Polthier

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