A collection of state-of-the-art presentations on visualization problems in mathematics, fundamental mathematical research in computer graphics, and software frameworks for the application of visualization to real-world problems. Contributions have been written by leading experts and peer-refereed by an international editorial team. The book grew out of the third international workshop 'Visualization and Mathematics', May 22-25, 2002 in Berlin. The variety of topics covered makes the book ideal for researcher, lecturers, and practitioners.

Inhalt

Table of Contents Part I Geometry and Combinatorics of Meshes Philip L. Bowers, Monica K. Hurdal: Planar Conformal Mappings of Piecewise Flat Surfaces Mark Meyer, Mathieu Desbrun, Peter Schröder, Alan H. Barr: Discrete Differential-Geometry Operators for Triangulated 2-Manifolds Boris A. Springborn: Constructing Circle Patterns Using a New Functional Gabriel Taubin: Meshes Constructing Hamiltonian Triangle Strips on Quadrilateral Part II Discrete Vector Fields and Topology Thomas Lewiner, Helio Lopes, Geovan Tavares: Visualizing Forman's Discrete Vector Field Konrad Polthier and Eike Preuß: Identifying Vector Field Singularities Using a Discrete Hodge Decomposition Dennis Roseman: Searching for Knotted Spheres in 4-dimensional Space Thomas Wischgoll, Gerik Scheuermann: 3D Loop Detection and Visualization in Vector Fields Part III Geometric Modelling Rida T. Farouki, Hwan Pyo Moon: Minkowski Geometric Algebra and the Stability of Characteristic Polynomials Stefanie Hahmann, Georges-Pierre Bonneau, Alex Yvart: Subdivision Invariant Polynomial Interpolation Heinrich Müller, Markus Rips: Another Metascheme of Subdivision Surfaces Helmut Pottmann, Michael Hofer: Geometry of the Squared Distance Function to Curves and Surfaces Part IV Image Based Visualization Ulrich Clarenz, Udo Diewald, Martin Rumpf: A Multiscale Fairing Method for Textured Surfaces Michel Leblond, Fran cois Rousselle, Christophe Renaud: Generalized Block Iterative Methods Ravi Malladi, Igor Ravve: Fast Difference Schemes for Edge Enhancing Beltrami Flow and Subjective Surfaces Part V Software Environments and Applications George K. Francis, Camille M.A. Goudeseune, Henry J. Kaczmarski, Benjamin J. Schaeffer, John M. Sullivan: Alice on the Eightfold Way: Exploring Curved Spaces in an Enclosed Virtual Reality Theater Joseph M.L. Maubach, Alexandru C. Telea: Computation and Visualisation in the NumLab Numerical Laboratory Vinícius Mello, Luiz Velho, Paulo Roma Cavalcanti, Cláudio T. Silva: A Generic Programming Approach to Multiresolution Spatial Decompositions Alfio Quarteroni, Marzio Sala, M.L. Sawley, N. Parolini, G. Cowles: Mathematical Modelling and Visualisation of Complex Three-dimensional Flows Tom Wickham-Jones: webMathematica Part VI Education and Communication Michele Emmer: Films: A Communicating Tool for Mathematics Beau Janzen:The Potentials of Math Visualization and their Impact on the Curriculum Appendix: Color Plates