Visualization and Mathematics III

Prof. Dr. Konrad Polthier ist Professor für Mathematik an der Freien Universität Berlin und am DFG-Forschungszentrum MATHEON. Er hat mehrere Fachbücher zur mathematischen Visualisierung und unterhaltsame Videos zur Mathematik veröffentlicht.

Mathematical Visualization aims at an abstract framework for fundamen tal objects appearing in visualization and at the application of the manifold visualization techniques to problems in geometry, topology and numerical mathematics. The articles in this volume report on new research results in this field, on the development of software and educational material and on mathematical applications. The book grew out of the third international workshop "Visualization and Mathematics", which was held from May 22-25, 2002 in Berlin (Germany). The workshop was funded by the DFG-Sonderforschungsbereich 288 "Dif ferential Geometry and Quantum Physics" at Technische Universitat Berlin and supported by the Zuse Institute Berlin (ZIB) and the DFG research cen ter "Mathematics for Key Technologies" (FZT 86) in Berlin. Five keynote lectures, eight invited presentations and several contributed talks created a stimulating atmosphere with many scientific discussions. The themes of this book cover important recent developments in the fol lowing fields: - Geometry and Combinatorics of Meshes - Discrete Vector Fields and Topology - Geometric Modelling - Image Based Visualization - Software Environments and Applications - Education and Communication We hope that the research articles of this book will stimulate the readers' own work and will further strenghten the development of the field of Mathe matical Visualization. VI Preface We appreciate the thorough work of the authors and reviewers on each of the individual articles, and we thank you all.

3rd book arising from the series of successful Vis.

Planar Conformal Mappings of Piecewise Flat Surfaces.- Discrete Differential-Geometry Operators for Triangulated 2-Manifolds.- Constructing Circle Patterns Using a New Functional.- Constructing Hamiltonian Triangle Strips on Quadrilateral Meshes.- Visualizing Forman's Discrete Vector Field.- Identifying Vector Field Singularities Using a Discrete Hodge Decomposition.- Searching for Knotted Spheres in 4-dimensional Space.- 3D Loop Detection and Visualization in Vector Fields.- Minkowski Geometric Algebra and the Stability of Characteristic Polynomials.- Subdivision Invariant Polynomial Interpolation.- Another Metascheme of Subdivision Surfaces.- Geometry of the Squared Distance Function to Curves and Surfaces.- A Multiscale Fairing Method for Textured Surfaces.- Generalized Block Iterative Methods.- Fast Difference Schemes for Edge Enhancing Beltrami Flow and Subjective Surfaces.- Alice on the Eightfold Way: Exploring Curved Spaces in an Enclosed Virtual Reality Theater.- Computation and Visualisation in the NumLab Numerical Laboratory.- A Generic Programming Approach to Multiresolution Spatial Decompositions.- Mathematical Modelling and Visualisation of Complex Three-dimensional Flows.- webMathematica.- Films: A Communicating Tool for Mathematics.- The Potentials of Math Visualization and their Impact on the Curriculum.- Appendix: Color Plates.