Visualization and Mathematics III

ISBN-13: 9783540012955 / Angielski / Twarda / 2003 / 457 str.

Hans-Christian Hege; Konrad Polthier

Opis

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.

Spis treści

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

O autorze

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.