Visualization and Mathematics III

1. Front Matter

   Pages I-XII

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2. Geometry and Combinatorics of Meshes

   1. Front Matter

      Pages 1-1

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   2. Planar Conformal Mappings of Piecewise Flat Surfaces

      • Philip L. Bowers, Monica K. Hurdal

      Pages 3-34

   3. Discrete Differential-Geometry Operators for Triangulated 2-Manifolds

      • Mark Meyer, Mathieu Desbrun, Peter Schröder, Alan H. Barr

      Pages 35-57

   4. Constructing Circle Patterns Using a New Functional

      • Boris A. Springborn

      Pages 59-68

   5. Constructing Hamiltonian Triangle Strips on Quadrilateral Meshes

      • Gabriel Taubin

      Pages 69-91

3. Discrete Vector Fields and Topology

   1. Front Matter

      Pages 93-93

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   2. Visualizing Forman’s Discrete Vector Field

      • Thomas Lewiner, Helio Lopes, Geovan Tavares

      Pages 95-112

   3. Identifying Vector Field Singularities Using a Discrete Hodge Decomposition

      • Konrad Polthier, Eike Preuß

      Pages 113-134

   4. Searching for Knotted Spheres in 4-dimensional Space

      • Dennis Roseman

      Pages 135-150

   5. 3D Loop Detection and Visualization in Vector Fields

      • Thomas Wischgoll, Gerik Scheuermann

      Pages 151-160

4. Geometric Modelling

   1. Front Matter

      Pages 161-161

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   2. Minkowski Geometric Algebra and the Stability of Characteristic Polynomials

      • Rida T. Farouki, Hwan Pyo Moon

      Pages 163-188

   3. Subdivision Invariant Polynomial Interpolation

      • Stefanie Hahmann, Georges-Pierre Bonneau, Alex Yvart

      Pages 189-200

   4. Another Metascheme of Subdivision Surfaces

      • Heinrich Müller, Markus Rips

      Pages 201-220

   5. Geometry of the Squared Distance Function to Curves and Surfaces

      • Helmut Pottmann, Michael Hofer

      Pages 221-242

5. Image Based Visualization

   1. Front Matter

      Pages 243-243

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   2. A Multiscale Fairing Method for Textured Surfaces

      • Ulrich Clarenz, Udo Diewald, Martin Rumpf

      Pages 245-260

   3. Generalized Block Iterative Methods

      • Michel Leblond, François Rousselle, Christophe Renaud

      Pages 261-285

   4. Fast Difference Schemes for Edge Enhancing Beltrami Flow and Subjective Surfaces

      • Ravi Malladi, Igor Ravve

      Pages 287-302

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.

• Discrete Geometry of Meshes
• Image Based Visualization
• Mathematical Visualization
• Software Environments
• Vector Fields and Flow Visualization
• computer graphics
• programming

• Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB), Berlin, Germany

  Hans-Christian Hege

• Institut für Mathematik, MA 8–3, Technische Universität Berlin, Berlin, Germany

  Konrad Polthier

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