Visualization and Mathematics III / Edition 1

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This research book on Mathematical Visualization contains state of the art presentations on visualization problems in mathematics, on fundamental mathematical research in computer graphics, and on software frameworks for the application of visualization to real-world problems.All contributions were written by leading experts in the field and peer-refereed by an international editorial team. The book grew out of the third international workshop 'Visualization and Mathematics', which was held from May 22-25, 2002 in Berlin. The themes of the book cover important recent developments on Geometry and Combinatorics of Meshes Discrete Vector Fields and Topology Geometric Modelling Image Based Visualization Software Environments and Applications- Education and Communication The variety of topics makes the book a suitable resource for researcher, lecturers, and practitioners.

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Product Details

  • ISBN-13: 9783540012955
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 8/13/2003
  • Series: Mathematics and Visualization Series
  • Edition description: 2003
  • Edition number: 1
  • Pages: 457

Table of Contents

Planar Conformal Mappings of Piecewise Flat Surfaces 3
Discrete Differential-Geometry Operators for Triangulated 2-Manifolds 35
Constructing Circle Patterns Using a New Functional 59
Constructing Hamiltonian Triangle Strips on Quadrilateral Meshes 69
Visualizing Forman's Discrete Vector Field 95
Identifying Vector Field Singularities Using a Discrete Hodge Decomposition 113
Searching for Knotted Spheres in 4-dimensional Space 135
3D Loop Detection and Visualization in Vector Fields 151
Minkowski Geometric Algebra and the Stability of Characteristic Polynomials 163
Subdivision Invariant Polynomial Interpolation 189
Another Metascheme of Subdivision Surfaces 201
Geometry of the Squared Distance Function to Curves and Surfaces 221
A Multiscale Fairing Method for Textured Surfaces 245
Generalized Block Iterative Methods 261
Fast Difference Schemes for Edge Enhancing Beltrami Flow and Subjective Surfaces 287
Alice on the Eightfold Way: Exploring Curved Spaces in an Enclosed Virtual Reality Theater 305
Computation and Visualisation in the NumLab Numerical Laboratory 317
A Generic Programming Approach to Multiresolution Spatial Decompositions 337
Mathematical Modelling and Visualisation of Complex Three-dimensional Flows 361
web Mathematica 379
Films: A Communicating Tool for Mathematics 393
The Potentials of Math Visualization and their Impact on the Curriculum 407
App.: Color Plates 423
Index 453
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