Ebook: Mathematical Visualization: Algorithms, Applications and Numerics

Mathematical Visualization is a young new discipline. It offers efficient visualization tools to the classical subjects of mathematics, and applies mathematical techniques to problems in computer graphics and scientific visualization.
Originally, mathematical visualization started in the interdisciplinary area of differential geometry, numerical mathematics, and computer graphics. In recent years, the methods developed have found important applications, and the subject has evolved to a discipline in its own right. The current volume is the quintessence of an international workshop in September 1997in Berlin, focusing on recent developments in this emerging area. Experts present selected research work on new algorithms for visualization problems, describe the application and experiments in geometry, and develop new numerical or computer graphical techniques. The sections of the book contain topics on Meshes in Numerics and Visualization, Applications in Geometry and Numerics, Graphics Algorithms and Implementations, Geometric Visualization Techniques, and Vectorfields and Flow Visualization. The book is the second in a series of publications on this subject. It offers the reader insight to latest research and developments in this fascinating new area.

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Mathematical Visualization is a young new discipline. It offers efficient visualization tools to the classical subjects of mathematics, and applies mathematical techniques to problems in computer graphics and scientific visualization.
Originally, mathematical visualization started in the interdisciplinary area of differential geometry, numerical mathematics, and computer graphics. In recent years, the methods developed have found important applications, and the subject has evolved to a discipline in its own right. The current volume is the quintessence of an international workshop in September 1997in Berlin, focusing on recent developments in this emerging area. Experts present selected research work on new algorithms for visualization problems, describe the application and experiments in geometry, and develop new numerical or computer graphical techniques. The sections of the book contain topics on Meshes in Numerics and Visualization, Applications in Geometry and Numerics, Graphics Algorithms and Implementations, Geometric Visualization Techniques, and Vectorfields and Flow Visualization. The book is the second in a series of publications on this subject. It offers the reader insight to latest research and developments in this fascinating new area.

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Mathematical Visualization is a young new discipline. It offers efficient visualization tools to the classical subjects of mathematics, and applies mathematical techniques to problems in computer graphics and scientific visualization.
Originally, mathematical visualization started in the interdisciplinary area of differential geometry, numerical mathematics, and computer graphics. In recent years, the methods developed have found important applications, and the subject has evolved to a discipline in its own right. The current volume is the quintessence of an international workshop in September 1997in Berlin, focusing on recent developments in this emerging area. Experts present selected research work on new algorithms for visualization problems, describe the application and experiments in geometry, and develop new numerical or computer graphical techniques. The sections of the book contain topics on Meshes in Numerics and Visualization, Applications in Geometry and Numerics, Graphics Algorithms and Implementations, Geometric Visualization Techniques, and Vectorfields and Flow Visualization. The book is the second in a series of publications on this subject. It offers the reader insight to latest research and developments in this fascinating new area.
Content:
Front Matter....Pages I-XX
Front Matter....Pages 1-1
Tetrahedra Based Volume Visualization....Pages 3-18
Mesh Optimization and Multilevel Finite Element Approximations....Pages 19-30
Efficient Visualization of Data on Sparse Grids....Pages 31-44
A Meta Scheme for Iterative Refinement of Meshes....Pages 45-59
A Scheme for Edge-based Adaptive Tetrahedron Subdivision....Pages 61-70
Front Matter....Pages 71-71
Finite Element Approximations and the Dirichlet Problem for Surfaces of Prescribed Mean Curvature....Pages 73-87
Efficient Volume-Generation During the Simulation of NC-Milling....Pages 89-106
Constant Mean Curvature Surfaces with Cylindrical Ends....Pages 107-116
Discrete Rotational CMC Surfaces and the Elliptic Billiard....Pages 117-124
Zonotope Dynamics in Numerical Quality Control....Pages 125-134
Straightest Geodesics on Polyhedral Surfaces....Pages 135-150
Front Matter....Pages 151-151
Support of Explicit Time and Event Flows in the Object-Oriented Visualization Toolkit MAM/VRS....Pages 153-166
A Survey of Parallel Coordinates....Pages 167-179
Hierarchical Techniques for Global Illumination Computations — Recent Trends and Developments....Pages 181-194
Two-Dimensional Image Rotation....Pages 195-206
An Object-Oriented Interactive System for Scientific Simulations: Design and Applications....Pages 207-220
Front Matter....Pages 221-221
Auditory Morse Analysis of Triangulated Manifolds....Pages 223-236
Computing Sphere Eversions....Pages 237-255
Morse Theory for Implicit Surface Modeling....Pages 257-268
Special Relativity in Virtual Reality....Pages 269-279
Front Matter....Pages 221-221
Exploring Low Dimensional Objects in High Dimensional Spaces....Pages 281-291
Front Matter....Pages 293-293
Fast LIC with Piecewise Polynomial Filter Kernels....Pages 295-314
Visualizing Poincar? Maps together with the Underlying Flow....Pages 315-328
Accuracy in 3D Particle Tracing....Pages 329-341
Clifford Algebra in Vector Field Visualization....Pages 343-351
Visualization of Complex ODE Solutions....Pages 353-362
Back Matter....Pages 363-393

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Mathematical Visualization is a young new discipline. It offers efficient visualization tools to the classical subjects of mathematics, and applies mathematical techniques to problems in computer graphics and scientific visualization.
Originally, mathematical visualization started in the interdisciplinary area of differential geometry, numerical mathematics, and computer graphics. In recent years, the methods developed have found important applications, and the subject has evolved to a discipline in its own right. The current volume is the quintessence of an international workshop in September 1997in Berlin, focusing on recent developments in this emerging area. Experts present selected research work on new algorithms for visualization problems, describe the application and experiments in geometry, and develop new numerical or computer graphical techniques. The sections of the book contain topics on Meshes in Numerics and Visualization, Applications in Geometry and Numerics, Graphics Algorithms and Implementations, Geometric Visualization Techniques, and Vectorfields and Flow Visualization. The book is the second in a series of publications on this subject. It offers the reader insight to latest research and developments in this fascinating new area.
Content:
Front Matter....Pages I-XX
Front Matter....Pages 1-1
Tetrahedra Based Volume Visualization....Pages 3-18
Mesh Optimization and Multilevel Finite Element Approximations....Pages 19-30
Efficient Visualization of Data on Sparse Grids....Pages 31-44
A Meta Scheme for Iterative Refinement of Meshes....Pages 45-59
A Scheme for Edge-based Adaptive Tetrahedron Subdivision....Pages 61-70
Front Matter....Pages 71-71
Finite Element Approximations and the Dirichlet Problem for Surfaces of Prescribed Mean Curvature....Pages 73-87
Efficient Volume-Generation During the Simulation of NC-Milling....Pages 89-106
Constant Mean Curvature Surfaces with Cylindrical Ends....Pages 107-116
Discrete Rotational CMC Surfaces and the Elliptic Billiard....Pages 117-124
Zonotope Dynamics in Numerical Quality Control....Pages 125-134
Straightest Geodesics on Polyhedral Surfaces....Pages 135-150
Front Matter....Pages 151-151
Support of Explicit Time and Event Flows in the Object-Oriented Visualization Toolkit MAM/VRS....Pages 153-166
A Survey of Parallel Coordinates....Pages 167-179
Hierarchical Techniques for Global Illumination Computations — Recent Trends and Developments....Pages 181-194
Two-Dimensional Image Rotation....Pages 195-206
An Object-Oriented Interactive System for Scientific Simulations: Design and Applications....Pages 207-220
Front Matter....Pages 221-221
Auditory Morse Analysis of Triangulated Manifolds....Pages 223-236
Computing Sphere Eversions....Pages 237-255
Morse Theory for Implicit Surface Modeling....Pages 257-268
Special Relativity in Virtual Reality....Pages 269-279
Front Matter....Pages 221-221
Exploring Low Dimensional Objects in High Dimensional Spaces....Pages 281-291
Front Matter....Pages 293-293
Fast LIC with Piecewise Polynomial Filter Kernels....Pages 295-314
Visualizing Poincar? Maps together with the Underlying Flow....Pages 315-328
Accuracy in 3D Particle Tracing....Pages 329-341
Clifford Algebra in Vector Field Visualization....Pages 343-351
Visualization of Complex ODE Solutions....Pages 353-362
Back Matter....Pages 363-393
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