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TitleMathematical Visualization [electronic resource] : Algorithms, Applications and Numerics / edited by Hans-Christian Hege, Konrad Polthier
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1998
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Descript XX, 393 p. online resource


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


Tetrahedra Based Volume Visualization -- Mesh Optimization and Multilevel Finite Element Approximations -- Efficient Visualization of Data on Sparse Grids -- A Meta Scheme for Iterative Refinement of Meshes -- A Scheme for Edge-based Adaptive Tetrahedron Subdivision -- Finite Element Approximations and the Dirichlet Problem for Surfaces of Prescribed Mean Curvature -- Efficient Volume-Generation During the Simulation of NC-Milling -- Constant Mean Curvature Surfaces with Cylindrical Ends -- Discrete Rotational CMC Surfaces and the Elliptic Billiard -- Zonotope Dynamics in Numerical Quality Control -- Straightest Geodesics on Polyhedral Surfaces -- Support of Explicit Time and Event Flows in the Object-Oriented Visualization Toolkit MAM/VRS -- A Survey of Parallel Coordinates -- Hierarchical Techniques for Global Illumination Computations โ{128}{148} Recent Trends and Developments -- Two-Dimensional Image Rotation -- An Object-Oriented Interactive System for Scientific Simulations: Design and Applications -- Auditory Morse Analysis of Triangulated Manifolds -- Computing Sphere Eversions -- Morse Theory for Implicit Surface Modeling -- Special Relativity in Virtual Reality -- Exploring Low Dimensional Objects in High Dimensional Spaces -- Fast LIC with Piecewise Polynomial Filter Kernels -- Visualizing Poincarรฉ Maps together with the Underlying Flow -- Accuracy in 3D Particle Tracing -- Clifford Algebra in Vector Field Visualization -- Visualization of Complex ODE Solutions -- Appendix: Color Plates

Mathematics Computer graphics Global analysis (Mathematics) Manifolds (Mathematics) Visualization Numerical analysis Differential geometry Topology Mathematics Differential Geometry Visualization Numerical Analysis Computer Graphics Global Analysis and Analysis on Manifolds Topology


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