Mathematical Visualization: Algorithms, Applications and Numerics

ISBN-13: 9783540639916 / Angielski / Twarda / 1998 / 393 str.

Hege, H. -C

Opis

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, it started in the interdisciplinary area of differential geometry, numerical mathematics, and computer graphics. In recent years, the methods developed have found important applications.
The current volume is the quintessence of an international workshop in September 1997 in 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.

Spis treści

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 — 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 Poincaré 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.

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.

Blurb

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.