Visualization and Mathematics

This book is based on an international workshop held in Berlin in 1995. The workshop was met with great approval by mathematicians and computer graphic experts. It was considered a link between the fields "Visualization in Mathematics" and "Mathematical Methods in Computer Graphics".

Inhalt
I. Visualizing Mathematics.- The Minimax Sphere Eversion.- Exploring Plane Hyperbolic Geometry.- Visualizing Nonlinear Electrodynamics.- The Use of Computer Graphics for Solving Problems in Singularity Theory.- What Should a Surface in 4-Space Look Like?.- Animation of Algebraic Surfaces.- II. Geometric Algorithms and Experiments.- Using Symmetry Features of the Surface Evolver to Study Foams.- Constant Mean Curvature Surfaces Derived from Delaunay's and Wente's Examples.- Visualization of Periodic Tilings.- An Algorithm for Discrete Constant Mean Curvature Surfaces.- III. Visualization Algorithms and Data Structures.- Efficient Calculation of Subdivision Surfaces for Visualization.- Fast Line Integral Convolution for Arbitrary Surfaces in 3D.- Visualization of Parallel Data based on Procedural Access.- IV. Visualization Environments.- A new 3D Graphics Library: Concepts, Implementation, and Examples.- A Generic Approach to Computer Graphics.- MRT A Visualization Tool Addressing Problems 'outside' the Classical Rendering Domain.- Oorange: A Virtual Laboratory for Experimental Mathematics.- Linear Inductive Reductive Dataflow System for ViSC.- See what I mean? Using Graphics Toolkits to Visualise Numerical Data.- V. Visualization and Simulation Techniques.- Numerical Algorithms and Visualization in Medical Treatment Planning.- Level Set Methods for Curvature Flow, Image Enchancement, and Shape Recovery in Medical Images.- Numerical Methods, Simulations and Visualization for Compressible Flows.- Appendix: Color Plates.