Visualization and Mathematics: Experiments, Simulations and Environments

ISBN-13: 9783642638916 / Angielski / Miękka / 2012 / 388 str.

H. -C Hege; K. Polthier

Opis

Visualization and mathematics have begun a fruitful relationship, establishing links between problems and solutions of both fields. In some areas of mathematics, like differential geometry and numerical mathematics, visualization techniques are applied with great success. However, visualization methods are relying heavily on mathematical concepts.
Applications of visualization in mathematical research and the use of mathematical methods in visualization have been topic of an international workshop in Berlin in June 1995. Selected contributions treat topics of particular interest in current research. Experts are reporting on their latest work, giving an overview on this fascinating new area. The reader will get insight to state-of-the-art techniques for solving visualization problems and mathematical questions.

Spis treści

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.

Blurb

Visualization and mathematics have begun a fruitful relationship, establishing many links between problems and solutions of both fields. In some areas of mathematics, such as numerical mathematics and differential geometry, visualization techniques are applied with great success. On the other hand, visualization methods are relying heavily on mathematical concepts.
Applications of visualization in mathematical research as well as the use of mathematical methods in visualization have been topic of an international workshop in Berlin in June 1995. Selected contributions treat topics of particular interest in current research, addressing subjects like visualization of mathematical spaces, visualization and simulation techniques, mathematical experiments, graphics environments, and description and modeling of geometric objects. Experts in these fields are reporting on their latest work, giving an overview on this fascinating new area. The reader will get insight to state-of-the-art techniques for solving visualization problems and mathematical questions.