Topological modeling for visualization [electronic resource] / A.T. Fomenko, T.L. Kunii.
The main goal of this textbook is to establish a bridge between the theoretical aspects of modern geometry and topology on the one hand and computer experimental geometry on the other. Thus the theory and application of mathematical visualization are given equal emphasis. This, along with the ample...
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| Format: | Electronic eBook |
| Language: | English |
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Tokyo ; New York :
Springer,
1997.
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Table of Contents:
- Part I. Foundation. Curves ; The notion of a Riemannian metric ; Local theory of surfaces ; The classification of surfaces ; Abstract manifolds ; Critical points and Morse theory ; Analyzing human body motions using manifolds and critical points ; Computer examination of surfaces and Morse functions ; Height functions and discrete functions ; Homotopies and surface generation ; Homology ; Geodesics ; Transformation groups
- Part II. Advanced subjects. Hyperbolic geometry and topology ; Hamiltonian system with two degrees of freedom ; Topological and orbital analysis of integrable problems ; Orbital invariant of integrable Hamiltonian systems ; Ridges, ravines and singularities
- Bibliography
- Index.