Topological modeling for visualization
著者
書誌事項
Topological modeling for visualization
Springer, c1997
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
This work focuses on the contribution of topology to computer visualization methods. It covers not only linear but also non-linear problems. It contains examples, and only requires knowledge of high-school mathematics.
目次
- Part 1 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 2 Advanced subjects: hyperbolic geometry and topology
- Hamiltonian system with two degrees of freedom
- topological and orbital analysis of integrable Hamiltonian systems
- ridges, ravines and singularities.
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