Geometric differentiation : for the intelligence of curves and surfaces
著者
書誌事項
Geometric differentiation : for the intelligence of curves and surfaces
Cambridge University Press, 1994
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注記
Includes references and index
内容説明・目次
内容説明
Geometry is to the fore in this textbook. Inspired by the work of Thom and Arnol'd on Singularity Theory, topics such as umbilics, ridges and subparabolic lines, all robust features of a smooth surface, which are rarely treated in elementary courses on differential geometry, are here considered in detail. These features are of immediate relevance in modern areas of application including pattern recognition, computer vision, electronic scanning and remote sensing. Central to the exposition is the role of certain cubic forms associated with a surface; using this theory many interesting results are proved and illustrative examples explored. The text is based on extensive teaching at Liverpool University to audiences of advanced undergraduate and beginning postgraduate students in mathematics, but its wide applicability will mean that it will also appeal to scientists and engineers from a variety of other disciplines.
目次
- 1. Plane curves
- 2. Linear and projective spaces
- 3. Plane kinematics
- 4. The derivatives of a map
- 5. Curves on the unit sphere
- 6. Space curves
- 7. k-times linear forms
- 8. Probes
- 9. Contact
- 10. Surfaces in R3
- 11. Ridges and ribs
- 12. Umbilics
- 13. Parabolic lines
- 14. Involutes of geodesic foliations
- 15. The circles of a surfaces
- 16. Examples of surfaces
- References.
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