Geometric Differentiation
For the Intelligence of Curves and Surfaces
Seiten
2001
|
2nd Revised edition
Cambridge University Press (Verlag)
978-0-521-81040-1 (ISBN)
Cambridge University Press (Verlag)
978-0-521-81040-1 (ISBN)
This is a revised and up-dated version of the popular first edition. The topics covered here are of immediate relevance to many modern applications. As such this text will appeal to scientists and engineers from a variety of other disciplines. There are many exercises and examples illustrating the results proved.
This is a revised and extended version of the popular first edition. Inspired by the work of Thom and Arnol'd on singularity theory, such topics as umbilics, ridges and subparabolic lines, all robust features of a smooth surface, which are rarely treated in elementary courses on differential geometry, are considered here in detail. These features are of immediate relevance in modern areas of application such as interpretation of range data from curved surfaces and the processing of magnetic resonance and cat-scan images. The text is based on extensive teaching at Liverpool University to audiences of advanced undergraduate and beginning postgraduate students in mathematics. However, the wide applicability of this material means that it will also appeal to scientists and engineers from a variety of other disciplines. The author has included many exercises and examples to illustrate the results proved.
This is a revised and extended version of the popular first edition. Inspired by the work of Thom and Arnol'd on singularity theory, such topics as umbilics, ridges and subparabolic lines, all robust features of a smooth surface, which are rarely treated in elementary courses on differential geometry, are considered here in detail. These features are of immediate relevance in modern areas of application such as interpretation of range data from curved surfaces and the processing of magnetic resonance and cat-scan images. The text is based on extensive teaching at Liverpool University to audiences of advanced undergraduate and beginning postgraduate students in mathematics. However, the wide applicability of this material means that it will also appeal to scientists and engineers from a variety of other disciplines. The author has included many exercises and examples to illustrate the results proved.
fm.author_biographical_note1
1. Plane curves; 2. Some elementary geometry; 3. Plane kinetics; 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. The parabolic line; 14. Involutes of geodesic foliations; 15. The circles of a surface; 16. Examples of surfaces; 17. Flexicords of surfaces; 18. Duality.
| Erscheint lt. Verlag | 13.12.2001 |
|---|---|
| Zusatzinfo | 26 Plates, color; 39 Line drawings, unspecified |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 158 x 237 mm |
| Gewicht | 704 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-10 | 0-521-81040-X / 052181040X |
| ISBN-13 | 978-0-521-81040-1 / 9780521810401 |
| Zustand | Neuware |
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