Geometric Differentiation
For the Intelligence of Curves and Surfaces
Seiten
1994
Cambridge University Press (Verlag)
978-0-521-39063-7 (ISBN)
Cambridge University Press (Verlag)
978-0-521-39063-7 (ISBN)
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In this book elementary differential geometry is approached from a new standpoint, one inspired by Thom's work on singularity theory. This textbook provides a unique exposition of surface theory.
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.
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.
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.
| Erscheint lt. Verlag | 9.6.1994 |
|---|---|
| Zusatzinfo | 4 Plates, color; 2 Halftones, unspecified |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 156 x 236 mm |
| Gewicht | 635 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-10 | 0-521-39063-X / 052139063X |
| ISBN-13 | 978-0-521-39063-7 / 9780521390637 |
| Zustand | Neuware |
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