Geometric Differentiation For the Intelligence of Curves and Surfaces [Hardcover]

This is a revised version of the popular Geometric Differentiation, first edition.This is a revised and up-dated version of the popular first edition. Topics rarely treated in elementary courses on differential geometry are considered here in detail. Many of these 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 wide applicability of this material means that it will 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 up-dated version of the popular first edition. Topics rarely treated in elementary courses on differential geometry are considered here in detail. Many of these 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 wide applicability of this material means that it will 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 Arnold 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 author has included many exercises and examples to illustrate the results proved.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 ll#+