A Generative Theory of Shape

Michael Leyton

554 pages, parution le 21/01/2002

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Résumé

In this book, the author develops a generative theory of shape with two properties fundamental to intelligence: maximizing transfer of structure, and maximizing recoverability of generative operations. The theory is applied in considerable detail to CAD, perception, and robotics. A significant aspect of this book is the development of an object-oriented theory of geometry. This includes a group-theoretic formulation of object-oriented inheritance. In particular, a class of groups is developed called "unfolding groups", which define any complex shape as unfolded from a maximally collapsed version of itself called an "alignment kernel". The group is decomposed into levels corresponding to the inheritance hierarchy within the complex object. This achieves one of the main goals of the theory - the conversion of complexity into understandability. The advantages of the theory are demonstrated with lengthy studies of robot manipulators, perceptual organization, constructive solid geometry, assembly planning, architectural CAD, and mechanical CAD/CAM.

Contents

1.Transfer
2. Recoverability
3. Mathematical Theory of Transfer, I
4. Mathematical Theory of Transfer, II
5. Theory of Grouping
6. Robot Manipulators
7. Algebraic Theory of Inheritance
8. Reference Frames
9. Relative Motion
10. Surface Primitives
11. Unfolding Groups, I
12. Unfolding Groups, II
13. Unfolding Groups, III
14. Mechanical Design and Manufacturing
15. A Mathematical Theory of Architecture
16. Solid Structure
17. Wreath Formulation of Splines
18. Wreath Formulation of Sweep Representations
19. Process Grammar
20. Conservation Laws of Physics
21. Music
22. Against the Erlanger Program
A. Semi-direct Products
B. Symbols
References
Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Michael Leyton
Parution	21/01/2002
Nb. de pages	554
Format	15,5 x 23,5
Couverture	Broché
Poids	814g
Intérieur	Noir et Blanc
EAN13	9783540427179