Overview

"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."

Full Product Details

Author:   Michael Leyton
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   2001 ed.
Volume:   2145
Dimensions:   Width: 15.50cm , Height: 2.90cm , Length: 23.30cm
Weight:   1.760kg
ISBN:  

9783540427179

ISBN 10:   3540427171
Pages:   549
Publication Date:   26 October 2001
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Transfer.- Recoverability.- Mathematical Theory of Transfer, I.- Mathematical Theory of Transfer, II.- Theory of Grouping.- Robot Manipulators.- Algebraic Theory of Inheritance.- Reference Frames.- Relative Motion.- Surface Primitives.- Unfolding Groups, I.- Unfolding Groups, II.- Unfolding Groups, III.- Mechanical Design and Manufacturing.- A Mathematical Theory of Architecture.- Solid Structure.- Wreath Formulation of Splines.- Wreath Formulation of Sweep Representations.- Process Grammar.- Conservation Laws of Physics.- Music.- Against the Erlanger Program.

Reviews

From the reviews: This book is intended for a general scientifically interested audience a ] . The author develops a generative theory of shape along two principles fundamental to intelligence a maximization of transfer and maximization of recoverability. He proceeds by using an algebraically flavoured approach characterizing features as symmetry groups while the addition of features corresponds to group extension. a ] The generative theory is used in several application areas like visual perception, robotics and computer-aided geometric design. (GA1/4nter Landsman, Zentralblatt MATH, Vol. 1012, 2003)

From the reviews: <p> This book is intended for a general scientifically interested audience a ] . The author develops a generative theory of shape along two principles fundamental to intelligence a maximization of transfer and maximization of recoverability. He proceeds by using an algebraically flavoured approach characterizing features as symmetry groups while the addition of features corresponds to group extension. a ] The generative theory is used in several application areas like visual perception, robotics and computer-aided geometric design. (GA1/4nter Landsman, Zentralblatt MATH, Vol. 1012, 2003)

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