  The purpose of the book is to develop a generative theory of shape that has two properties regarded as fundamental to intelligence  maximizing transfer of structure and maximizing recoverability of the generative operations. These two properties are particularly important in the representation of complex shape  which is the main concern of the book. The primary goal of the theory is the conversion of complexity into understandability. For this purpose, a mathematical theory is presented of how understandability is created in a structure. This is achieved by developing a grouptheoretic approach to formalizing transfer and recoverability. To handle complex shape, a new class of groups is developed, called unfolding groups. These unfold structure from a maximally collapsed version of that structure. A principal aspect of the theory is that it develops a grouptheoretic formalization of major objectoriented concepts such as inheritance. The result is an objectoriented theory of geometry. The algebraic theory is applied in detail to CAD, perception, and robotics. In CAD, lengthy chapters are presented on mechanical and architectural design. For example, using the theory of unfolding groups, the book works in detail through the main stages of mechanical CAD/CAM: partdesign, assembly and machining. And within partdesign, an extensive algebraic analysis is given of sketching, alignment, dimensioning, resolution, editing, sweeping, featureaddition, and intentmanagement. The equivalent analysis is also done for architectural design. In perception, extensive theories are given for grouping and the main Gestalt motion phenomena (induced motion, separation of systems, the Johannson relative/absolute motion effects); as well as orientation and form. In robotics, several levels of analysis are developed for manipulator structure, using the author's algebraic theory of objectoriented structure. This book can be viewed electronically at the following site: SpringerVerlag: Leyton's book Author's address: Professor Michael Leyton, Center for Discrete Mathematics, & Theoretical Computer Science (DIMACS) Rutgers University, Busch Campus, New Brunswick, NJ 08854, USA Email address: mleyton@dimacs.rutgers.edu
