[vslist] Generative Theory of Shape

[James Johnson]

The following book has just appeared in Springer-Verlag.






             A Generative Theory of Shape


            Michael Leyton

            Springer-Verlag, 550 pages


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            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 group-theoretic 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 group-theoretic formalization of major object-oriented
concepts such as inheritance. The result is an object-oriented 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:
part-design, assembly and machining. And within part-design, an extensive
algebraic analysis is given of sketching, alignment, dimensioning,
resolution, editing, sweeping, feature-addition, and intent-management. 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 object-oriented
structure.




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            This book can be viewed electronically at the following site:


            http://link.springer.de/link/service/series/0558/tocs/t2145.htm


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            Author's address:


            Professor Michael Leyton,
            Center for Discrete Mathematics,
            & Theoretical Computer Science (DIMACS)
            Rutgers University, Busch Campus,
            New Brunswick, NJ 08854,
            USA



            E-mail address: mleyton@dimacs.rutgers.edu

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