A 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


--------------------------------------------------------------------


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.
            

--------------------------------------------------------------------



            This book can be viewed electronically at the following site:


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


--------------------------------------------------------------------


            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 at dimacs.rutgers.edu

--------------------------------------------------------------------