

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
