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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
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