Members of the list will be interested in the following important book in
Springer.
A Generative Theory of Shape
Michael Leyton
Springer-Verlag
The purpose of the book is to develop a generative theory that has two
properties regarded as fundamental to intelligence -
maximizing reusability of structure and maximizing recoverability of the
generative operations. These two properties are
particularly important in the representation of complex organization - 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 reusability and recoverability. To handle highly complex structure,
a new class of groups is invented, 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
new algebraic formalization of major object-oriented concepts such as
inheritance. The consequence that the book establishes
a representational language for complex organizational structure, that is
interoperable by virtue of the principles on which the theory
is based: reusability and recoverability.
The book gives extensive applications of the theory to CAD/CAM, human and
machine vision, robotics, software engineering, and physics.
For example, the theory is used to give new and detailed insights into the main
stages of mechanical CAD/CAM: part-design, assembly a
nd machining. And within part-design, an extensive analysis is given of
sketching, alignment, dimensioning, resolution, editing, sweeping,
feature-addition, and intent-management. In robotics, several levels of
analysis are developed for manipulator structure and kinematics.
In software, a new theory is given of the principal factors such as text and
class structure, object creation cloning and modification, as
well as inheritance and hierarchy prediction. In physics, a new theory is given
of the conservation laws, and motion decomposition
theorems in classical and quantum mechanics. In perception, extensive theories
are developed for Gestalt grouping criteria, orientation
and form, the prototype phenomena, and the main Gestalt motion phenomena
(induced motion, separation of systems, the Johannson
relative/absolute motion effects.
Springer-Verlag allows the book to be viewed on-line at institutions that have
a Springer subscription:
On-line link: http://www.rci.rutgers.edu/~mleyton/homepage.htm
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