GENERATIVE THEORY OF SHAPE

["David Weiss" <dweiss@computational-aesthetics.com>]

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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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