Theory of Design
Year: 2002 Authors: Michael Leyton
Core claim
A group-theoretic, object-oriented theory of geometry can formalize design, perception, and robotics by maximizing structural transfer and recoverability.
Topics
generative theory of shape, complex shape, object-oriented geometry, CAD and design
Domains
group theory, algebraic theory, geometry, unfolding groups, mechanical CAD/CAM, architectural design, sketching, form and orientation
Methods
group-theoretic formalization, algebraic analysis, generative modeling, Gestalt analysis
Media
book, CAD/CAM workflows, architectural design models, robotic manipulators
Paper text
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BRIDGES Mathematical Connections in Art, Music, and Science
Theory of Design
Michael Leyton Center for Discrete Mathematics & Theoretical Computer Science (DIMACS), Busch Campus, Rutgers University, New Brunswick, NJ 08904, USA. mleyton@dimacs.rutgers.edu
This talk gives an introduction to my book, A Generative Theory of Shape (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 book’s algebraic theory of object-oriented structure.
The book can be read on-line at the following site of the publisher Springer –Verlag: http://link.springer.de/link/service/series/0558/tocs/t2145.htm