Lecture Notes in Computer Science 2145 1st edition by Michael Leyton 3540427171 978‎-3540427179

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Product details:

ISBN-10 ‏ : ‎ 3540427171

ISBN-13 ‏ : ‎ 978-3540427179

Author :  Michael Leyton

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 itself. 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 a mathematical language that brings interoperability into the very foundations of geometry.

 

Lecture Notes in Computer Science 2145 1st Table of contents:

Mathematical Theory of Transfer, I

Mathematical Theory of Transfer, II

Theory of Grouping

Robot Manipulators

Algebraic Theory of Inheritance

Reference Frames

Relative Motion

Surface Primitives

Unfolding Groups, I

Unfolding Groups, II

Unfolding Groups, III

Mechanical Design and Manufacturing

A Mathematical Theory of Architecture

Solid Structure

Wreath Formulation of Splines

Wreath Formulation of Sweep Representations

 

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