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The Resource A Generative Theory of Shape, edited by Gerhard Goos, Juris Hartmanis, Jan Leeuwen, (electronic resource)

A Generative Theory of Shape, edited by Gerhard Goos, Juris Hartmanis, Jan Leeuwen, (electronic resource)

Creator
Editor
Contributor
Summary
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. The book gives extensive applications of the theory to CAD/CAM, human and machine vision, robotics, software engineering, and physics. 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. 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 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
Language
eng
Work
Publication
Extent
XV, 549 p.
Contents
  • Transfer
  • Recoverability
  • 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
  • Process Grammar
  • Conservation Laws of Physics
  • Music
  • Against the Erlanger Program
Isbn
9783540454885
Instance
Label
A Generative Theory of Shape
Title
A Generative Theory of Shape
Statement of responsibility
edited by Gerhard Goos, Juris Hartmanis, Jan Leeuwen
Creator
Contributor
Editor
Provider
Subject
Language
eng
Summary
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. The book gives extensive applications of the theory to CAD/CAM, human and machine vision, robotics, software engineering, and physics. 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. 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 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
Member of
http://library.link/vocab/creatorName
Goos, Gerhard
Image bit depth
0
LC call number
  • TA1637-1638
  • TA1637-1638
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
  • Hartmanis, Juris.
  • Leeuwen, Jan.
  • SpringerLink
Series statement
Lecture Notes in Computer Science,
Series volume
2145
http://library.link/vocab/subjectName
  • Computer science
  • Computer graphics
  • Computer vision
  • Computer aided design
  • Group theory
  • Geometry
  • Computer Science
  • Image Processing and Computer Vision
  • Computer Graphics
  • Geometry
  • Group Theory and Generalizations
  • Computer-Aided Engineering (CAD, CAE) and Design
Label
A Generative Theory of Shape, edited by Gerhard Goos, Juris Hartmanis, Jan Leeuwen, (electronic resource)
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Transfer -- Recoverability -- 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 -- Process Grammar -- Conservation Laws of Physics -- Music -- Against the Erlanger Program
Dimensions
unknown
Extent
XV, 549 p.
File format
multiple file formats
Form of item
electronic
Isbn
9783540454885
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/3-540-45488-8
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-540-45488-5
Label
A Generative Theory of Shape, edited by Gerhard Goos, Juris Hartmanis, Jan Leeuwen, (electronic resource)
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Transfer -- Recoverability -- 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 -- Process Grammar -- Conservation Laws of Physics -- Music -- Against the Erlanger Program
Dimensions
unknown
Extent
XV, 549 p.
File format
multiple file formats
Form of item
electronic
Isbn
9783540454885
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/3-540-45488-8
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-540-45488-5

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