05166nam 22007935 450 99646601830331620200706073615.03-540-45488-810.1007/3-540-45488-8(CKB)1000000000016865(SSID)ssj0000323450(PQKBManifestationID)11243265(PQKBTitleCode)TC0000323450(PQKBWorkID)10299609(PQKB)10305450(DE-He213)978-3-540-45488-5(MiAaPQ)EBC3073251(PPN)155164236(EXLCZ)99100000000001686520121227d2001 u| 0engurnn#008mamaatxtccrA Generative Theory of Shape[electronic resource] /by Michael Leyton1st ed. 2001.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2001.1 online resource (XV, 549 p.)Lecture Notes in Computer Science,0302-9743 ;2145Bibliographic Level Mode of Issuance: Monograph3-540-42717-1 Includes bibliographical references and index.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.The purpose of this book is to develop a generative theory of shape that has two properties we regard as fundamental to intelligence –(1) maximization of transfer: whenever possible, new structure should be described as the transfer of existing structure; and (2) maximization of recoverability: the generative operations in the theory must allow maximal inferentiability from data sets. We shall show that, if generativity satis?es these two basic criteria of - telligence, then it has a powerful mathematical structure and considerable applicability to the computational disciplines. The requirement of intelligence is particularly important in the gene- tion of complex shape. There are plenty of theories of shape that make the generation of complex shape unintelligible. However, our theory takes the opposite direction: we are concerned with the conversion of complexity into understandability. In this, we will develop a mathematical theory of und- standability. The issue of understandability comes down to the two basic principles of intelligence - maximization of transfer and maximization of recoverability. We shall show how to formulate these conditions group-theoretically. (1) Ma- mization of transfer will be formulated in terms of wreath products. Wreath products are groups in which there is an upper subgroup (which we will call a control group) that transfers a lower subgroup (which we will call a ?ber group) onto copies of itself. (2) maximization of recoverability is insured when the control group is symmetry-breaking with respect to the ?ber group.Lecture Notes in Computer Science,0302-9743 ;2145Optical data processingGeometryApplication softwareComputer graphicsGroup theoryComputer-aided engineeringImage Processing and Computer Visionhttps://scigraph.springernature.com/ontologies/product-market-codes/I22021Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M21006Computer Applicationshttps://scigraph.springernature.com/ontologies/product-market-codes/I23001Computer Graphicshttps://scigraph.springernature.com/ontologies/product-market-codes/I22013Group Theory and Generalizationshttps://scigraph.springernature.com/ontologies/product-market-codes/M11078Computer-Aided Engineering (CAD, CAE) and Designhttps://scigraph.springernature.com/ontologies/product-market-codes/I23044Optical data processing.Geometry.Application software.Computer graphics.Group theory.Computer-aided engineering.Image Processing and Computer Vision.Geometry.Computer Applications.Computer Graphics.Group Theory and Generalizations.Computer-Aided Engineering (CAD, CAE) and Design.516Leyton Michaelauthttp://id.loc.gov/vocabulary/relators/aut553383MiAaPQMiAaPQMiAaPQBOOK996466018303316Generative theory of shape977447UNISA