Algebraic geometry and group theory in geometric constraint satisfaction for computer-aided design and assembly planning

Mechanical design and assembly planning inherently involve geometric constraint satisfaction or scene feasibility (GCS/SF) problems -- Such problems imply the satisfaction of proposed relations placed between undefined geometric entities in a given scenario -- If the degrees of freedom remaining in...

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Autores:
Ruíz, Óscar E.
Ferreira, Placid M.
Tipo de recurso:
Fecha de publicación:
1996
Institución:
Universidad EAFIT
Repositorio:
Repositorio EAFIT
Idioma:
eng
OAI Identifier:
oai:repository.eafit.edu.co:10784/9782
Acceso en línea:
http://hdl.handle.net/10784/9782
Palabra clave:
GEOMETRÍA ALGEBRÁICA
TEORÍA DE LOS GRUPOS
TEORÍA DE LA FORMA (TOPOLOGÍA)
POLINOMIOS
DISEÑO CON AYUDA DE COMPUTADOR
Geometry, algebraic
Groups, Theory of
Shape theory
Polynomials
Computer-aided Design
Geometry
algebraic
Groups
Theory of
Shape theory
Polynomials
Computer-aided Design
Restricciones geométricas
Bases de Gröbner
Razonamiento geométrico
Rights
License
Acceso cerrado
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spelling 2016-11-30T15:20:17Z19962016-11-30T15:20:17Z0740-817Xhttp://hdl.handle.net/10784/978210.1080/07408179608966276Mechanical design and assembly planning inherently involve geometric constraint satisfaction or scene feasibility (GCS/SF) problems -- Such problems imply the satisfaction of proposed relations placed between undefined geometric entities in a given scenario -- If the degrees of freedom remaining in the scene are compatible with the proposed relations or constraints, a set of entities is produced that populate the scenario satisfying the relations -- Otherwise, a diagnostic of inconsistency of the problem is emitted -- This problem appears in various forms in assembly planning (assembly model generation), process planning, constraint driven design, computer vision, etc -- Previous attempts at solution using separate numerical, symbolic or procedural approaches suffer serious shortcomings in characterizing the solution space, in dealing simultaneously with geometric (dimensional) and topological (relational) inconsistencies, and in completely covering the possible physical variations of the problem -- This investigation starts by formulating the problem as one of characterizing the solution space of a set of polynomials -- By using theories developed in the area of algebraic geometry, properties of Grobner Bases are used to assess the consistency and ambiguity of the given problem and the dimension of its solution space -- This method allows for die integration of geometric and topological reasoning -- The high computational cost of Grobner Basis construction and the need for a compact and physically meaningful set of variables lead to the integration of known results on group theory -- These results allow the characterization of geometric constraints in terms of the subgroups of the Special Group of Euclidean displacements in E^3, SE(3) -- Several examples arc developed which were solved with computer algebra systems (MAPLE and Mathematica) -- They are presented to illustrate the use of the Euclidean group-based variables, and to demonstrate the theoretical completeness of the algebraic geometry analysis over the domain of constraints expressible as polynomialsengTaylor & FrancisIIE Transactions, Volume 28, Issue 4, pp 281-294http://dx.doi.org/10.1080/07408179608966276Acceso cerradohttp://purl.org/coar/access_right/c_14cbAlgebraic geometry and group theory in geometric constraint satisfaction for computer-aided design and assembly planninginfo:eu-repo/semantics/articlearticleinfo:eu-repo/semantics/publishedVersionpublishedVersionArtículohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1GEOMETRÍA ALGEBRÁICATEORÍA DE LOS GRUPOSTEORÍA DE LA FORMA (TOPOLOGÍA)POLINOMIOSDISEÑO CON AYUDA DE COMPUTADORGeometry, algebraicGroups, Theory ofShape theoryPolynomialsComputer-aided DesignGeometryalgebraicGroupsTheory ofShape theoryPolynomialsComputer-aided DesignRestricciones geométricasBases de GröbnerRazonamiento geométricoUniversidad EAFIT. Departamento de Ingeniería MecánicaRuíz, Óscar E.Ferreira, Placid M.Laboratorio CAD/CAM/CAEIIE TransactionsIIE Transactions284281294LICENSElicense.txtlicense.txttext/plain; charset=utf-82556https://repository.eafit.edu.co/bitstreams/b7e0477f-ea53-4df1-8ccf-d88937f7ebf0/download76025f86b095439b7ac65b367055d40cMD51ORIGINALAlgebraicGeometry.pdfAlgebraicGeometry.pdfapplication/pdf1199774https://repository.eafit.edu.co/bitstreams/d7f2f16f-6252-4000-b90b-4b46bbb0e14b/download671f67250faa371faa596c998c911d64MD5210784/9782oai:repository.eafit.edu.co:10784/97822021-09-03 15:43:58.081restrictedhttps://repository.eafit.edu.coRepositorio Institucional Universidad EAFITrepositorio@eafit.edu.co
dc.title.eng.fl_str_mv Algebraic geometry and group theory in geometric constraint satisfaction for computer-aided design and assembly planning
title Algebraic geometry and group theory in geometric constraint satisfaction for computer-aided design and assembly planning
spellingShingle Algebraic geometry and group theory in geometric constraint satisfaction for computer-aided design and assembly planning
GEOMETRÍA ALGEBRÁICA
TEORÍA DE LOS GRUPOS
TEORÍA DE LA FORMA (TOPOLOGÍA)
POLINOMIOS
DISEÑO CON AYUDA DE COMPUTADOR
Geometry, algebraic
Groups, Theory of
Shape theory
Polynomials
Computer-aided Design
Geometry
algebraic
Groups
Theory of
Shape theory
Polynomials
Computer-aided Design
Restricciones geométricas
Bases de Gröbner
Razonamiento geométrico
title_short Algebraic geometry and group theory in geometric constraint satisfaction for computer-aided design and assembly planning
title_full Algebraic geometry and group theory in geometric constraint satisfaction for computer-aided design and assembly planning
title_fullStr Algebraic geometry and group theory in geometric constraint satisfaction for computer-aided design and assembly planning
title_full_unstemmed Algebraic geometry and group theory in geometric constraint satisfaction for computer-aided design and assembly planning
title_sort Algebraic geometry and group theory in geometric constraint satisfaction for computer-aided design and assembly planning
dc.creator.fl_str_mv Ruíz, Óscar E.
Ferreira, Placid M.
dc.contributor.department.spa.fl_str_mv Universidad EAFIT. Departamento de Ingeniería Mecánica
dc.contributor.author.none.fl_str_mv Ruíz, Óscar E.
Ferreira, Placid M.
dc.contributor.researchgroup.spa.fl_str_mv Laboratorio CAD/CAM/CAE
dc.subject.lemb.spa.fl_str_mv GEOMETRÍA ALGEBRÁICA
TEORÍA DE LOS GRUPOS
TEORÍA DE LA FORMA (TOPOLOGÍA)
POLINOMIOS
DISEÑO CON AYUDA DE COMPUTADOR
topic GEOMETRÍA ALGEBRÁICA
TEORÍA DE LOS GRUPOS
TEORÍA DE LA FORMA (TOPOLOGÍA)
POLINOMIOS
DISEÑO CON AYUDA DE COMPUTADOR
Geometry, algebraic
Groups, Theory of
Shape theory
Polynomials
Computer-aided Design
Geometry
algebraic
Groups
Theory of
Shape theory
Polynomials
Computer-aided Design
Restricciones geométricas
Bases de Gröbner
Razonamiento geométrico
dc.subject.keyword.spa.fl_str_mv Geometry, algebraic
Groups, Theory of
Shape theory
Polynomials
Computer-aided Design
dc.subject.keyword.eng.fl_str_mv Geometry
algebraic
Groups
Theory of
Shape theory
Polynomials
Computer-aided Design
dc.subject.keyword..keywor.fl_str_mv Restricciones geométricas
Bases de Gröbner
Razonamiento geométrico
description Mechanical design and assembly planning inherently involve geometric constraint satisfaction or scene feasibility (GCS/SF) problems -- Such problems imply the satisfaction of proposed relations placed between undefined geometric entities in a given scenario -- If the degrees of freedom remaining in the scene are compatible with the proposed relations or constraints, a set of entities is produced that populate the scenario satisfying the relations -- Otherwise, a diagnostic of inconsistency of the problem is emitted -- This problem appears in various forms in assembly planning (assembly model generation), process planning, constraint driven design, computer vision, etc -- Previous attempts at solution using separate numerical, symbolic or procedural approaches suffer serious shortcomings in characterizing the solution space, in dealing simultaneously with geometric (dimensional) and topological (relational) inconsistencies, and in completely covering the possible physical variations of the problem -- This investigation starts by formulating the problem as one of characterizing the solution space of a set of polynomials -- By using theories developed in the area of algebraic geometry, properties of Grobner Bases are used to assess the consistency and ambiguity of the given problem and the dimension of its solution space -- This method allows for die integration of geometric and topological reasoning -- The high computational cost of Grobner Basis construction and the need for a compact and physically meaningful set of variables lead to the integration of known results on group theory -- These results allow the characterization of geometric constraints in terms of the subgroups of the Special Group of Euclidean displacements in E^3, SE(3) -- Several examples arc developed which were solved with computer algebra systems (MAPLE and Mathematica) -- They are presented to illustrate the use of the Euclidean group-based variables, and to demonstrate the theoretical completeness of the algebraic geometry analysis over the domain of constraints expressible as polynomials
publishDate 1996
dc.date.issued.none.fl_str_mv 1996
dc.date.available.none.fl_str_mv 2016-11-30T15:20:17Z
dc.date.accessioned.none.fl_str_mv 2016-11-30T15:20:17Z
dc.type.eng.fl_str_mv info:eu-repo/semantics/article
article
info:eu-repo/semantics/publishedVersion
publishedVersion
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dc.type.coar.fl_str_mv http://purl.org/coar/resource_type/c_6501
http://purl.org/coar/resource_type/c_2df8fbb1
dc.type.local.spa.fl_str_mv Artículo
status_str publishedVersion
dc.identifier.issn.none.fl_str_mv 0740-817X
dc.identifier.uri.none.fl_str_mv http://hdl.handle.net/10784/9782
dc.identifier.doi.none.fl_str_mv 10.1080/07408179608966276
identifier_str_mv 0740-817X
10.1080/07408179608966276
url http://hdl.handle.net/10784/9782
dc.language.iso.eng.fl_str_mv eng
language eng
dc.relation.ispartof.spa.fl_str_mv IIE Transactions, Volume 28, Issue 4, pp 281-294
dc.relation.uri.none.fl_str_mv http://dx.doi.org/10.1080/07408179608966276
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dc.rights.local.spa.fl_str_mv Acceso cerrado
rights_invalid_str_mv Acceso cerrado
http://purl.org/coar/access_right/c_14cb
dc.publisher.spa.fl_str_mv Taylor & Francis
institution Universidad EAFIT
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