Detecting when an implicit equation or a rational parametrization defines a conical or cylindrical surface, or a surface of revolution

Given an implicit polynomial equation or a rational parametrization, we develop algorithms to determine whether the set of real and complex points defined by the equation, i.e. the surface defined by the equation, in the sense of Algebraic Geometry, is a cylindrical surface, a conical surface, or a...

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Detalles Bibliográficos
Autores: Alcázar Arribas, Juan Gerardo|||0000-0002-1665-9710, Goldman, Ron
Tipo de recurso: artículo
Fecha de publicación:2016
País:España
Institución:Universidad de Alcalá (UAH)
Repositorio:e_Buah Biblioteca Digital Universidad de Alcalá
Idioma:inglés
OAI Identifier:oai:ebuah.uah.es:10017/27210
Acceso en línea:http://hdl.handle.net/10017/27210
https://dx.doi.org/10.1109/TVCG.2016.2625786
Access Level:acceso abierto
Palabra clave:Equations of a surface
Conical surface
Surface of revolution
Shape recognition
Cylindrical surface
Ciencia
Matemáticas
Mathematics
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spelling Detecting when an implicit equation or a rational parametrization defines a conical or cylindrical surface, or a surface of revolutionAlcázar Arribas, Juan Gerardo|||0000-0002-1665-9710Goldman, RonEquations of a surfaceConical surfaceSurface of revolutionShape recognitionCylindrical surfaceCienciaMatemáticasMathematicsGiven an implicit polynomial equation or a rational parametrization, we develop algorithms to determine whether the set of real and complex points defined by the equation, i.e. the surface defined by the equation, in the sense of Algebraic Geometry, is a cylindrical surface, a conical surface, or a surface of revolution. The algorithms are directly applicable to, and formulated in terms of, the implicit equation or the rational parametrization. When the surface is cylindrical, we show how to compute the direction of its rulings; when the surface is conical, we show how to compute its vertex; and when the surface is a surface of revolution, we show how to compute its axis of rotation directly from the defining equationsMinisterio de Economía y Competitividad20162016-11-07journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10017/27210https://dx.doi.org/10.1109/TVCG.2016.2625786reponame:e_Buah Biblioteca Digital Universidad de Alcaláinstname:Universidad de Alcalá (UAH)InglésengMinisterio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 Not available MTM2014-54141-P CONSTRUCCIONES ALGEBRO-GEOMETRICAS: FUNDAMENTOS, ALGORITMOS Y APLICACIONESopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-ShareAlike 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-sa/4.0/info:eu-repo/semantics/openAccessoai:ebuah.uah.es:10017/272102026-06-18T11:13:07Z
dc.title.none.fl_str_mv Detecting when an implicit equation or a rational parametrization defines a conical or cylindrical surface, or a surface of revolution
title Detecting when an implicit equation or a rational parametrization defines a conical or cylindrical surface, or a surface of revolution
spellingShingle Detecting when an implicit equation or a rational parametrization defines a conical or cylindrical surface, or a surface of revolution
Alcázar Arribas, Juan Gerardo|||0000-0002-1665-9710
Equations of a surface
Conical surface
Surface of revolution
Shape recognition
Cylindrical surface
Ciencia
Matemáticas
Mathematics
title_short Detecting when an implicit equation or a rational parametrization defines a conical or cylindrical surface, or a surface of revolution
title_full Detecting when an implicit equation or a rational parametrization defines a conical or cylindrical surface, or a surface of revolution
title_fullStr Detecting when an implicit equation or a rational parametrization defines a conical or cylindrical surface, or a surface of revolution
title_full_unstemmed Detecting when an implicit equation or a rational parametrization defines a conical or cylindrical surface, or a surface of revolution
title_sort Detecting when an implicit equation or a rational parametrization defines a conical or cylindrical surface, or a surface of revolution
dc.creator.none.fl_str_mv Alcázar Arribas, Juan Gerardo|||0000-0002-1665-9710
Goldman, Ron
author Alcázar Arribas, Juan Gerardo|||0000-0002-1665-9710
author_facet Alcázar Arribas, Juan Gerardo|||0000-0002-1665-9710
Goldman, Ron
author_role author
author2 Goldman, Ron
author2_role author
dc.subject.none.fl_str_mv Equations of a surface
Conical surface
Surface of revolution
Shape recognition
Cylindrical surface
Ciencia
Matemáticas
Mathematics
topic Equations of a surface
Conical surface
Surface of revolution
Shape recognition
Cylindrical surface
Ciencia
Matemáticas
Mathematics
description Given an implicit polynomial equation or a rational parametrization, we develop algorithms to determine whether the set of real and complex points defined by the equation, i.e. the surface defined by the equation, in the sense of Algebraic Geometry, is a cylindrical surface, a conical surface, or a surface of revolution. The algorithms are directly applicable to, and formulated in terms of, the implicit equation or the rational parametrization. When the surface is cylindrical, we show how to compute the direction of its rulings; when the surface is conical, we show how to compute its vertex; and when the surface is a surface of revolution, we show how to compute its axis of rotation directly from the defining equations
publishDate 2016
dc.date.none.fl_str_mv 2016
2016-11-07
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10017/27210
https://dx.doi.org/10.1109/TVCG.2016.2625786
url http://hdl.handle.net/10017/27210
https://dx.doi.org/10.1109/TVCG.2016.2625786
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 Not available MTM2014-54141-P CONSTRUCCIONES ALGEBRO-GEOMETRICAS: FUNDAMENTOS, ALGORITMOS Y APLICACIONES
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-ShareAlike 4.0 International
http://creativecommons.org/licenses/by-nc-sa/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-ShareAlike 4.0 International
http://creativecommons.org/licenses/by-nc-sa/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:e_Buah Biblioteca Digital Universidad de Alcalá
instname:Universidad de Alcalá (UAH)
instname_str Universidad de Alcalá (UAH)
reponame_str e_Buah Biblioteca Digital Universidad de Alcalá
collection e_Buah Biblioteca Digital Universidad de Alcalá
repository.name.fl_str_mv
repository.mail.fl_str_mv
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