Detecting Symmetries of Rational Plane Curves

Given a rational algebraic curve defined by means of a rational parametrization, we address here the problem of deterministically detecting whether the curve exhibits some kind of symmetry (central, mirror, rotation), and of computing the elements of the symmetry in the affirmative case. We provide...

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Detalhes bibliográficos
Autores: Alcázar Arribas, Juan Gerardo|||0000-0002-1665-9710, Hermoso Ortíz, Carlos|||0000-0002-5556-1839
Formato: artículo
Fecha de publicación:2013
País:España
Recursos:Universidad de Alcalá (UAH)
Repositorio:e_Buah Biblioteca Digital Universidad de Alcalá
Idioma:inglés
OAI Identifier:oai:ebuah.uah.es:10017/20452
Acesso em linha:http://hdl.handle.net/10017/20452
https://dx.doi.org/10.1016/j.cagd.2014.02.004
Access Level:acceso abierto
Palavra-chave:Rational planar curve
Rational space curve
Symmetry
Central symmetry
Mirror symmetry
Rotation symmetry
Symmetry center
Symmetry axis
Involution
Ciencia
Matemáticas
Science
Mathematics
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spelling Detecting Symmetries of Rational Plane CurvesAlcázar Arribas, Juan Gerardo|||0000-0002-1665-9710Hermoso Ortíz, Carlos|||0000-0002-5556-1839Rational planar curveRational space curveSymmetryCentral symmetryMirror symmetryRotation symmetrySymmetry centerSymmetry axisInvolutionCienciaMatemáticasScienceMathematicsGiven a rational algebraic curve defined by means of a rational parametrization, we address here the problem of deterministically detecting whether the curve exhibits some kind of symmetry (central, mirror, rotation), and of computing the elements of the symmetry in the affirmative case. We provide effective methods for solving these questions without any conversion to implicit form. The underlying idea is the existing relationship between two proper parametrizations of a same curve, which in turn leads to algorithms where only univariate polynomials are involved. These methods have been implemented and tested in the computer algebra system Maple 15; evidence of their applicability, as well as a detailed theoretical analysis, is given.Ministerio de Ciencia e InnovaciónElsevier20132013-01-01journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10017/20452https://dx.doi.org/10.1016/j.cagd.2014.02.004reponame:e_Buah Biblioteca Digital Universidad de Alcaláinstname:Universidad de Alcalá (UAH)InglésengMinisterio de Ciencia e Innovación http://dx.doi.org/10.13039/501100004837 Not available MTM2011-25816-C02-01 ALGORITMOS Y APLICACIONES EN GEOMETRIA DE CURVAS Y SUPERFICIESopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:ebuah.uah.es:10017/204522026-06-18T11:13:07Z
dc.title.none.fl_str_mv Detecting Symmetries of Rational Plane Curves
title Detecting Symmetries of Rational Plane Curves
spellingShingle Detecting Symmetries of Rational Plane Curves
Alcázar Arribas, Juan Gerardo|||0000-0002-1665-9710
Rational planar curve
Rational space curve
Symmetry
Central symmetry
Mirror symmetry
Rotation symmetry
Symmetry center
Symmetry axis
Involution
Ciencia
Matemáticas
Science
Mathematics
title_short Detecting Symmetries of Rational Plane Curves
title_full Detecting Symmetries of Rational Plane Curves
title_fullStr Detecting Symmetries of Rational Plane Curves
title_full_unstemmed Detecting Symmetries of Rational Plane Curves
title_sort Detecting Symmetries of Rational Plane Curves
dc.creator.none.fl_str_mv Alcázar Arribas, Juan Gerardo|||0000-0002-1665-9710
Hermoso Ortíz, Carlos|||0000-0002-5556-1839
author Alcázar Arribas, Juan Gerardo|||0000-0002-1665-9710
author_facet Alcázar Arribas, Juan Gerardo|||0000-0002-1665-9710
Hermoso Ortíz, Carlos|||0000-0002-5556-1839
author_role author
author2 Hermoso Ortíz, Carlos|||0000-0002-5556-1839
author2_role author
dc.subject.none.fl_str_mv Rational planar curve
Rational space curve
Symmetry
Central symmetry
Mirror symmetry
Rotation symmetry
Symmetry center
Symmetry axis
Involution
Ciencia
Matemáticas
Science
Mathematics
topic Rational planar curve
Rational space curve
Symmetry
Central symmetry
Mirror symmetry
Rotation symmetry
Symmetry center
Symmetry axis
Involution
Ciencia
Matemáticas
Science
Mathematics
description Given a rational algebraic curve defined by means of a rational parametrization, we address here the problem of deterministically detecting whether the curve exhibits some kind of symmetry (central, mirror, rotation), and of computing the elements of the symmetry in the affirmative case. We provide effective methods for solving these questions without any conversion to implicit form. The underlying idea is the existing relationship between two proper parametrizations of a same curve, which in turn leads to algorithms where only univariate polynomials are involved. These methods have been implemented and tested in the computer algebra system Maple 15; evidence of their applicability, as well as a detailed theoretical analysis, is given.
publishDate 2013
dc.date.none.fl_str_mv 2013
2013-01-01
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/10017/20452
https://dx.doi.org/10.1016/j.cagd.2014.02.004
url http://hdl.handle.net/10017/20452
https://dx.doi.org/10.1016/j.cagd.2014.02.004
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Ciencia e Innovación http://dx.doi.org/10.13039/501100004837 Not available MTM2011-25816-C02-01 ALGORITMOS Y APLICACIONES EN GEOMETRIA DE CURVAS Y SUPERFICIES
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/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-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
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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