Asymptotic behavior of an implicit algebraic plane curve

In this paper, we introduce the notion of infinity branches as well as approaching curves. We present some properties which allow us to obtain an algorithm that compares the behavior of two implicitly defined algebraic plane curves at the infinity. As an important result, we prove that if two plane...

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Detalles Bibliográficos
Autores: Blasco Lorenzo, Ángel|||0000-0001-6658-9338, Pérez Díaz, Sonia|||0000-0002-0174-5325
Tipo de recurso: artículo
Fecha de publicación:2014
País:España
Institución:Universidad de Alcalá (UAH)
Repositorio:e_Buah Biblioteca Digital Universidad de Alcalá
Idioma:inglés
OAI Identifier:oai:ebuah.uah.es:10017/49577
Acceso en línea:http://hdl.handle.net/10017/49577
https://dx.doi.org/10.1016/j.cagd.2014.04.002
Access Level:acceso abierto
Palabra clave:Implicit algebraic plane curve
Infinity branches
Convergent branches
Asymptotic behavior
Approaching curves
Matemáticas
Mathematics
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spelling Asymptotic behavior of an implicit algebraic plane curveBlasco Lorenzo, Ángel|||0000-0001-6658-9338Pérez Díaz, Sonia|||0000-0002-0174-5325Implicit algebraic plane curveInfinity branchesConvergent branchesAsymptotic behaviorApproaching curvesMatemáticasMathematicsIn this paper, we introduce the notion of infinity branches as well as approaching curves. We present some properties which allow us to obtain an algorithm that compares the behavior of two implicitly defined algebraic plane curves at the infinity. As an important result, we prove that if two plane algebraic curves have the same asymptotic behavior, the Hausdorff distance between them is finite.Elsevier20142014-10-01journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10017/49577https://dx.doi.org/10.1016/j.cagd.2014.04.002reponame:e_Buah Biblioteca Digital Universidad de Alcaláinstname:Universidad de Alcalá (UAH)Inglésengopen 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:10017/495772026-06-18T11:13:07Z
dc.title.none.fl_str_mv Asymptotic behavior of an implicit algebraic plane curve
title Asymptotic behavior of an implicit algebraic plane curve
spellingShingle Asymptotic behavior of an implicit algebraic plane curve
Blasco Lorenzo, Ángel|||0000-0001-6658-9338
Implicit algebraic plane curve
Infinity branches
Convergent branches
Asymptotic behavior
Approaching curves
Matemáticas
Mathematics
title_short Asymptotic behavior of an implicit algebraic plane curve
title_full Asymptotic behavior of an implicit algebraic plane curve
title_fullStr Asymptotic behavior of an implicit algebraic plane curve
title_full_unstemmed Asymptotic behavior of an implicit algebraic plane curve
title_sort Asymptotic behavior of an implicit algebraic plane curve
dc.creator.none.fl_str_mv Blasco Lorenzo, Ángel|||0000-0001-6658-9338
Pérez Díaz, Sonia|||0000-0002-0174-5325
author Blasco Lorenzo, Ángel|||0000-0001-6658-9338
author_facet Blasco Lorenzo, Ángel|||0000-0001-6658-9338
Pérez Díaz, Sonia|||0000-0002-0174-5325
author_role author
author2 Pérez Díaz, Sonia|||0000-0002-0174-5325
author2_role author
dc.subject.none.fl_str_mv Implicit algebraic plane curve
Infinity branches
Convergent branches
Asymptotic behavior
Approaching curves
Matemáticas
Mathematics
topic Implicit algebraic plane curve
Infinity branches
Convergent branches
Asymptotic behavior
Approaching curves
Matemáticas
Mathematics
description In this paper, we introduce the notion of infinity branches as well as approaching curves. We present some properties which allow us to obtain an algorithm that compares the behavior of two implicitly defined algebraic plane curves at the infinity. As an important result, we prove that if two plane algebraic curves have the same asymptotic behavior, the Hausdorff distance between them is finite.
publishDate 2014
dc.date.none.fl_str_mv 2014
2014-10-01
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/10017/49577
https://dx.doi.org/10.1016/j.cagd.2014.04.002
url http://hdl.handle.net/10017/49577
https://dx.doi.org/10.1016/j.cagd.2014.04.002
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
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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score 15.301603

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