New algebraic conditions for the identification of the relative position of two coplanar ellipses

The identification of the relative position of two real coplanar ellipses can be reduced to the identification of the nature of the singular conics in the pencil they define and, in general, their location with respect to these singular conics in the pencil. This latter problem reduces to find the r...

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Detalles Bibliográficos
Autores: Alberich-Carramiñana, Maria, Elizalde Masiá, Borja, Thomas, Federico
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2017
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/166745
Acceso en línea:http://hdl.handle.net/10261/166745
Access Level:acceso abierto
Palabra clave:Interference detection
Pencils of conics
Ellipses
Positional relationships
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spelling New algebraic conditions for the identification of the relative position of two coplanar ellipsesAlberich-Carramiñana, MariaElizalde Masiá, BorjaThomas, FedericoInterference detectionPencils of conicsEllipsesPositional relationshipsThe identification of the relative position of two real coplanar ellipses can be reduced to the identification of the nature of the singular conics in the pencil they define and, in general, their location with respect to these singular conics in the pencil. This latter problem reduces to find the relative location of the roots of univariate polynomials. Since it is usually desired that all generated expressions are algebraic to simplify further analysis, including the case in which the ellipses undergone temporal variations, all recent methods available in the literature rely mathematical tools such as Sturm–Habicht sequences or subresultant sequences. This paper presents an alternative based on more elementary tools which results in a binary decision tree to classify the relative location of two ellipses in 12 different classes. The decision at each node is taken based on the sign of a set of algebraic/rational expressions on the ellipses coefficients, the most complex of them being third and second order polynomial discriminants.Peer ReviewedElsevierConsejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]2018201820172018info:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501Preprintinfo:eu-repo/semantics/submittedVersionhttp://hdl.handle.net/10261/166745reponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)Ingléshttps://doi.org/10.1016/j.cagd.2017.03.013Síinfo:eu-repo/semantics/openAccessoai:digital.csic.es:10261/1667452026-05-22T06:33:51Z
dc.title.none.fl_str_mv New algebraic conditions for the identification of the relative position of two coplanar ellipses
title New algebraic conditions for the identification of the relative position of two coplanar ellipses
spellingShingle New algebraic conditions for the identification of the relative position of two coplanar ellipses
Alberich-Carramiñana, Maria
Interference detection
Pencils of conics
Ellipses
Positional relationships
title_short New algebraic conditions for the identification of the relative position of two coplanar ellipses
title_full New algebraic conditions for the identification of the relative position of two coplanar ellipses
title_fullStr New algebraic conditions for the identification of the relative position of two coplanar ellipses
title_full_unstemmed New algebraic conditions for the identification of the relative position of two coplanar ellipses
title_sort New algebraic conditions for the identification of the relative position of two coplanar ellipses
dc.creator.none.fl_str_mv Alberich-Carramiñana, Maria
Elizalde Masiá, Borja
Thomas, Federico
author Alberich-Carramiñana, Maria
author_facet Alberich-Carramiñana, Maria
Elizalde Masiá, Borja
Thomas, Federico
author_role author
author2 Elizalde Masiá, Borja
Thomas, Federico
author2_role author
author
dc.contributor.none.fl_str_mv Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]
dc.subject.none.fl_str_mv Interference detection
Pencils of conics
Ellipses
Positional relationships
topic Interference detection
Pencils of conics
Ellipses
Positional relationships
description The identification of the relative position of two real coplanar ellipses can be reduced to the identification of the nature of the singular conics in the pencil they define and, in general, their location with respect to these singular conics in the pencil. This latter problem reduces to find the relative location of the roots of univariate polynomials. Since it is usually desired that all generated expressions are algebraic to simplify further analysis, including the case in which the ellipses undergone temporal variations, all recent methods available in the literature rely mathematical tools such as Sturm–Habicht sequences or subresultant sequences. This paper presents an alternative based on more elementary tools which results in a binary decision tree to classify the relative location of two ellipses in 12 different classes. The decision at each node is taken based on the sign of a set of algebraic/rational expressions on the ellipses coefficients, the most complex of them being third and second order polynomial discriminants.
publishDate 2017
dc.date.none.fl_str_mv 2017
2018
2018
2018
dc.type.none.fl_str_mv info:eu-repo/semantics/article
http://purl.org/coar/resource_type/c_6501
Preprint
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10261/166745
url http://hdl.handle.net/10261/166745
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv https://doi.org/10.1016/j.cagd.2017.03.013
Sí
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:DIGITAL.CSIC. Repositorio Institucional del CSIC
instname:Consejo Superior de Investigaciones Científicas (CSIC)
instname_str Consejo Superior de Investigaciones Científicas (CSIC)
reponame_str DIGITAL.CSIC. Repositorio Institucional del CSIC
collection DIGITAL.CSIC. Repositorio Institucional del CSIC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.812429

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