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

dc.contributor.authorAlcázar Arribas, Juan Gerardo 
dc.contributor.authorGoldman, Ron
dc.date.accessioned2016-11-30T11:47:03Z
dc.date.available2016-11-30T11:47:03Z
dc.date.issued2016-11-07
dc.identifier.bibliographicCitationIEEE Transactions on Visualization and Computer Graphics, 2016, p. 1-11en
dc.identifier.issn1077-2626
dc.identifier.urihttp://hdl.handle.net/10017/27210
dc.description.abstractGiven 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 equationsen
dc.description.sponsorshipMinisterio de Economía y Competitividades_ES
dc.format.mimetypeapplication/pdfen
dc.language.isoengen
dc.rightsAttribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/4.0/*
dc.subjectEquations of a surfaceen
dc.subjectConical surfaceen
dc.subjectSurface of revolutionen
dc.subjectShape recognitionen
dc.subjectCylindrical surfaceen
dc.titleDetecting when an implicit equation or a rational parametrization defines a conical or cylindrical surface, or a surface of revolutionen
dc.typeinfo:eu-repo/semantics/articleen
dc.subject.ecienciaCienciaes_ES
dc.subject.ecienciaMatemáticases_ES
dc.subject.ecienciaMathematicsen
dc.contributor.affiliationUniversidad de Alcalá. Departamento de Física y Matemáticases_ES
dc.date.updated2016-11-16T13:40:28Z
dc.relation.publisherversionhttp://dx.doi.org/10.1109/TVCG.2016.2625786
dc.type.versioninfo:eu-repo/semantics/acceptedVersionen
dc.identifier.doi10.1109/TVCG.2016.2625786
dc.relation.projectIDinfo:eu-repo/grantAgreement/MINECO//MTM2014-54141-P/ES/CONSTRUCCIONES ALGEBRO-GEOMETRICAS: FUNDAMENTOS, ALGORITMOS Y APLICACIONES/en
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessen
dc.identifier.uxxiAR/0000024978
dc.identifier.publicationtitleIEEE Transactions on Visualization and Computer Graphicsen
dc.identifier.publicationlastpage11
dc.identifier.publicationfirstpage1


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Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
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