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dc.contributor.authorAlcázar Arribas, Juan Gerardo 
dc.contributor.authorDíaz Toca, Gema Maria
dc.date.accessioned2014-09-10T12:49:26Z
dc.date.available2014-09-10T12:49:26Z
dc.date.issued2012
dc.identifier.bibliographicCitationComputer Aided Geometric Design, v. 29, n. 9, p. 665-675.en
dc.identifier.issn0167-8396
dc.identifier.urihttp://hdl.handle.net/10017/20444
dc.descriptionThe final version of this paper was published as Alcázar J.G., Díaz Toca G.M. (2012), On the Shape of Curves that are Rational in Polar Coordinates, Computer Aided Geometric Design, Vol. 29 Issue 9, pp. 665-675.en
dc.description.abstractIn this paper we provide a computational approach to the shape of curves which are rational in polar coordinates. Our study includes theoretical aspects on the shape of these curves, and algorithmic results which eventually lead to an algorithm for plotting the ``interesting parts" of the curve, i.e. the parts showing the main geometrical features of it. On the theoretical side, we prove that these curves, with the exceptions of lines and circles, cannot be algebraic (in cartesian coordinates), we characterize the existence of infinitely many self-intersections, and we connect this with certain phenomena which are not possible in the algebraic world, namely the existence of limit circles, limit points, or spiral branches. On the practical side, we provide an algorithm which has been implemented in the computer algebra system Maple to visualize this kind of curves. Our implementation makes use (and improves some aspects of) the command "polarplot" currently available in Maple for plotting curves in polar form.en
dc.description.sponsorshipMinisterio de Ciencia e Innovaciónes_ES
dc.format.mimetypeapplication/pdfen
dc.language.isoengen
dc.publisherElsevier
dc.rights(c) Computer Aided Geometric Design, 2012en
dc.subjectPolar coordinatesen
dc.subjectPlanar curveen
dc.subjectSpiralen
dc.subjectRational curveen
dc.titleOn the Shape of Curves that are Rational in Polar Coordinatesen
dc.typeinfo:eu-repo/semantics/articleen
dc.subject.ecienciaCienciaes_ES
dc.subject.ecienciaMatemáticases_ES
dc.subject.ecienciaScienceen
dc.subject.ecienciaMathematicsen
dc.contributor.affiliationUniversidad de Alcalá. Departamento de Física y Matemáticas. Unidad docente Matemáticases_ES
dc.relation.publisherversionhttp://dx.doi.org/10.1016/j.cagd.2012.09.001
dc.type.versioninfo:eu-repo/semantics/submittedVersionen
dc.identifier.doi10.1016/j.cagd.2012.09.001
dc.relation.projectIDinfo:eu-repo/grantAgreement/MICINN//MTM2011-25816-C02-01/ES/ALGORITMOS Y APLICACIONES EN GEOMETRIA DE CURVAS Y SUPERFICIES/en
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessen


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