dc.contributor.author | Alcázar Arribas, Juan Gerardo | |
dc.contributor.author | Díaz Toca, Gema Maria | |
dc.date.accessioned | 2014-09-10T12:49:26Z | |
dc.date.available | 2014-09-10T12:49:26Z | |
dc.date.issued | 2012 | |
dc.identifier.bibliographicCitation | Computer Aided Geometric Design, v. 29, n. 9, p. 665-675. | en |
dc.identifier.issn | 0167-8396 | |
dc.identifier.uri | http://hdl.handle.net/10017/20444 | |
dc.description | The 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.abstract | In 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.sponsorship | Ministerio de Ciencia e Innovación | es_ES |
dc.format.mimetype | application/pdf | en |
dc.language.iso | eng | en |
dc.publisher | Elsevier | |
dc.rights | (c) Computer Aided Geometric Design, 2012 | en |
dc.subject | Polar coordinates | en |
dc.subject | Planar curve | en |
dc.subject | Spiral | en |
dc.subject | Rational curve | en |
dc.title | On the Shape of Curves that are Rational in Polar Coordinates | en |
dc.type | info:eu-repo/semantics/article | en |
dc.subject.eciencia | Ciencia | es_ES |
dc.subject.eciencia | Matemáticas | es_ES |
dc.subject.eciencia | Science | en |
dc.subject.eciencia | Mathematics | en |
dc.contributor.affiliation | Universidad de Alcalá. Departamento de Física y Matemáticas. Unidad docente Matemáticas | es_ES |
dc.relation.publisherversion | http://dx.doi.org/10.1016/j.cagd.2012.09.001 | |
dc.type.version | info:eu-repo/semantics/submittedVersion | en |
dc.identifier.doi | 10.1016/j.cagd.2012.09.001 | |
dc.relation.projectID | info:eu-repo/grantAgreement/MICINN//MTM2011-25816-C02-01/ES/ALGORITMOS Y APLICACIONES EN GEOMETRIA DE CURVAS Y SUPERFICIES/ | en |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | en |