On the Shape of Curves that are Rational in Polar Coordinates
Identificadores
Enlace permanente (URI): http://hdl.handle.net/10017/20444DOI: 10.1016/j.cagd.2012.09.001
ISSN: 0167-8396
Editor
Elsevier
Fecha de publicación
2012Patrocinadores
Ministerio de Ciencia e Innovación
Cita bibliográfica
Computer Aided Geometric Design, v. 29, n. 9, p. 665-675.
Palabras clave
Polar coordinates
Planar curve
Spiral
Rational curve
Descripción
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.
Proyectos
info:eu-repo/grantAgreement/MICINN//MTM2011-25816-C02-01/ES/ALGORITMOS Y APLICACIONES EN GEOMETRIA DE CURVAS Y SUPERFICIES/
Tipo de documento
info:eu-repo/semantics/article
Versión
info:eu-repo/semantics/submittedVersion
Versión del editor
http://dx.doi.org/10.1016/j.cagd.2012.09.001Derechos
(c) Computer Aided Geometric Design, 2012
Derechos de acceso
info:eu-repo/semantics/openAccess
Resumen
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.
Ficheros en el ítem
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Rational_Polar_UAH.pdf | 1.043Mb |
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Rational_Polar_UAH.pdf | 1.043Mb |
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Colecciones
- MATEMATIC - Artículos [172]