On the Shape of Curves that are Rational in Polar Coordinates
IdentifiersEnlace permanente (URI): http://hdl.handle.net/10017/20444
Supported by the Spanish “Ministerio de Ciencia e Innovacion” under the Project MTM2011-25816-C02-01. Member of the Research Group asynacs (Ref. ccee2011/r34)
Computer Aided Geometric Design, v. 29, n. 9, p. 665-675.
Description / Notes
Note of the authors: 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.
MTM2011-25816-C02-01 (Ministerio de Ciencia e Innovación)
Tipo de documento
Versión del editorhttp://dx.doi.org/10.1016/j.cagd.2012.09.001
(c) Computer Aided Geometric Design, 2012
Derechos de acceso
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.