RT info:eu-repo/semantics/article
T1 On the Shape of Curves that are Rational in Polar Coordinates
A1 Alcázar Arribas, Juan Gerardo
A1 Díaz  Toca, Gema Maria
K1 Polar coordinates
K1 Planar curve
K1 Spiral
K1 Rational curve
K1 Ciencia
K1 Matemáticas
K1 Science
K1 Mathematics
AB In this paper we provide a computational approach to the shapeof 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.
PB Elsevier
SN 0167-8396
YR 2012
FD 2012
LK http://hdl.handle.net/10017/20444
UL http://hdl.handle.net/10017/20444
LA eng
NO The final version of this paper was published as AlcázarJ.G., Díaz Toca G.M. (2012), On the Shape of Curves that are Rational in PolarCoordinates, Computer Aided Geometric Design, Vol. 29 Issue 9, pp. 665-675.
NO Ministerio de Ciencia e Innovación
DS MINDS@UW
RD 25-abr-2024