On the shape of curves that are rational in polar coordinates

In this paper we provide a computational approach to the shape of curves which are rational in polar coordinates, i.e. which are defined by means of a parametrization (r(t),θ(t))(r(t),θ(t)) where both r(t)r(t), θ(t)θ(t) are rational functions. 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.

► We address the shape of curves which are rational in polar coordinates, i.e., curves defined by (r(t),θ(t))(r(t),θ(t)) where r(t)r(t), θ(t)θ(t) are rational functions.
► We study theoretical aspects on the shape of these curves.
► We present an algorithm for plotting the “interesting parts” of the curve, i.e., the parts showing its main geometrical features.