34 citations · 111 across the 16 of their papers we have counts for
5 papers · 1 filter
On the Shape of Curves that are Rational in Polar Coordinates
J. G. Alcázar, G. M. Díaz-Toca
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)) w…
Local Shape of Generalized Offsets to Algebraic Curves
Juan Gerardo Alcazar
In this paper we study the local behavior of an algebraic curve under a geometric construction which is a variation of the usual offsetting construction, namely the {\it generalize…
Topology of 2D and 3D Rational Curves
Juan Gerardo Alcazar, Gema Maria Diaz-Toca
In this paper we present algorithms for computing the topology of planar and space rational curves defined by a parametrization. The algorithms given here work directly with the pa…
On the Different Shapes Arising in a Family of Rational Curves Depending on a Parameter
Juan Gerardo Alcazar
Given a family of rational curves depending on a real parameter, defined by its parametric equations, we provide an algorithm to compute a finite partition of the parameter space (…
Analyzing the Topology Types arising in a Family of Algebraic Curves Depending On Two Parameters
Juan Gerardo Alcazar
Given the implicit equation of a family of algebraic plane curves depending on the parameters , we provide an algorithm for studying the topology types arising in…