PTOPO: a maple package for the topology of parametric curves

Abstract

PTOPO is a maple package computing the topology and describing the geometry of a parametric plane curve. The algorithm behind PTOPO constructs an abstract graph that is isotopic to the curve. PTOPO exploits the benefits of the parametric representation and performs all computations in the parameter space using exact computing. PTOPO computes the topology and visualizes the curve in less than a second for most examples in the literature. Comparison of maple parametric plot vs PTOPO 1 Topology of Parametric Curves The study of parametric curves is a classical topic in computational algebra and geometry (Sendra and Winkler (1999); Boissonnat and Teillaud (2006)). The interest for computing with parametric curves has been motivated, among others, by the omnipresence of parametric representations in computer modeling and computer aided geometric design (Manocha and Canny (1992); Pérez-Dı́az (2006); Sendra et al. (2008)). ⇤Supported by the Fondation Sciences Mathématiques de Paris (FSMP)