A survey on recent advances in the computation of asymptotes

Abstract

AbstractIn this paper, we summarize two algorithms for computing all the generalized asymptotes of a plane algebraic curve implicitly or parametrically defined. The approach is based on the notion of perfect curve introduced from the concepts and results presented in Blasco and Pérez-Díaz (Comput Aided Geom Des 31(2):81–96, 2014), Blasco and Pérez-Díaz (Comput Aided Geom Des 31(7-8):345–357, 2014), and Blasco and Pérez-Díaz (J Comput Appl Math 278:231–247, 2015). From these results, we derive a new method that allow to easily compute horizontal and vertical asymptotes.