We develop a method for computing all the generalized asymptotes of a real plane algebraic curve C implicitly defined by an irreducible polynomial f ( x , y ) ∈ R [ x , y ] . The approach is based on the notion of perfect curve introduced from the concepts and results presented in Blasco and Pérez-Díaz (2013). In addition, we study some properties concerning perfect curves and in particular, we provide a necessary and sufficient condition for a plane curve to be perfect. Finally, we show that the equivalent class of generalized asymptotes for a branch of a plane curve can be described as an affine space R m for a certain m. 
Asymptotes and perfect curves