Asymptotes and perfect curves ?
We introduce the notions of perfect curve and generalized asymptote (g-asymptote). We provide an algorithm that computes a g-asymptote for each infinity branch of an algebraic plane curve. We state necessary and sufficient conditions for a curve to be perfect. We propose a method to obtain, under general conditions, all the g-asymptotes approaching a given infinity branch.
asymptotes perfect curves infinity branches implicit algebraic plane curve