Asymptotes and perfect curves
IdentifiersPermanent link (URI): http://hdl.handle.net/10017/49575
Blasco, A. & Pérez Díaz, S. 2014, “Asymptotes and perfect curves”, Computer Aided Geometric Design, vol. 31, no. 2, pp. 81-96.
Implicit algebraic plane curve
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
© 2014 Elsevier
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 P´erez-D´ıaz (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.
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