A survey on recent advances in the computation of asymptotes

In 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...

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Bibliographic Details
Published in:São Paulo Journal of Mathematical Sciences 2024, Vol.18 (2), p.1986-2002
Main Authors: Magdalena-Benedicto, R., de Sevilla, M. A. Fernández, Pérez-Díaz, S.
Format: Article
Language:English
Subjects:
Algorithms
Asymptotes
Mathematics
Mathematics and Statistics
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Summary:In 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.
ISSN:1982-6907
2316-9028
2306-9028
DOI:10.1007/s40863-024-00444-5