A survey on recent advances in the computation of asymptotes

被引：0
|
作者：
Magdalena-Benedicto, R. [1 ,2 ,3 ]
de Sevilla, M. A. Fernandez [2 ,3 ]
Perez-Diaz, S. [2 ,3 ]
机构：
[1] Univ Valencia, Dept Elect Engn, Ave Univ S-N, Burjassot 46100, Valencia, Spain
[2] Univ Alcala, Dept Ciencias Comp, Ctra Madrid Barcelona Km 33-6, Alcala De Henares 28871, Madrid, Spain
[3] Dept Fis & Matemat, Ctra Madrid Barcelona Km 33-6, Alcala De Henares 28871, Madrid, Spain
来源：
SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES | 2024年
关键词：
Implicit algebraic plane curve; Parametric plane curve; Infinity branches; Asymptotes; Perfect curves; Approaching curves; PARAMETRIZATION;
D O I：
10.1007/s40863-024-00444-5
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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 P & eacute;rez-D & iacute;az (Comput Aided Geom Des 31(2):81-96, 2014), Blasco and P & eacute;rez-D & iacute;az (Comput Aided Geom Des 31(7-8):345-357, 2014), and Blasco and P & eacute;rez-D & iacute;az (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.
引用
收藏
页码：1986 / 2002
页数：17
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