Asymptotic behavior of an implicit algebraic plane curve

DOI10.1016/j.cagd.2014.04.002zbMath1364.14024arXiv1302.2522OpenAlexW2019307524MaRDI QIDQ2396287

Angel Blasco, Sonia Pérez-Díaz

Publication date: 8 June 2017

Published in: Computer Aided Geometric Design (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.2522

zbMATH Keywords

asymptotic behaviorimplicit algebraic plane curveinfinity branchesconvergent branchesapproaching curves

Mathematics Subject Classification ID

Plane and space curves (14H50) Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items (11)

A simple formula for the computation of branches and asymptotes of curves and some applications ⋮ An effective algorithm for computing the asymptotes of an implicit curve ⋮ Globally certified \(G^1\) approximation of planar algebraic curves ⋮ Computing branches and asymptotes of meromorphic functions ⋮ Design and implementation of symbolic algorithms for the computation of generalized asymptotes ⋮ Computing the form of highest degree of the implicit equation of a rational surface ⋮ Asymptotes of space curves ⋮ Characterizing the finiteness of the Hausdorff distance between two algebraic curves ⋮ Numerical polynomial reparametrization of rational curves ⋮ A new approach for computing the asymptotes of a parametric curve ⋮ Determining the asymptotic family of an implicit curve

Uses Software

• CASA

Cites Work

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• An efficient method for analyzing the topology of plane real algebraic curves.
• Efficient topology determination of implicitly defined algebraic plane curves.
• Computing the asymptotes for a real plane algebraic curve
• Parametrization of approximate algebraic surfaces by lines
• Beta-conjugates of real algebraic numbers as Puiseux expansions

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