Asymptotes of space curves
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/49504DOI: 10.1016/j.cam.2014.10.013
ISSN: 0377-0427
Publisher
Elsevier
Date
2015-04-15Bibliographic citation
Blasco, A. & Pérez Díaz, S. 2015, "Asymptotes of space curves", Journal of Computational and Applied Mathematics, vol. 278, pp. 231-247.
Keywords
Algebraic space curve
Convergent branches
Infinity branches
Asymptotes
Perfect curves
Document type
info:eu-repo/semantics/article
Version
info:eu-repo/semantics/publishedVersion
Publisher's version
https://doi.org/10.1016/j.cam.2014.10.013Rights
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
© 2014 Elsevier
Access rights
info:eu-repo/semantics/openAccess
Abstract
In Blasco and Pérez-Díaz (2014), a method for computing generalized asymptotes of a real algebraic plane curve implicitly defined is presented. Generalized asymptotes are curves that describe the status of a branch at points with sufficiently large coordinates and thus, it is an important tool to analyze the behavior at infinity of an algebraic curve. This motivates that in this paper, we analyze and compute the generalized asymptotes of a real algebraic space curve which could be parametrically or implicitly defined. We present an algorithm that is based on the computation of the infinity branches (this concept was already introduced for plane curves in Blasco and Pérez-Díaz (2014)). In particular, we show that the computation of infinity branches in the space can be reduced to the computation of infinity branches in the plane and thus, the methods in Blasco and Pérez-Díaz (2014) can be applied.
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