Asymptotic behavior of an implicit algebraic plane curve

Authors
Blasco Lorenzo, ÁngelUniversity of Alcalá Author; Pérez Díaz, SoniaUniversity of Alcalá Author
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/49577
DOI: 10.1016/j.cagd.2014.04.002
ISSN: 0167-8396
Publisher
Elsevier
Date
2014-10
Affiliation
Universidad de Alcalá. Departamento de Física y Matemáticas. Unidad docente Matemáticas
Bibliographic citation
Blasco, A. & Pérez Díaz, S. 2014, “Asymptotic behavior of an implicit algebraic plane curve”, Computer Aided Geometric Design, vol. 31, no. 7-8, pp. 345-357.
Keywords
Implicit algebraic plane curve
Infinity branches
Convergent branches
Asymptotic behavior
Approaching curves
Document type
info:eu-repo/semantics/article
Version
info:eu-repo/semantics/acceptedVersion
Publisher's version
https://doi.org/10.1016/j.cagd.2014.04.002
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
© 2014 Elsevier
Access rights
info:eu-repo/semantics/openAccess
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Abstract
In this paper, we introduce the notion of infinity branches as well as approaching curves. We present some properties which allow us to obtain an algorithm that compares the behavior of two implicitly defined algebraic plane curves at the infinity. As an important result, we prove that if two plane algebraic curves have the same asymptotic behavior, the Hausdorff distance between them is finite.
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