Characterizing the finiteness of the Hausdorff distance between two algebraic curves
AuthorsBlasco Lorenzo, Ángel; Pérez Díaz, Sonia
IdentifiersPermanent link (URI): http://hdl.handle.net/10017/49503
Blasco, A. & Pérez Díaz, S. 2015, "Characterizing the finiteness of the Hausdorff distance between two algebraic curves", Journal of Computational and Applied Mathematics, vol. 280, pp. 327-346.
Algebraic space curves
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
© 2014 Elsevier
In this paper, we present a characterization for the Hausdorff distance between two given algebraic curves in the n-dimensional space (parametrically or implicitly defined) to be finite. The characterization is related with the asymptotic behavior of the two curves and it can be easily checked. More precisely, the Hausdorff distance between two curves C and C is finite if and only if for each infinity branch of C there exists an infinity branch of C such that the terms with positive exponent in the corresponding series are the same, and reciprocally.
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