Approximate parametrization of plane algebraic curves by linear systems of curves.
IdentifiersPermanent link (URI): http://hdl.handle.net/10017/49579
Ministerio de Ciencia e Innovación
Pérez Díaz, S., Sendra, J.R., Rueda, S.L. & Sendra, J. 2010, “Approximate parametrization of plane algebraic curves by linear systems of curves”, Computer Aided Geometric Design, vol. 27, no. 2, pp. 212-231.
Plane algebraic curves
Linear systems of curves
MTM2008-04699-C03-01 (Ministerio de Ciencia e Innovación)
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
© 2009 Elsevier
It is well known that an irreducible algebraic curve is rational (i.e. parametric) if and only if its genus is zero. In this paper, given a tolerance ² > 0 and an ²-irreducible algebraic affine plane curve C of proper degree d, we introduce the notion of ²-rationality, and we provide an algorithm to parametrize approximately affine ²-rational plane curves by means of linear systems of (d−2)-degree curves. The algorithm outputs a rational parametrization of a rational curve C of degree d which has the same points at infinity as C. Moreover, although we do not provide a theoretical analysis, our empirical analysis shows that C and C are close in practice.
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