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Approximate parametrization of plane algebraic curves by linear systems of curves
Perez Diaz, Sonia and Sendra Pons, J. Rafael and Rueda Perez, Sonia and Sendra Pons, Juana
Approximate parametrization of plane algebraic curves by linear systems of curves.
"Computer Aided Geometric Design", v. 27
t 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 ϵ>0 and an ϵ-irreducible algebraic affine plane curve C of proper degree d, we introduce the notion of ϵ-rationality, and we provide an algorithm to parametrize approximately affine ϵ-rational plane curves by means of linear systems of (d−2)-degree curves. The algorithm outputs a rational parametrization of a rational curve 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 and C are close in practice.
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