Approximate parametrization of plane algebraic curves by linear systems of curves
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 epsilon > 0 and an epsilon-irreducible algebraic affine plane curve C of proper degree d, we introduce the notion of epsilon-rationality, and we provide an algorithm to parametrize approximately affine epsilon-rational plane curves by means of linear systems of (d - 2)-degree curves. The algorithm outputs a rational parametrization of a rational curve (C) over bar of degree d which has the same points at infinity as (C) over bar. Moreover, although we do not provide a theoretical analysis, our empirical analysis shows that and C are close in practice. (C) 2009 Elsevier B.V. All rights reserved.
approximate parametrization plane algebraic curves linear systems of curves