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In this paper we introduce the notion of rational Hausdorff divisor, weanalyze the dimension and irreducibility of its associated linear system ofcurves, and we prove that all irreducible real curves belonging to the linearsystem are rational and are at finite Hausdorff distance among them. As aconsequence, we provide a projective linear subspace where all (irreducible)elements are solutions to the approximate parametrization problem for a givenalgebraic plane curve. Furthermore, we identify the linear system with a planecurve that is shown to be rational and we develop algorithms to parametrize itanalyzing its fields of parametrization. Therefore, we present a generic answerto the approximate parametrization problem. In addition, we introduce thenotion of Hausdorff curve, and we prove that every irreducible Hausdorff curvecan always be parametrized with a generic rational parametrization havingcoefficients depending on as many parameters as the degree of the input curve.

Rational Hausdorff Divisors: a New approach to the Approximate Parametrization of Curves