  In [Computer Aided Geometric Design 27 (2010), 212-231] the authors present
an algorithm to parametrize approximately $\epsilon$-rational curves, and they
show in 2 examples that the Hausdorff distance, w.r.t. to the Euclidean
distance, between the input and output curves is small. In this paper, we
analyze this distance for a whole family of curves randomly generated and we
automatize the strategy used in [Computer Aided Geometric Design 27 (2010),
212-231]. We find a reasonable upper bound of the Hausdorff distance between
each input and output curve of the family.
