On the performance of the approximate parametrization algorithm for curves

In Pérez-Díaz et al. (2009) [5], the authors present an algorithm to parametrize approximately ϵ-rational curves, and they show that the Hausdorff distance, w.r.t. the Euclidean distance, between the input and output curves is finite. In this paper, we analyze this distance for a family of curves randomly generated and we empirically find a reasonable upper bound of the Hausdorff distance between each input and output curve of the family.

► We evaluate the performance of the approximate parametrization algorithm for plain curves.
► We generate a random family of ϵ-rational curves and we apply the approximate parametrization algorithm to the curves obtained.
► We analyze the Hausdorff distance between each input and output curve of the family.
► The empirically computed upper bound of the Hausdorff distance is 2.16.
► We obtain evidences that the actual distance is experimentally less than or equal to 0.14.