C1 continuous rational re-parameterization using monotonic parametric speed partition

A new method to obtain explicit re-parameterization using piecewise rational linear functions is presented in this paper. Based on the outstanding performance of Mobius transformation on modifying pieces with monotonic parametric speed, we create a partition of the original curve, in which the parametric speed of each segment is of monotonic variation. The values of new parameters corresponding to the subdivision points are specified a priori as the ratio of its cumulative arc length and its total arc length. C¹ continuity conditions are imposed to each segment, thus, with respect to the new parameters, the objective function is linear and admits a closed-form optimization. Analysis of examples shows that, our method brings a curve very close to the arc length parameterization under L₂ norm but with fewer segments.