A new method for approximating optimal parameterization of polynomial curves

Rational re-parameterizations of a polynomial curve that preserve the curve degree and [0,1] parameter domain are characterized by a single degree of freedom. The optimal re-parameterization in this family can be identified but the existing methods may exhibit too much residual parametric speed variation for motion control and other applications. In this paper, a new re-parameterization method to optimal parameterization is presented and the optimal parameterization in this family obtained by the new method satisfies that the maximum deviation from unit-speed is the minimum. Experiments for comparing the efficiency of this algorithm with other methods are also included.