Abstract: In the domain of CAGD and CG, optimal parameterization of specified segment
on the algebraic curves is a hot question. Take the optimal approximation of arc-length
parameterization as the criterion of optimal parameterization, and the optimal or close to optimal
rational parameterization formula of any specified segment on the conic curves is obtained. The
new method has strong self-adaptability. Finally, a experimental comparison of the results
obtained by this method and by the traditional parametric algorithm is conducted.

Key words: optimal parameterization, algebraic curve, parametric curve, arc-length
parameterization