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Abstract: In this paper, the equation of algebraic curve segment with the geometric information of both ends is rewritten. The optimal or nearly optimal rational parameterization formula is determined according to the principle that parametric speeds at both ends are equal. Comparing with literature [8] and literature [9], the method in this paper has advantage in efficiency and is easy to realize. The equation of optimal rational parameterization can be obtained directly by the information of both ends. A lot of number of numerical experimental data shows that our method has more self-adaptability and accuracy than that of literature [10], and if the parametric speed at any end reaches its maximum or minimum value, the parameterization is optimal; otherwise it's nearly optimal rational parameterization.#br# Key words: algebraic curve; parametric curve; optimal parameterization; arc-length parameterization
