Optimal Rational Parameterization of Quadratic Curves Based on the Geographic Information of Both Ends

摘要

cqvip:In this paper, we rewrote the equation of algebraic curve segments with the geometric information on both ends. The optimal or nearly optimal rational parametric equation is determined by the principle that parametric speeds at both ends are equal. Comparing with other literatures, the method of 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. Large numbers of experimental data show that our method has been given with more self-adaptability and accuracy than that of other literatures, and if the parametric speed at any end reaches its maximum or minimum value, the parameterization is optimal; otherwise it is close to optimal rational parameterization.