一种有理曲线多项式逼近的方法

文章讨论了有理曲线的多项式逼近问题,采用L2准则作为度量的标准,考虑将有理曲线表达式中的分母部分‘去掉’,将逼近的式子做变形。这种方法避免了有理函数的积分问题,降低了运算的难度。通过相应的数值实例可以知道：在无端点限制时具有良好的逼近效果;插值端点时,可以通过提高逼近多项式曲线的次数达到较好的逼近效果;在端点处保持几何连续性时,通过非线性规划问题的解决,得到不错的逼近曲线。

A method for polynomial approximation of rational curve

The polynomial approximation problem of rational curve was discussed by using the criterion of L2 as metric standard,‘removing＇the numerator of the rational curve expression,and doing deformation of the approximation formulas. This method avoids the problem of rational function integral and reduces the difficulty of the operations. The corresponding numerical examples showed that： a good approximation effect can be achieved when there is no limit of endpoint; with interpolation endpoints,a good approximation effect can be achieved by increasing the order of polynomial curve; as the endpoint keeps geometric continuity,through the solution of the nonlinear programming problem,a good approximation curve is obtained.