应变能最小的保形有理四次样条插值曲线

Shape Preserving Rational Quartic Spline Interpolation Curve of Minimum Strain Energy

为构造光顺的保形有理四次样条插值曲线,以形状控制参数和插值函数在节点处的导数为决策变量,以插值曲线应变能最小为目标函数,以插值函数保形以及形状控制参数和节点处的导数大于0作为约束条件,建立优化模型,求解获得应变能最小的保形有理四次样条插值曲线。给出的数值实例表明新方法能获得光顺的插值曲线。

In order to obtain the most fairing shape preserving rational quartic spline interpolation curve, an optimization model is established,with the shape control parameters and the derivative of the interpolation function at the nodes being decision variables, the minimum strain energy of the interpolation curve being the objective function,and the interpolation function for monotony as well as the shape control parameters and the derivative of the node greater than zero being the constraint conditions.The shape preserving rational quartic spline interpolation curve with minimum strain energy is obtained based on the optimization model.The numerical ex-amples are given to show that the new method can obtain fairing interpolation curve.