一种新的带有优化参数的曲线插值算法

提出了一种带有优化参数的有序点列插值算法.以给定的有序插值点列中每相邻两点划为一个插值区间;在0 360°]的角度空间中,选取一系列固定间距的角度jθ并构建插值初始向量cos(jθ)sin(jθ)];依次把初始向量代入首个插值区间中,按照算法选用适当的插值函数进行此区间内的插值并得到此区间内的插值曲线,并把插值曲线在此区间结束点处的切向方向向量作为下个相邻插值区间的初始向量,直至完成所有区间的插值;计算每条曲线的指标函数值,取使其达到最小值的θ所生成的插值曲线为最终结果.实验表明,此方法生成的插值曲线具有稳定性好、适应能力强和曲线光滑等良好性质,在计算机造型、反求工程及运动轨迹描述等工程领域有重要的实用价值.

New Interpolation Algorithm of the Curve with Optimized Parameter

This paper introduces an interpolation algorithm with optimized parameter for ordered points.In an ordered interpolation point range,we defined every two neighboring points as an interpolation interval,in a 0 360°] angle interval,we chose a series of fixed spacing angle θj and defined an interpolation initial vectorcos（θj） sin（θj）],then substituted the initial vector to the first interpolation interval,according to the algorithm,this interval was interpolated with proper interpolation function and we got the interpolation curve and a tangent vector of the last point,which was regarded as the initial vector of the next neighboring interpolation interval.The same process was repeated in the following intervals until finishing the interpolation of all intervals.Then we calculated the indicator function value of every curve,and chose the curve whose θ causes the minimum indicator function value.It is proved that the interpolation curve get from this arithmetic has many characters such as good stability,strong adoption ability,and great smoothness.It would be of great practical value in many fields such as computer sculpting,reverse-getting engineering and describing moving orbit.