【摘要】 给出了具有线性分母的有理三次样条函数的误差估计,并在柱面坐标系下对一类空间闭曲线的插值问题进行了研究;通过将柱面展开,把空间闭曲线的插值问题转化为平面中的插值问题,利用具有线性分母的有理三次样条函数进行插值;最终得到的空间曲线能达到曲率连续.对该方法的误差进行了分析,数值例子显示插值效果较好.更多还原

【Abstract】 The error estimation of rational cubic spline with linear denominators is given,and then the interpolation of a kind of space closed curves under cylindrical coordinate system is investigated.The main idea is to transform the interpolation problem of space closed curves into the one of plane curves by rational cubic splines with linear denominators through expanding circular cylindrical surface.The space curves finally obtained are shown to be curvature continuous.The error estimation of this method is also analyzed,and numerical examples show that the effect of interpolation is improved.更多还原