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中文摘要：
构造了一种带参数的有理三次样条函数,它是标准三次样条函数的推广.选择合适的参数,该样条曲线比标准三次插值曲线更加逼近被插值曲线.参数还能局部调节曲线的形状,这给约束控制带来了方便.研究了该种插值曲线的区域控制问题.给出了将其约束于给定的二次曲线之上、之下或之间的充分条件.文中给出了两个数值例子.
英文摘要：
A kind of rational cubic spline with parameters is constructed,which is the extension of the standard cubic spline.Selecting proper parameters,the given spline can more approximate the interpolated curve than the standard cubic spline.The shape of the interpolating curve can be adjusted by parameters locally,which is convenient for user to restrict the interpolating curves.How to constrain the interpolating curve to be in the given region is studied.The sufficient conditions for the interpolating curves to be above,below or between the given piecewise quadratic curves are derived.Two examples are given in this paper.
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