中文摘要：

构造了一种有理四次插值样条，其分子为四次多项式分母为二次多项式．该有理插值样条是有界的、保单调且C2连续的，仅带有一个调节参数δi研究了有理四次插值样条的性质，同时给出了相应的函数值控制、导数值控制方法．这种方法的优点在于能够根据实际设计需要简单地选取适宜的参数，达到对曲线的形状进行局部调控的目的．

英文摘要：

A new rational quartic interpolating spline based on derivative values with quadratic denominators are constructed. The monotonicity-preserving and C2 continuity of rational quartic interpolating curves can be confirmed. The rational interpolating spline has simple and explicit representation with parameters δi. The function value control and derivative value control methods of the rational quartic interpolating curves are given respectively. The advantage of these control methods is that they can be applied to modifying the local shape of an interpolating curve by simple selecting suitable parameters according to the practical design requirements.