中文摘要：

将插值曲线约束于给定的区域之内是曲线形状控制中的重要问题。本文利用分母为二次的有理三次插值样条和仅基于函数值的有理三次插值样条构造了一类加权有理三次插值样条函数,这类新的插值样条中含有权系数,因而增加了处理问题的灵活性,给约束控制带来了方便。给出了将该种插值曲线约束于给定的折线、二次曲线之上、之下或之间的充分条件及将其约束于给定折线之上、之下或之间的充分必要条件。证明了满足约束条件的加权有理样条的存在性。

英文摘要：

Constraining interpolation curves to be in the given region is an important problem in curve design. A kind of weighted rational cubic spline interpolation is constructed by using the rational cubic spline with quadratic polynomial denominators and the rational cubic spline based on function values.Suffcient conditions for the interpolating curves to be above, below or between the given broken lines or piecewise quadratic curves, and suffcient and necessary conditions for the interpolating curves to be above, below or between the given broken lines are derived, respectively.