【摘要】 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 .文中利用分母为线性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种加权有理三次插值样条 ,由于这种有理三次插值样条中含有新的参数 ,给约束控制带来了方便 .给出了将插值曲线约束于给定的折线、二次曲线之上 (下 )或之间的条件 ,最后给出了数值例子 .更多还原

【Abstract】 To constrain the interpolating curves to be bounded in the given region is an important problem in curve design. In this paper, the weighted rational cubic spline interpolation has been constructed using the rational cubic spline with linear denominator and the rational cubic spline based on function values. Because of the new parameters in the interpolating functions, the problems to constrain the weighted rational interpolating curves to lie strictly above or below the given piecewise linear curves (or quadratic curves) and even between them can be solved.更多还原