一类基于函数值的有理三次样条曲线的形状控制

Shape Control of a Rational Cubic Interpolating Spline Based on Function Values

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。构造了一种基于函数值的分母为二次的C1连续有理三次插值样条。这种有理三次插值样条中含有调节参数,因而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。

To constrain the interpolating curves to be bounded in the given region is an important problem in curve design .A rational cubic interpolating spline based on function values and with quadratic denominators is constructed. The sufficient conditions for the interpolating curves to be above, below or between the given broken lines or piecewise quadratic curves and the sufficient and necessary conditions for the interpolating curves to be above, below or between the given broken lines are derived.