基于三次样条插值的采样数据光滑曲线形成法

Smooth Curve Output for Dynamic Process Sampling Data Based on Cubic Polynomial Interpolation

计算机辅助测试所得记录为一系列经滤波的离散采样数据，要把它恢复成不失真的连续光滑曲线打印输出，应对数据进行处理。对变化平缓的稳态过程可采用拟合法；而对波动较大，采样点较多的动态过程必须用插值法才能真实反映这种波动。介绍了三次样条插值函数的形成法。指出常规方法仅能指定过程始、终点被测物理量变化的速度或加速度，不能完整描述物理量的变化状况。提出在始端和末端规定两个不独立的附加虚拟采样节点可以增加方程组的两个自由度，使其能同时指定过程始终点被测物理量的速度和加速度，从而得到符合实际情况的完美结果。

The record of CAT is a series of sampling data. In order to print out the record as a smooth curve, the data should be fitted or interpolated. The former is for steady process and the latter is especially for dynamic process that may have big fluctuation. Approaches for solving cubic polynomial spline interpolation are introduced, that can only define the accelerations or velocities at the beginning and the end. This is not complete to describe the moving status of a physical variable. By defining two extra knots the freedom of the equations is increased and both velocities and accelerations at the two ends be defined. This results in a complete output curve.