任意三维抛物线的一种高速插补方法

A High Speed Interpolation Algorithm for an Arbitrary 3 Dimensional Parabola in CNC Systems

基于参数方程的矢量表示方法，导出了一种ＣＮＣ系统中任意三维抛物线的高速插补算法．该算法不仅理论上可使所有插补点均落在抛物线上，而且由于实时插补过程中只有加法运算，插补速度极高，因而适用于任何硬件环境．误差分析表明，只要合理选择参数增量，总能保证插补的弓高误差满足加工精度要求．

Based on the vector representation of parametric equation, a high speed interpolation algorithm for an arbitrary 3 dimensional parabola in CNC systems is proposed. By the algorithm proposed, not only can all of the interpolated points be made to fall on the parabola in theory, but also it is of very high speed because there is only add operation in the real time interpolation process. Therefore it is applicable to any hardware environment. An error analysis shows that by proper selection of the parameter increment the sagitt a tolerance of interpolation can always be guaranteed to meet the requirements of machining accuracy. The algorithm can be used also in the case of 2 dimensional parabola.