一种基于最小二乘法的离散点螺旋线式拟合算法

针对数控加工中，小线段刀路轨迹数据量较大的问题，提出了一种利用阿基米德螺线拟合小线段轨迹（离散点）的算法，分析了阿基米德螺线参数与切矢、径矢夹角的关系，给出了拟合误差的计算方法。基于最小二乘原理，通过前寻、回溯离散点集，在满足精度要求的前提下，用较少段螺旋线拟合该离散点集。仿真结果表明，阿基米德螺线拟合离散点具有数据量小、拟合精度较高的优势。

A Fitting Algorithm Based on Least Square Method and Spiral for Discrete Points

In order to solve the problems of large amount of small line segments tool path data in NC machining processes，a fitting algorithm was proposed based on Archimedes spiral for small line segments or discrete points.The relationship between parameters of Archimedes spiral and angles between tangent vector and radius vector were analyzed，and a calculation method of fitting errors was given.Based on the principles of least square，through forward and backward searching the discrete points to fit them with small numbers of Archimedes spirals under the premise of meeting the precision requirements.Simulation results show the advantages of Archimedes spiral fitting discrete points whose data amount is small while fitting precision is high.