一种自由曲线廓形误差的高效可靠评价方法

为实现对自由曲线廓形误差的高效可靠评价，提出了一种结合多项式方程求根与 实数编码遗传算法(RCGA)的评价方法。首先，根据最小二乘准则建立了廓形误差评价的优化模 型；进而，通过构造多项式方程，并采用 Halley 迭代对方程求根，实现了点到自由曲线距离的 高效计算；然后，采用 RCGA 完成了优化模型的求解，并与分割逼近法得到的结果进行了对比。 结果表明，该方法高效可靠，相同条件下计算时间约为分割逼近法的 5%，能够满足自由曲线 廓形误差的评价。

An Efficient and Robust Method for Profile Error Evaluation of Freeform Curves

To obtain the profile error of the freeform curves, an efficient evaluation method is brought out which is based on root-finding of polynomial equations and real coded genetic algorithm (RCGA). Firstly, the optimization model for the profile error evaluation was established based on the least squares criterion. Then, the polynomial equations were constructed and the point to curve distance can be obtained effectively by solving the polynomial equations via the Halley iteration. After that, the optimization model was solved by the RCGA and the profile error was obtained. The computation results were also compared with the subdivision method. From the evaluation process, it can be seen that the proposed method is efficient and robust. The computing time is about 5% of that the subdivision method needs under the same condition. Thus, it is more suitable for evaluating the profile error of the freeform curves.