平面曲线轮廓度误差评定的算法分析

Algorithmic analysis of error evaluation for a planar free-form curve profile

为准确测定平面曲线轮廓度误差,提出一种平面曲线轮廓度误差评定的数学模型及其计算方法。首先通过对测量曲线特征点的平移和旋转完成粗调,进而通过坐标轮换法按最小条件原则实现平面曲线的最佳匹配以消除测量时的定位误差;针对测量的关键问题———点到曲线的最短距离,文中提出了一种新颖的法矢定界法,不必事先对复杂曲线进行单调处理,通过矢量积运算得出测量点到曲线最短距离的所有局部解,再求出其最小值即为测量点到曲线的最短距离。计算实例验证了该算法的可行性和实用性。

An efficient model and algorithm are presented for planar free-form curve profile error evaluation. By means of rotation and movement of a featured point on a free-form curve, the rough pre-location is realized. Adjustment is then carried out using the mathematics of coordinate alternation in order to deal with the problem of curve matching based on the least condition principle. A new method, named delimiter of normal vectors, is introduced in order to calculate the minimum distance from the point to the curve, which is the key problem in scaling. In the method, all the local minimum distances from the point to the curve are calculated by vector products, of which the minimum value is the required solution. Several examples have validated the feasibility and accuracy of this algorithm.