基于近似凸壳的直线度误差评定方法

A Method of Evaluating Straightness Errors Based on Approximate Convex Hull

针对需要快速求解直线度误差的场合,提出了利用二维空间中测量点集近似凸壳评定直线度误差的近似算法,在此基础上构造真实凸壳求解直线度误差最小域值的精确算法.针对近似算法的原理误差进行误差分析,得到了近似算法的最大误差值.精确算法首先得到点集的近似凸壳,再插入近似凸壳外的点得到真实凸壳,然后查找该凸壳的对极元以求解直线度误差.通过仿真示例对提出的方法进行验证,结果显示算法是有效的,并且具有较强的鲁棒性和稳定性.

As to the situation where fast correcting straightness errors are of necessity, this paper puts forward an approximation algorithm to evaluate straightness errors by using the approximate convex hull of measured points set in twodimensional space. Accordingly, an exact algorithm was obtained to evaluate minimum zone straightness errors. As far as the principle errors of approximation algorithm are concerned, an analysis was conducted which produced the maximum error value. After having got the approximate convex hull of point set with the aid of exact algorithm, real convex hull was obtained by inserting the points out of the approximate convex hull, followed by the process in which the antipodal pairs of the convex hull were checked so as to get straightness errors. Testified by simulation experiments, the proposed method proves to be effective with remarkable robustness and stability.