平面度和直线度误差的快速评定——增量算法

A Fast Evaluation Method for Flatness and Straightness Tolerance by Means of Incremental Algorithm

在平面度(直线度)误差评定的最小包容区域法中,提出一个新的、快速的实施方法———增量算法。该法以计算几何中凸壳的理论为依据,结合平面度(直线度)误差评定中数据的特点,从4个(3个)测点的子集开始,通过评定子集的平面度(直线度)以及增加距子集包容面最远的点构成新的子集的方法,逐步逼近精确解。该算法单调递增收敛到精确解,时间复杂度为O(n1)。几个算例证实了方法和结论的正确性。

A fast and accurate method called incremental algorithm is proposed to implement the minimum zone tolerance for evaluating flatness or straightness errors. The algorithm is based on the convex - hull theory in computational geometry and also explores the properties of the measurement data. The algorithm starts from a subset with four （three） measurement points. If the bounding flats or straights determined by current subset can cover the whole remaining set, the distance between the bounding planes （lines） is the final accurate flatness （straightness）. Otherwise, put the point with maximum distance from the bounding planes into current subset, and repeat the previous step for the new subset. It is proved that the sequence of flatness （straightness） of these subsets monotonously increasingly converges to the accurate result. The timing complexity is only O （n1）. Several examples verify the correctness of this algorithm.