Abstract: Aiming at the problems of poor registration accuracy,low stability,strict requirements for initial pose and the low calculation efficiency of the shortest distance from point to curve in the traditional method for the evaluation of line profile error,a target circle shrinkage algorithm with coarse-fine combined registration and a subdivision circle approximation algorithm were presented.The target circle shrinkage algorithm with coarse-fine combined registration was used to search for the corresponding feature point pairs in the measured point set and the theoretical design profile discrete point set;then the coordinate rotation variable could be calculated by analyzing the azimuth relationship between feature point pairs,and the coordinate translation variable were obtained by calculating the center of gravity of measured point set and the center of theoretical design profile discrete point set to complete the coarse registration.The value range of coordinate transformation variable obtained by calculating the accuracy of coarse registration was used as the initial target circle area for fine registration,and the shortest distance was used as the optimization target,the optimal registration between measured points and theoretical design profile could be realized by iteratively shrinking the target circle area finally.The subdivision circle approximation algorithm improved the subdivision approach approximation by using micro-arc to approximate the theoretical design profile and the shortest distance was then obtained based on the geometric properties of circle to evaluate the line profile error.The simulation experiment results showed that the proposed algorithms had good convergence and high accuracy.

Key words: flat curve, line profile error, target circle shrinkage, subdivision circle approximation, minimum zone

摘要： 针对传统方法在线轮廓度误差评定中的配准精度差、稳定性不高、对初始位姿要求苛刻和点到曲线最短距离计算效率较低等问题,提出一种粗精配准结合的目标圆收缩法和一种分割圆逼近法进行求解。粗精配准结合的目标圆收缩法首先在实际测量点集与理论设计轮廓离散点集中搜寻曲率对应的特征点对;其次通过特征点对之间的方位关系计算坐标旋转变量,以实际测量点集的重心和理论设计轮廓离散点集的重心计算坐标平移变量,完成粗配准;然后以粗配准精度计算得到的坐标变换变量取值范围作为精配准的初始目标圆区域,以最短距离为优化目标,对其进行迭代收缩,最终实现实际测量点与理论设计轮廓的最优配准。分割圆逼近法改进了分割点逼近法,采用微圆弧逼近理论设计轮廓,由圆的几何性质计算点到微圆弧的最短距离来评定线轮廓度误差。仿真实验验证结果表明,所提方法收敛性好,计算精度高。

关键词: 平面曲线, 线轮廓度误差, 目标圆收缩, 分割圆逼近, 最小区域