中文摘要：

为提高微小型结构件圆度误差评定的准确性和快速性,本文研究提出一种基于计算几何的圆度误差评定算法。该算法利用计算几何中的凸包理论,将圆轮廓采样点集依据凸点判定准则进行分类,形成外接圆和内接圆两个点集,用较少的数据点进行后期拟合计算;在此基础上,建立了三种改进的圆度误差评定方法的优化算法,包括最小外接圆法（MCC）、最大内接圆法（MIC）和最小包容区域法（MZC）;将改进的算法应用于圆度误差测量中,实验结果表明：采用同一组测量数据时,本文提出的算法与传统算法相比较,大大降低了后期数据拟合的时间,极大提高了圆度误差评定方法的效率。

英文摘要：

In order to improve accuracy and efficiency for Roundness Error Evaluation （REE） in micro part measurements, a novel algorithm based on Computational Geometry is developed in this paper. In the algorithm the convex theory hull of Computational Geometry is used to identify relevant data for the following REE. Compared with traditional REE methods, the identification process can improve computational performance significantly. Based on the identification process, three optimized algorithms, Minimum Circumscribed Circle （MCC）, Maximum Inscribed Circle （MIC） and Minimum Zone Circle （MZC） , are also designed. Simulation results of REE show that the efficiency of REE is enhanced obviously.