中文摘要：

针对目前基于离散采样点进行基准平面拟合时没有考虑基准平面受约束的问题，提出一种基于三维凸包的带约束的基准平面拟合方法。该方法利用计算几何中的凸包理论，使用增量算法快速构建平面特征离散采样点的三维凸包。其次根据基准平面的定义，确定基准平面处于不同基准优先级时被其他基准特征约束的自由度以及建立基准的方法。在此基础上利用三维凸包建立基准平面无约束、转动约束、平动约束的数学模型，结合基准的相关实体要求实现了基准平面变动空间的求解。试验结果表明：采用一组采样数据建立基准平面时，所提出的算法与传统的最小二乘法进行比较更加符合基准平面的建立原则，保证了基准平面的准确性，满足了工程需求。

英文摘要：

In order to fit datum plane with discrete sampling points, a method used to fit the datum plane based on 3D convex hull theory is proposed. A 3D convex hull of discrete sampling points is set up through using incremental algorithm in computational geometry. Second, according the definition of da~rn plane in ASME, the constrained freedom of datum plane is confirmed through analyzing the priority of datum plane and the features of other datum. The fitting mathematical model of datum plane is established through using the constrained freedom of datum plane and the points （edges） of convex hull. And finally, variable domain of datum plane is obtained through analyzing material requirement of datum plane. The experiment proves that the algorithm proposed in this paper is principles compared with the traditional least square method when use the same group of sampling points to establish the datum plane, ensures the accuracy of datum plane, meet the engineering requirements.