Method of datum plane fitting for tolerances based on 3D convex hulls

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 datum 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.