Sphericity Evaluation Using Maximum Inscribed Sphere Method

Abstract

The maximum inscribed sphere (MIS) method is an important method to evaluate sphericity error suitable for the sphere with the maximum material condition of a concave. It is proven that the MIS of a data point set is decided only by four points in the paper. An algorithm of sphericity evaluation based on the MIS is proposed. Six points with extreme coordinates are selected as an initial subset and the MIS is constructed by four of them. Another point which is the farthest from the center among the set replaces one of the former four points each time. According with the minimum criterion, the final sphere is just the MIS of the data point set when all data points is outside the sphere. The validated results show that the proposed strategy offers an effective way to identify the control data points at few iterative turns and gives an efficient approach to solve the sphericity problems.