Determining a pair of concentric spheres for assessing sphericity errors using discrete Voronoi diagrams

Abstract

In this paper, we propose a new procedure Soi computing a pair of concentric spheres with a minimum radial separation for assessing sphericity errors by constructing discrete farthest and nearest Voronoi diagrams. The properties of 3D Voronoi diagrams are explored to determine a pair of concentric spheres with minimum radial separation such that all the data points are bounded by these two spheres. A voxel map is used to construct a discrete Voronoi diagram. The convergence of die proposed procedure to the true global minimum sphericity error is guaranteed. This procedure works for various forms of spherical measurement data, including scattered measurement points. The proposed procedure is simple in implementation and effective in computation.