Assessing roundness errors using discrete Voronoi diagrams

Abstract

In this paper we propose a new procedure for measuring roundness errors by computing a pair of concentric circles with the minimum radial separation for assessing the errors by constructing the discrete farthest and nearest Voronoi diagrams. The properties of Voronoi diagrams are exploited to determine a pair of concentric circles,with minimum radial separation such that all the data points are bounded by these two circles. A pixel map is used to construct a discrete Voronoi diagram. The convergence of the proposed procedure to the true global minimum roundness error is guaranteed. This procedure based on discrete Voronoi diagrams is robust even for ct large number of data points. The proposed procedure is simple in implementation and effective in computation.