Development and application of voronoi diagrams in the assessment of roundness error in an industrial environment

This paper discusses a robust, computational geometry based technique to establish the roundness error of a measured workpiece in an industrial environment. For evaluating the roundness error, a mathematical formalization has been developed. The properties of a convex hull and the nearest and farthest Voronoi diagrams have been exploited to establish the ideal geometric features required in the assessment problem as per the standards. The methodology has been implemented and the examples have been presented to validate the computational effectiveness of the approach. The proposed method can be easily adopted and installed in the Coordinate Measuring Machines (CMMs) and other computer aided measuring instruments for ready industrial applications.