ESTABLISHMENT OF A PAIR OF CONCENTRIC CIRCLES WITH THE MINIMUM RADIAL SEPARATION FOR ASSESSING ROUNDNESS ERROR

The paper presents a computational-geometry-based method of determining the roundness error of a measured workpiece. A set of n points (obtained from the measured workpiece) in a plane being given, it is required that the center and the radii of a pair of concentric circles be found such that no point is exterior to the space bounded by the circles, with the condition that the radial separation between the circles is minimum. The paper addresses the mathematical formalization of the problem. The properties of convex-hull and Voronoi diagrams have been exploited to develop a faster algorithm for establishing the circles. The methodology has been implemented, and the results have been presented to validate the computational effectiveness of the approach.