EFFECTS OF DATA POINT DISTRIBUTION AND MATHEMATICAL-MODEL ON FINDING THE BEST-FIT SPHERE TO DATA

Probe calibration on a coordinate measuring machine is dependent on th e accuracy with which the center of a reference sphere can be located. In this article, a theoretical model for sphere is fitted to a set of sampled surface points using the least-squares criterion. An analysis is conducted of various errors involved during the steps leading to t he identification of the sphere and location of its center. The errors include those associated with surface accessibility for sampling, poi nts sampling strategies, optimization algorithm, and probe diameter ve rsus reference sphere diameter. Inferences are drawn regarding the rel ative influence of these errors, and a calibration strategy is propose d as a function of sampled points, optimization algorithm, and the geo metric surface involved.