Generalized regression for CMMs

Abstract

This paper modifies the usual meaning of regression from ‘minimizing the sum of squared distances’ to ‘minimizing the sum of square perpendicular distances’. With this modified definition, the best‐fit plane, circle, and sphere may be meaningfully considered. These regression problems are motivated by the current development of software to control robotized coordinate measuring machines (CMMs) used to perform quality assurance work. A brief outline of CMMs is given and the application of the modified regression definition to a plane, circle and sphere is illustrated. In §3 the equation of the best fitting plane is calculated for various sets of data points.