Geometrical tolerances: Improved linear approximation of least squares evaluation of circularity by minimum variance

We present a new computational algorithm for the least squares evaluation of circularity of a two-dimensional (2D) circle in coordinate metrology. This algorithm takes a good geometrical approximation of the orthogonal Euclidean distance in measuring the deviational errors of sample data so that the assessment criterion of normal least squares is faithfully implemented. This algorithm provides the solution of best-fit circle in two steps; first the circle center coordinates are obtained by an eigenvalue analysis to minimize the total variance of deviational errors and then the circle radius is determined so as to minimize the mean of deviational errors. Several measurement examples are discussed to verify the robustness and goodness of the algorithm, and as a result it is concluded that the new algorithm provides improved performances as compared to existing relevant least squares algorithms.