Evaluation of One- and Two-sided Geometric

Recent work in testing and comparing maximum-inscribed, minimum-circumscribed, and minimum-zone (Chebyshev) fitting algorithms indicates that serious problems can exist in present commercial software packages. 1. Introduction The historical motivation for this work came as a result of the 1988 GIDEP alert [1] which warned of possible significant measurement uncertainty arising from least-squares fitting software embedded in coordinate measuring machines (CMMs). The National Institute of Standards and Technology (NIST) responded with the Algorithm Testing and Evaluation Program for Coordinate Measuring Systems (ATEP-CMS). This NIST special test service helps quantify the uncertainty of measurement due to least-squares fitting software for lines, planes, circles, spheres, cylinders, cones, and tori. The ATEP-CMS relies on internal least-squares reference fitting algorithms developed for all these geometries [2]. The test service proved successful, as it has revealed weak points in several least-squares fitting packages, which have been subsequently revised.