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Evaluation of One- and Two-Sided Geometric Fitting Algorithms in Industrial Software



Craig M. Shakarji


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 for coordinate measuring machines. Efforts at the National Institute of Standards and Technology (NIST) have been made to address software that performs feature fitting according to criteria that closely mirror the language of geometric dimensioning and tolerancing?namely, fitting using a minimum-zone, a maximum-inscribed, or a minimum-circumscribed criterion. In contrast to the least-squares case, there is no formal test service by a national lab for these types of fits. NIST recently developed reference fitting algorithms and compared results with those from some industrial vendor software packages. The results for these non-least-squares cases were alarming. In several cases the reported fits erred--often to an unacceptably large degree. Sometimes the reported maximum-inscribed fit was not even close to being an inscribed feature. This paper details the motivation, development, and rigorous testing of the new reference algorithms, which are based on simulated annealing optimization methods. An overview of the comparison with vendor software packages is given along with the documentation of some alarming results.
Proceedings Title
American Society of Precision Engineering Annual Meeting


Chebyshev, coordinate measuring machine, curve fitting, least-squares, maximum-inscribed, minimum-circumscribed, minimum-zone, simulated annealing, surface fitting


Shakarji, C. (2003), Evaluation of One- and Two-Sided Geometric Fitting Algorithms in Industrial Software, American Society of Precision Engineering Annual Meeting, [online], (Accessed April 14, 2024)
Created September 1, 2003, Updated February 17, 2017