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The Sensitivity of Three-Point Circle Fitting



Ted Hopp


This paper established to first order the sensitivity of the center coordinates and radius of a circle through three points in terms of small, random perturbations of those points. This problem arises in the estimation of measurement errors, from coordinate measurement systems. Formulas developed herein express the uncertainty of circle parameters as functions of point measurement uncertainty and the arc angle between points. We show that for practical measurement procedures, task uncertainties depend only on the mean and variance of the point measurement errors and are essentially independent of the NISTIR statistical distribution.
NIST Interagency/Internal Report (NISTIR) - 5501
Report Number


coordinate measurement systems, circle parameters, statistical distribution, practical measurement procedure


Hopp, T. (1994), The Sensitivity of Three-Point Circle Fitting, NIST Interagency/Internal Report (NISTIR), National Institute of Standards and Technology, Gaithersburg, MD, [online], (Accessed July 22, 2024)


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Created September 1, 1994, Updated November 10, 2018