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Recovering Circles and Spheres from Point Data



Christoph J. Witzgall, Geraldine Cheok, Anthony J. Kearsley


Methods for fitting circles and spheres to point sets are discussed. LADAR (LAser Detection And Ranging) scanners, in particular, are capable of generating "point clouds" containing the x, y, z coordinates of up to several millions of points reflecting the laser signals. Coordinates collected off objects such as spheres may then be used to model these objects. Fitting amounts to minimizing what is called here a "gauge function", which quantifies the quality of a particular fit. This work analyses and experimentally examines the impact of the choice of three such gauge functions. One referred to here as "algebraic" fitting formulates the minimization problem as a regression. The second, referred to as "geometric" fitting, minimizes the sum of squares of the Euclidean distances of the data points from the tentative sphere. This method, based on orthogonal distance minimization is most highly regarded and widely used. The third method represents a novel way of fitting. It is based on the distances in which the individual data points have been acquired.
Perspectives in Operations Research: Papers in Honor of Saul
Publisher Info
Springer Science Publisher,


BFGS, circles, fitting, LADAR, optimization, point clouds, registration, spheres


Witzgall, C. , Cheok, G. and Kearsley, A. (2006), Recovering Circles and Spheres from Point Data, Springer Science Publisher, , [online], (Accessed June 13, 2024)


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Created June 30, 2006, Updated October 12, 2021