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Least-squares fitting of circles and ellipses. (English) Zbl 0817.65008
The problems of fitting circles and ellipses to given points in the plane are discussed. Two fitting principles are considered: (i) The “geometric fit” where the sum of the squares of the (orthogonal) distances to the given points is minimized and (ii) the “algebraic fit” where the parameters of a circle or an ellipse are determined in the usual least- squares sense. The “geometric fit” is also considered for the parametric form of a circle or an ellipse, respectively.
Various algorithms for the “geometric fit” problems are compared. Further methods for the approximate solution of the “geometric fit” problem based on iterative “algebraic fit” solutions are discussed. Numerical examples are given. The paper contains outstanding and inspiring work in this area.

65D10 Numerical smoothing, curve fitting
Full Text: DOI
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