# Least-squares fitting of circles and ellipses

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## Abstract

Fitting circles and ellipses to given points in the plane is a problem that arises in many application areas, e.g., computer graphics, coordinate meteorology, petroleum engineering, statistics. In the past, algorithms have been given which fit circles and ellipses in*some* least-squares sense without minimizing the geometric distance to the given points.

In this paper we present several algorithms which compute the ellipse for which the*sum of the squares of the distances to the given points is minimal*. These algorithms are compared with classical simple and iterative methods.

Circles and ellipses may be represented algebraically, i.e., by an equation of the form*F*(x)=0. If a point is on the curve, then its coordinates x are a zero of the function*F*. Alternatively, curves may be represented in parametric form, which is well suited for minimizing the sum of the squares of the distances.

## AMS subject classifications

65H10 65F20## Key words

Least squares curve fitting singular value decomposition## Preview

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