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1998

Fitting a Set of Points by a Circle

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Fitting a Set of Points by a Circle
Given a set of points S = fp1; : : : ; png in Euclidean d-dimensional space, we address the problem of computing the d-dimensional annulus of smallest width containing the set. We give a complete characterization of the centers of annuli which are locally minimal in arbitrary dimension and we show that, for d = 2, a locally minimal annulus has two points on the inner circle and two points on the outer circle that interlace angle-wise as seen from the center of the annulus. Using this characterization, we show that, given a circular order of the points, there is at most one locally minimal annulus consistent with that order and it can be computed in time O(n logn) using a simple algorithm. Furthermore, when points are in convex position, the problem can be solved in optimal (n) time.
Jesus Garcia-Lopez, Pedro A. Ramos, Jack Snoeyink
Added 22 Dec 2010
Updated 22 Dec 2010
Type Journal
Year 1998
Where DCG
Authors Jesus Garcia-Lopez, Pedro A. Ramos, Jack Snoeyink
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