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.

• Type: Journal
• Year: 1998
• Where: DCG
• Authors: Jesus Garcia-Lopez, Pedro A. Ramos, Jack Snoeyink
• Keywords: D-dimensional Annulus, DCG 1998, Euclidean D-dimensional Space, Minimal Annulus