Geometric fit of a point set by generalized circles
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In our paper we approximate a set of given points by a general circle. More precisely, given two norms k 1 and k 2 and a set of points in the plane, we consider the problem of locating and scaling the unit circle of norm k 1 such that the sum of weighted distances between the circumference of the circle and the given points is minimized, where the distance is measured by a norm k 2. We present results for the general case. In the case that k 1 and k 2 are both polyhedral norms, we are able to solve the problem by investigating a finite candidate set.
KeywordsCircle location Dimensional facility Minisum Polyhedral norms
Mathematics Subject Classification (2000)62J02 65D10 90C26 90B85 97N50
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