In this paper we study the variations in the center and the radius of the minimum enclosing circle (MEC) of a set of fixed points and one mobile point, moving along a straight line . Given a set S of n points and a line in R 2 , we completely characterize the locus of the center of MEC of the set S∪{p}, for all p ∈ . We show that the locus is a continuous and piecewise differentiable linear function, and each of its differentiable piece lies either on the edges of the farthest-point Voronoi diagram of S, or on a line segment parallel to the line . Moreover, we prove that the locus can have at most O(n) differentiable pieces and can be computed in linear time, given the farthest-point Voronoi diagram of S.
Recently Banik et al. REF gave a complete geometric characterization of the locus of the mobile Euclidean 1-center for a set of n static points S and a single mobile point moving along a straight line l in the Euclidean plane.