Abstract
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 ℓ. Given a set S of n points and a line ℓ in \(\mathbb R^2\), we completely characterize the locus of the center of MEC of the set S ∪ {p}, for all p ∈ ℓ. 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 ℓ. 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.
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Banik, A., Bhattacharya, B.B., Das, S. (2011). Minimum Enclosing Circle of a Set of Fixed Points and a Mobile Point. In: Katoh, N., Kumar, A. (eds) WALCOM: Algorithms and Computation. WALCOM 2011. Lecture Notes in Computer Science, vol 6552. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19094-0_12
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DOI: https://doi.org/10.1007/978-3-642-19094-0_12
Publisher Name: Springer, Berlin, Heidelberg
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