Abstract
The family of separating circles of two finite sets S 1 and S 2 in the plane consists of all the circles that enclose S 1 but exclude S 2. We prove that the maximum and minimum distance between a point p and any separating circle in this family can be found by examining only a finite subset of circles, although the family itself is infinite. In addition, we introduce the concept of elementary circular separations to clarify some of the properties of separating circles.
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Veelaert, P. (2011). Distance between Separating Circles and Points. In: Debled-Rennesson, I., Domenjoud, E., Kerautret, B., Even, P. (eds) Discrete Geometry for Computer Imagery. DGCI 2011. Lecture Notes in Computer Science, vol 6607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19867-0_29
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DOI: https://doi.org/10.1007/978-3-642-19867-0_29
Publisher Name: Springer, Berlin, Heidelberg
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