Distance between separating circles and points

  • Authors:
  • Peter Veelaert

  • Affiliations:
  • University College Ghent, Engineering Sciences - Ghent University Association, Ghent, Belgium

  • Venue:
  • DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
  • Year:
  • 2011

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Abstract

The family of separating circles of two finite sets S1 and S2 in the plane consists of all the circles that enclose S1 but exclude S2. 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.