Distance between Separating Circles and Points

  • Peter Veelaert
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6607)

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.

Keywords

Parameter Domain Parameter Point Planar Point Digital Curve Circle Passing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Chazelle, B.: An optimal convex hull algorithm in any fixed dimension. Discrete and Computational Geometry 10, 377–409 (1993)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Clarkson, K.L., Shor, P.: Applications of random sampling in computational geometry, II. Discrete Computational Geometry 4, 387–421 (1989)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Coeurjolly, D., Gerard, Y., Reveilles, J.-P., Tougne, L.: An elementary algorithm for digital arc segmentation. Discrete Applied Mathematics 139, 31–50 (2004)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Damaschke, P.: The linear time recognition of digital arcs. Pattern Recognition Letters 16, 543–548 (1995)CrossRefMATHGoogle Scholar
  5. 5.
    Fisk, S.: Separating points sets by circles, and the recognition of digital disks. IEEE Transactions on Pattern Analysis and Machine Intelligence 8, 554–556 (1986)CrossRefGoogle Scholar
  6. 6.
    Kim, C.E., Anderson, T.A.: Digital disks and a digital compactness measure. In: Annual ACM Symposium on Theory of Computing, pp. 117–124 (1984)Google Scholar
  7. 7.
    O’Rourke, J., Koraraju, S.R., Meggido, N.: Computing circular separability. Discrete and Combinatorial Geometry 1, 105–113 (1986)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Roussillon, T., Tougne, L., Sivignon, I.: On three constrained versions of the digital circular arc recognition problem. In: Brlek, S., Reutenauer, C., Provençal, X. (eds.) DGCI 2009. LNCS, vol. 5810, pp. 34–45. Springer, Heidelberg (2009)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Peter Veelaert
    • 1
  1. 1.University College Ghent, Engineering Sciences - Ghent University AssociationGhentBelgium

Personalised recommendations