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Circle digitization and cellular automata

  • Laure Tougne
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1176)

Abstract

The article studies the discrete circles with the help of cellular automata. It is shown that if we consider a discrete circle as a succession of horizontal, diagonal and vertical segments which lean on a beam of parabolas, we can describe it by local properties and so, construct it by cellular automata. In fact, two algorithms are examined. The first one localizes the intersections between a given real circle and the grid. The second one constructs a well-known discrete circle: the arithmetical circle.

Keywords

discrete circles construction arithmetical circle cellular automata 

References

  1. 1.
    Eric Andres. Cercle discrets et rotations discrètes. Master's thesis, Université Louis Pasteur-Strasbourg, 1994.Google Scholar
  2. 2.
    Akira Nakamura and Kunio Aizawa. Digital circles. Computer vision, 26:242–255, 1984.Google Scholar
  3. 3.
    M. L. V. Pitteway. Integer circles, etc. some further thoughts. Computer graphics and image processing, 3:262–265, 1974.Google Scholar
  4. 4.
    Laure Tougne. Construction des cercles planchers par automates cellulaires plans. Technical Report 96-21, École Normale Supérieure de Lyon, 1996.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Laure Tougne
    • 1
  1. 1.Laboratoire de l'Informatique du ParallélismeEcole Normale Supérieure de LyonLyon Cedex 07France

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