Walking in the Farey Fan to Compute the Characteristics of a Discrete Straight Line Subsegment

  • Isabelle Sivignon
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7749)


Given a Digital Straight Line (DSL) of known characteristics (a,b,μ), we address the problem of computing the characteristics of any of its subsegments. We propose a new algorithm as a smart walk in the so called Farey Fan. We take profit of the fact that the Farey Fan of order n represents in a certain way all the digital segments of length n. The computation of the characteristics of a DSL subsegment is then equivalent to the localization of a point in the Farey Fan. Using fine arithmetical properties of the fan, we design a fast algorithm of theoretical complexity \(\mathcal{O}(\log(n))\) where n is the length of the subsegment. Experiments show that our algorithm is faster than the one previously proposed by Said and Lachaud in [15,14] for “short” segments.


Digital geometry Digital straight segment recognition Farey fan 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Isabelle Sivignon
    • 1
  1. 1.CNRS, UMR 5216gipsa-labFrance

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