Journal of Mathematical Imaging and Vision

, Volume 60, Issue 5, pp 707–716 | Cite as

Characterization of Bijective Digitized Rotations on the Hexagonal Grid

  • Kacper PlutaEmail author
  • Tristan Roussillon
  • David Cœurjolly
  • Pascal Romon
  • Yukiko Kenmochi
  • Victor Ostromoukhov


Digitized rotations on discrete spaces are usually defined as the composition of a Euclidean rotation and a rounding operator; they are in general not bijective. Nevertheless, it is well known that digitized rotations defined on the square grid are bijective for some specific angles. This infinite family of angles has been characterized by Nouvel and Rémila and more recently by Roussillon and Cœurjolly. In this article, we characterize bijective digitized rotations on the hexagonal grid using arithmetic properties of the Eisenstein integers.


Hexagonal grid Digital geometry Digital topology Honeycomb geometry Digitized rotations Bijective transformations Geometric transformations 



This work received funding from the project CoMeDiC (ANR–15–CE40–0006).


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.LAMA (UMR 8050), UPEM, UPEC, CNRSUniversité Paris-EstMarne-la-ValléeFrance
  2. 2.LIRIS (UMR 5205), CNRSUniversité de LyonLyonFrance
  3. 3.LIGM (UMR 8049), UPEM, CNRS, ESIEE Paris, ENPCUniversité Paris-EstMarne-la-ValléeFrance

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