Honeycomb Geometry: Rigid Motions on the Hexagonal Grid

  • Kacper PlutaEmail author
  • Pascal Romon
  • Yukiko Kenmochi
  • Nicolas Passat
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10502)


Euclidean rotations in \(\mathbb {R}^2\) are bijective and isometric maps, but they generally lose these properties when digitized in discrete spaces. In particular, the topological and geometric defects of digitized rigid motions on the square grid have been studied. This problem is related to the incompatibility between the square grid and rotations; in general, one has to accept either relatively high loss of information or non-exactness of the applied digitized rigid motion. Motivated by these facts, we study digitized rigid motions on the hexagonal grid. We establish a framework for studying digitized rigid motions in the hexagonal grid—previously proposed for the square grid and known as neighborhood motion maps. This allows us to study non-injective digitized rigid motions on the hexagonal grid and to compare the loss of information between digitized rigid motions defined on the two grids.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Kacper Pluta
    • 1
    Email author
  • Pascal Romon
    • 2
  • Yukiko Kenmochi
    • 3
  • Nicolas Passat
    • 4
  1. 1.LIGM (UMR 8049), LAMA (UMR 8050), UPEM, UPEC, CNRSUniversité Paris-EstMarne-la-ValléeFrance
  2. 2.LAMA (UMR 8050), UPEM, UPEC, CNRSUniversité Paris-EstMarne-la-ValléeFrance
  3. 3.LIGM (UMR 8049), UPEM, CNRS, ESIEE Paris, ENPCUniversité Paris-EstMarne-la-ValléeFrance
  4. 4.CReSTICUniversité de Reims Champagne-ArdenneReimsFrance

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