Characterization of bijective digitized rotations on the hexagonal grid

Kacper Pluta, Tristan Roussillon, David Coeurjolly, Pascal Romon, Yukiko Kenmochi, Victor Ostromoukhov

Journal of Mathematical Imaging and Vision January 2018

Abstract

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 charac- terized by Nouvel and Rémila and more recently by Roussillon and Coeurjolly. In this article, we characterize bijective digitized rotations on the hexagonal grid using arithmetical properties of the Eisenstein integers.

Type

Journal article

Publication

Journal of Mathematical Imaging and Vision

Caption: Distribution of angles whose digitized rotations by them are bijective in the hexagonal grids. Angles obtain from generators of the form s > 0 and t = s + 1 are colored in blue, while angles generated by s = 1 and t > 0, are colored in green.

@article{pluta18,
      author = {Kacper Pluta and Tristan Roussillon and David Coeurjolly and Pascal Romon and Yukiko Kenmochi and Victor Ostromoukhov},
      doi = {10.1007/s10851-018-0785-1},
      journal = {Journal of Mathematical Imaging and Vision},
      number = {5},
      pages = {707--716},
      title = {Characterization of bijective digitized rotations on the hexagonal grid},
      volume = {60},
      year = {2018}
}