Characterization of bijective digitized rotations on the hexagonal grid

Kacper Pluta (1, 2) , Tristan Roussillon (3) , David Cœurjolly (3) , Pascal Romon (2) , Yukiko Kenmochi (1) , Victor Ostromoukhov (4)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge
2 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
3 M2DisCo - Geometry Processing and Constrained Optimization
4 R3AM - Rendu Réaliste pour la Réalité Augmentée Mobile

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 arithmetical properties of the Eisenstein integers.

Mots clés: digital geometry; honeycomb geometry; digital topology; digitized rotations; bijective transformations; hexagonal grid

Domaines: Mathématique discrète [cs.DM]

Kacper Pluta, Tristan Roussillon, David Cœurjolly, Pascal Romon, Yukiko Kenmochi, et al.. Characterization of bijective digitized rotations on the hexagonal grid. Journal of Mathematical Imaging and Vision, 2018, 60 (5), pp.707-716. ⟨10.1007/s10851-018-0785-1⟩. ⟨hal-01540772v2⟩