Visiting bijective digitized reflections and rotations using geometric algebra

Stéphane Breuils (1) , Yukiko Kenmochi (2) , Akihiro Sugimoto (1)

1 NII - National Institute of Informatics
2 LIGM - Laboratoire d'Informatique Gaspard-Monge

Geometric algebra has become popularly used in applications dealing with geometry. This framework allows us to reformulate and redefine problems involving geometric transformations in a more intuitive and general way. In this paper, we focus on 2D bijective digitized reflections and rotations. After defining the digitization through geometric algebra, we characterize the set of bijective digitized reflections in the plane. We derive new bijective digitized rotations as compositions of bijective digitized reflections since any rotation is represented as the composition of two reflections. We also compare them with those obtained through geometric transformations by computing their distributions.

Domaines: Mathématique discrète [cs.DM]

Stéphane Breuils, Yukiko Kenmochi, Akihiro Sugimoto. Visiting bijective digitized reflections and rotations using geometric algebra. International Conference on Discrete Geometry and Mathematical Morphology, May 2021, Uppsala (virtuel), Sweden. pp.242-254, ⟨10.1007/978-3-030-76657-3_17⟩. ⟨hal-03168979⟩