3D discrete rotations using hinge angles

Yohan Thibault (1) , Akihiro Sugimoto (2) , Yukiko Kenmochi (1)

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

In this paper, we study 3D rotations on grid points computed by using only integers. For that purpose, we investigate the intersection between the 3D half-grid and the rotation plane. From this intersection, we define 3D hinge angles which determine a transit of a grid point from a voxel to its adjacent voxel during the rotation. Then, we give a method to sort all 3D hinge angles with integer computations. The study of 3D hinge angles allows us to design a 3D discrete rotation and to estimate the rotation between a pair of digital images in correspondence.

Mots clés: 3D discrete rotation; half-grid; multi-grid; hinge angle; integer computation

Domaines: Mathématique discrète [cs.DM]; Traitement des images [eess.IV]; Synthèse d'image et réalité virtuelle [cs.GR]

Yohan Thibault, Akihiro Sugimoto, Yukiko Kenmochi. 3D discrete rotations using hinge angles. Theoretical Computer Science, 2011, 412 (15), pp.1378-1391. ⟨10.1016/j.tcs.2010.10.031⟩. ⟨hal-00734881v1⟩