Hinge Angles for 3D Discrete Rotations

Authors:
Yohan Thibault;Akihiro Sugimoto;Yukiko Kenmochi
Affiliations:
Université Paris-Est, LIGM, UMR UPEMLV/ESIEE/CNRS 8049, France;National Institute of Informatics, Japan;Université Paris-Est, LIGM, UMR UPEMLV/ESIEE/CNRS 8049, France
Venue:
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
Year:
2009

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Abstract

In this paper, we focus on 3D rotations on grid points computed by using only integers. For that purpose, we study 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.