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3D discrete rotations using hinge angles

Abstract : 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.
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Yohan Thibault, Akihiro Sugimoto, Yukiko Kenmochi. 3D discrete rotations using hinge angles. Theoretical Computer Science, Elsevier, 2011, 412 (15), pp.1378-1391. ⟨10.1016/j.tcs.2010.10.031⟩. ⟨hal-00734881v2⟩

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