Publication
On Cayley's factorization of 4D rotations and applications
Journal Article (2017)
Journal
Advances in Applied Clifford Algebras
Pages
523-538
Volume
27
Number
1
Doc link
http://dx.doi.org/10.1007/s00006-016-0683-9
File
Authors
Projects associated
Abstract
A 4D rotation can be decomposed into a left- and a right-isoclinic rotation. This decomposition, known as Cayley’s factorization of 4D rotations, can be performed using the Elfrinkhof–Rosen method. In this paper, we present a more straightforward alternative approach using the corresponding orthogonal subspaces, for which orthogonal bases can be defined. This yields easy formulations, both in the space of 4x4 real orthogonal matrices representing 4D rotations and in the Clifford algebra C_{4,0,0}. Cayley’s factorization has many important applications. It can be used to easily transform rotations represented using matrix algebra to different Clifford algebras. As a practical application of the proposed method, it is shown how Cayley’s factorization can be used to efficiently compute the screw parameters of 3D rigid-body transformations.
Categories
automation.
Author keywords
4D Rotations
Scientific reference
A. Perez and F. Thomas. On Cayley's factorization of 4D rotations and applications. Advances in Applied Clifford Algebras, 27(1): 523-538, 2017.
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