The quaternion-based spatial-coordinate and orientation-frame alignment problems

Quaternion methods for obtaining solutions to the problem of finding global rotations that optimally align pairs of corresponding lists of 3D spatial and/or orientation data are critically studied. The existence of multiple literatures and historical contexts is pointed out, and the algebraic solutions of the quaternion approach to the classic 3D spatial problem are emphasized. The treatment is extended to novel quaternion-based solutions to the alignment problems for 4D spatial and orientation data.

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