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Figure 4
Geometric context involved in choosing a quaternion distance that will result in the correct average rotation matrix when the quaternion measures are optimized. Because the quaternion vectors represented by t and −t give the same rotation matrix, one must choose [|\!\cos\alpha|] or the minima, that is [\min\left(\alpha,\,\pi-\alpha\right)] or [\min\left(\| q-t\|,\,\| q+t\|\right)], of the alternative distance measures to get the correct items in the arc-length or chord measure summations. (a) and (b) represent the cases when the first or second choice should be made, respectively.

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ISSN: 2053-2733
Volume 76| Part 4| July 2020| Pages 432-457
https://doi.org/10.1107/S2053273320002648
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