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::: OK, maybe just something reminding people that there are two values for each orientation, which needs to be remembered when comparing two orientations. I just think this double cover needs to be mentioned as a (minor) complication, since I've been bitten by it once or twice myself. Tom. <span style="font-size: smaller;" class="autosigned">—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/124.171.141.46|124.171.141.46]] ([[User talk:124.171.141.46|talk]]) 01:00, 28 October 2009 (UTC)</span><!-- Template:UnsignedIP --> <!--Autosigned by SineBot-->
: These issues with the double cover are dealt with easily. See Michael Johnson's MIT PhD thesis, "[http://dspace.mit.edu/handle/1721.1/8031 Exploiting quaternions to support expressive interactive character motion]" for all the details. Briefly, a bundle of quaternions should be confined to one hemisphere by making sure they all have a positive dot product with the quaternion representing the average of the bundle. This way, there is no "jumping" when going from +180 to -180. The average is the 1st Eigenvector of the 4x4 Hermitian matrix given by the Einstein sum <math>A_{jk} = q_{ij}q_{ik}</math>. Notably, this is the ''only'' correct method for computing mean rotation. Really, his PhD thesis has the best explanation and diagrams for understanding quaternions that I've found. [[User:Reve etrange|Reve etrange]] ([[User talk:Reve etrange|talk]]) 14:53, 3 March 2019 (UTC)
== A doubt about ''z<sub>r</sub>'' in 4D rotation section ==
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