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@omar Quaternion nlerp (take the weighted linear average in R^4 of the unit quaternions then normalize the output to project back to the unit sphere) is extremely simple and what I think most people use in games at least. Any time you are trying to do a multiway average of several poses, but also just for lerping between two poses. In the latter case the geodesic arc is the same as slerp but with a different speed curve.

@omar I think Casey Muratori was the first to really understand and apply this (as compared to slerp-based methods) when he made Granny. Jon has an old GDMag column where he explains it: http://number-none.com/product/Understanding%20Slerp,%20Then%20Not%20Using%20It/

@omar Note that nested pairwise nlerp also isn't associative in this sense since the normalization after each nested nlerp ruins the associativity. You do the multiway averaging in the flat space (in this case R^4) and only normalize the final output.

@omar By the way, one reason that nlerp is better than it seems if you visualize the chord vs arc deviation is that the error on the unit sphere in R^4 isn't the same as the corresponding error in SO(3). The latter is much smaller for reasonable distances and if we're using quaternions to represent three-dimensional rotations that's the only error we care about.

(I haven't thought about this in a very long time, so apologies in advance for any inaccuracies.)