I had written a tangentially related comment a few days ago. Its related to rotation in a plane. In that case things become a lot simpler, especially if your programming environment support operations on complex numbers as a first class citizen.
The key intuition is that additions are translations and multiplications are rotations. So two model average translation one can use arithmetic mean, for average rotation the geometric mean.
https://news.ycombinator.com/item?id=40333541
The key intuition is that additions are translations and multiplications are rotations. So two model average translation one can use arithmetic mean, for average rotation the geometric mean.