[jacobolus]

From what I understand that would be (sorta; I’m not an expert in Lie theory) the logarithm of a rotation. I find the stereographic projection to be a more useful way to compress an arbitrary rotation down to 3 dimensions, for most purposes.

[mtourne]

Yes, precisely. exp() is the mapping from so(3) to SO(3), so you can use log to go the other way around.

Here is the relationship with the other representations [1]

Where it becomes interesting for our rigid-body transform application (or recovery of it, in the case of computer vision), is with Twist coordinates (6 element vector) which will map to a 4x4 Transform, again using the matrix exp() operator [2].

[1] https://en.wikipedia.org/wiki/Axis%E2%80%93angle_representat... [2] https://en.wikipedia.org/wiki/Screw_theory#Twists_as_element...