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 representation

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