4 ms·
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 usef
by jacobolus 10y ago
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 10y agoYes, 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...