I want to compare the rotation of two cameras with respect to a common frame. Let's call these
R_World_Cam1. When comparing these two rotations, one common approach is to compute the Euler angles (for example XYZ) and compare the components. This comparison is nice because it tells us which part of the rotation changes more (roll, pitch, or yaw).
I wonder if it is possible to do something similar with the tangent space vectors of the rotations. More specifically, we can compute
V_World_cam0 = Log(R_World_Cam0) and
V_World_cam1 = Log(R_World_Cam1). But I understand that we cannot compare these directly as we would do with Euler angles, because we are talking about components of a vector which represents
the rotations with the angle-axis representation (potentially not normalized).
Is my understanding that the tangent vectors should not be used for comparison? I have done some synthetic experiments trying to compare the Euler angles and the tangent space vectors, and they are different, but their numerical values are very close, which is something I wasn't expecting. For example (I omit code for brevity), I create a rotation using the Euler angles XYZ convention and I apply
Log operator to the created matrix:
Input: XYZ Euler angles: [ 45.00000936 -0. 30.00000624] Output: tangent vector: [43.94588114 11.77526336 28.42800051]
Is this just a coincidence?
Thank you in advance!