Disclaimer: first time using quaternions.
I needed to determine the distance between a orientation given by quaternion $q_1$ and a target orientation $q_t$. Both quaternions are normalized. Therefore: $$d = 2(1-q_1 \cdot q_t)$$
This works very well, but now I need to extend the problem to ignore one axis of rotation (the z-axis in my illustration, pardon my bad drawing skills).
Instead of the distance to a single orientation, drawn as one arrow, I require to know the distance to the entire circle of possibilities.
I figured I need to remove the yaw part of the two quaternions. Is this possible, preferably without converting to euler angles? Thank you in advance!