In the process of making a game where I have "Rooms" where exits/entrances are marked by an invisible arrow on the rim. If I can get these parallel and facing opposite I'm golden.
Basically I want to snap these arrows together, but mirrored. So getting the translation (x,y,z) right is simple, I take Room A's arrow and just set Room B's to it.
But rotation is not as simple, I tried some naive approaches, such as (roll,pitch,yaw)*-1 and (roll-180,pitch-180,yaw-180) but these are incorrect. Especially if a point ends up at translation (0,0,0).
Not sure if quaternion math would help with anything but I am open to any reasonable approach. Sorry if my terminology is off it's been about 10 years since I took linear algebra which I barely passed anyway hoho.
So: for any rotation+translation of A, get the opposite rotation of B.