I have 2 vectors, U1 and V1 (from origin) in 3D space, together forming a plane P1. The vectors then both changes to U2 and V2 (still from origin) forming a new plane P2. Is there there a way to obtain the quaternion representing the rotation between P1 and P2?
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I'll just post the full answer thanks to Shiyu in the comments. I'm an engineer and programmer, so the writing is probably not the way a mathematician would want to read it.