Let’s say I have a GameObject A with a child B. B has a local position B.localPosition and local rotation B.localRotation. Now let’s say I want to modify the forward axis of B such that it gets rotated by some new Quaternion c so that it points in rotation d.

To achieve this, I want to modify the rotation of A Instead of directly modifying the rotation of B. How would I calculate the necessary rotation to set to A to achieve this?

My guess would be: (A.rotation * B.localRotation) * c = d. I know B.localRotation, c, and d. However, I’m not sure how to calculate A.rotation given the non-commutative property and ordering of quaternion multiplication.

Well, quaternions are always relative rotations, always. When we used them as “absolute” rotations, it just means it relatively rotates from a given initial rotation. A.rotation * B.localRotation is the same as B.rotation since B.localRotation is a child of A. So if your “d” is a worldspace orientation, all you need is to calculate the difference between B.rotation and “d”. This difference can simply be applied to A.rotation

Something like this:

var q = d * Quaternion.Inverse(B.rotation);

Here q is the relative worldspace rotation that is required to rotate B from its current worldspace orientation to the new one. This relative rotation can be applied to A to achieve the same effect, since A and B are part of the same kinematic chain. So any relative rotation change that is applied to A will also be applied to B.