Rotating Object parallel to other object

Question

I try to rotate objects in the same direction as a reference object.

Normaly this would be easy:

object1.rotation = reference.rotation

But the same rotation can be expressed with different vectors:

(0, 45, 270) is the same as (0, 225, 90) 
(0, 0, 270) is the same as (0, 180, 90)

In my case the final rotation should account for this.

The reference object has a rotation of: (0, 45, 270)

Object1 Should Rotate from (0, 45, 270) to (0, 0, 270)

Object2 Should Rotate from (0, 225, 90) to (0, 180, 90)

How can i calculate this? Im using unity if this is any help.

Answer 1

If you know one start and end rotation, in this example, from (0, 45, 270) to (0, 0, 270), first calculate the rotation between the two. You can do that like this:

Quaternion startRot = Quaternion.EulerAngles(0, 45, 270);
Quaternion endRot = Quaternion.EulerAngles(0, 0, 270);
Quaternion betweenRot = endRot * Quaternion.Inverse(startRot)

Now, you can simply rotate anything by multiplying by betweenRot:

Quaternion startRot2 = Quaternion.Euler(0, 225, 90);
Quaternion endRot2 = startRot2 * betweenRot;

endRot2 should be equivalent to Quaternion.Euler(0, 180, 90).

Answer 2

I found the solution with help from @tyjkenn

Quaternion newRot = Quaternion.FromToRotation(
    object.transform.forward, 
    reference.transform.forward
);

object.transform.rotation = neRot * reference.transform.rotation;

A few important things with this:

• Both object and reference need to be aligned with unity's forward and up axis. (forward is the blue Z axis, up is the green Y axis). You can change this in your modeling software or within a parent gameObject.
• The order of quaternion multiplication matters. Its the same as changing the order of rotation matrices