Calculate quaternion rotations between two values

Question

I have a quaternion Q1:
X: -0.023995593190193176 Y: -0.4076451063156128 Z: 0.04357096180319786 W: 0.9117847681045532

and I have a keyframe value Q2 which is based on Q1: X: 0.176469 Y: -0.368251 Z: 0.479782 W: 0.776569

Now my question is how can I get the correct keyframe values if there would be no extra start values ? I mean if Q1 is 1,0,0,0 (w,x,y,z). (no extra start values) So basically I need to rotate my object to the same pose but from the default values (1,0,0,0) start not from Q1.

Answer 1

Let's see if I understand correctly...

• Q1 is our absolute starting rotation

• Q2 is our absolute ending rotation - ie. it includes both Q1 and some additional rotation

...and you want to get let's call it Q_delta, the change in rotation from Q1 to Q2? (Or, equivalently, the corresponding Q2 if Q1 were the identity quaternion (w=1, xyz = 0)), is that right?

If so, it's fairly straightforward:

Q_delta = Q2 * Inverse*(Q1)

To see why, we can derive it from the fact that Q2 is Q1 with an extra rotation of Q_delta applied on top (here using the convention that rotations stack from right to left):

$$\begin{align} Q_\Delta \cdot Q_1 &= Q_2\\ (Q_\Delta \cdot Q_1) \cdot Q_1^{-1} &= (Q_2) \cdot Q_1^{-1}\\ Q_\Delta &= Q_2 \cdot Q_1^{-1}\ \end{align}$$