Difference between the two quaternions

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I\'m making a 3D portal system in my engine (like Portal game). Each of the portals has its own orientation saved in a quaternion. To render the virtu

Answer 1

If you want to find a quaternion diff such that diff * q1 == q2, then you need to use the multiplicative inverse:

diff * q1 = q2  --->  diff = q2 * inverse(q1)

where:  inverse(q1) = conjugate(q1) / abs(q1)

and:  conjugate( quaternion(re, i, j, k) ) = quaternion(re, -i, -j, -k)

If your quaternions are rotation quaternions, they should all be unit quaternions. This makes finding the inverse easy: since abs(q1) = 1, your inverse(q1) = conjugate(q1) can be found by just negating the i, j, and k components.

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However, for the kind of scene-based geometric configuration you describe, you probably don't actually want to do the above, because you also need to compute the translation correctly.

The most straightforward way to do everything correctly is to convert your quaternions into 4x4 rotation matrices, and multiply them in the appropriate order with 4x4 translation matrices, as described in most introductory computer graphics texts.

It is certainly possible to compose Euclidean transformations by hand, keeping your rotations in quaternion form while applying the quaternions incrementally to a separate translation vector. However, this method tends to be technically obscure and prone to coding error: there are good reasons why the 4x4 matrix form is conventional, and one of the big ones is that it appears to be easier to get it right that way.