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# what does represent quaternions addition?

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I know that if q1 and q2 indicate rotations, then q2q1 represents the composite rotation of q1 followed by q2. but what about addition?

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Addition will in general result in non-unit quaternions which don''t then represent pure rotations. It doesn''t have any intuitive geometric interpretation.

Q1 = w1 + x1 * i + y1 * j + z1 * k
Q2 = w2 + x2 * i + y2 * j + z2 * k

Q1 + Q2 = (w1 + w2) + (x1 + x2) * i + (y1 + y2) * j + (z1 + z2) * k

So by itself not particularly useful. Addition is used in interpolation where the quaternions are carefully scaled to end up being unit length.

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thank you.

I have been seeing some codes of physical
simulations where use sum of quaternions.

For example.

orientation + = angular_velocity * orientation * (step * 0.5f);

or similar with the Runge-Kutta method.
(here my doubt arises)

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Mathematically the addition is perfectly well defined, and whatever derivations you are seeing are (probably ) correct.

There isn''t any nice geometric way of visualizing the addition though, so it''s best not to waste too much time on trying and accept that the math works (or go through the derivations and convince yourself you wind up with unit quaternions where you are using them for rotations).

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