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why multiply by the inverse at the end of quaternion rotations

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I''ve slowly been learning quaternions and I believe I''m almost ready to implement it but I just have one question. The formula for the rotation is p = qpq^-1. Now I''ve noticed that if I just do qp, I get a rotation of half the angle that I asked for. Now, when coverting the rotation vector and angles into quaternions, you take the angle and divide it by two. If you skipped the division, couldn''t you just do qp? The answer is most likely no but I''m curious to know what the answer is. Thanks in advance. Etran

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> If you skipped the division, couldn''t you just do qp?

No. This only works for vectors perpendicular to the axis of rotation. If all your vectors are like this then you can use this, but otherwise the two-sided version is necessary.

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