<ul><li>Every rotation in 3D fixes an axis, as per Euler’s rotation theorem from 1775.</li><li>The composition of two rotations is a rotation, where the first rotation fixes an axis, the second rotation fixes another axis, and the composition fixes a third axis.</li><li>To represent rotations using quaternions: a rotation by θ about an axis given by a unit vector v corresponds to a specific quaternion.</li><li>Composing rotations represented by quaternions is straightforward, as rotating by two quaternions q and r is equivalent to rotating by rq.</li></ul>

Composing rotations using quaternions

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