Quaternion Composition
Since a quaternion basically stores the axis vector and angle of rotation, it is not
surprising that we can write the components of a rotation matrix given the quaternion
components.
Crucially, the composition of two rotations given by quaternions is simply their quaternion
product.
- Note that the product of two unit quaternions is another unit quaternion.
- Note that quaternion multiplication, like matrix multiplication, is not commutative.
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