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A
Rotation with
Quaternions
It is perfectly feasible to define the orientation of an object in 3D space using
only three numbers, such as the Euler angles ( , , ). However, when we
make the jump to animation, these three values are no longer adequate to
represent the orientation of the object at a given frame and how it rotates
from that orientation to a new orientation at the next frame. Indeed, we can
represent this change by a 3 × 3 transformation matrix, but a nine-element
matrix is difficult to manipulate, and there is an easier way to achieve the
same results with only four numbers! That’s where quaternion mathematics
gets involved.
In 1843, ...