A quaternion rotation represents a three-dimensional rotation by a unit quaternion. If 
is a unit vector along the
rotation axis and 
is the rotation angle, then the unit quaternion
 |
represents the rotation. A vector 
is identified with the pure quaternion 
and is rotated according to
 |
where 
is the quaternion conjugate. The quaternions 
and 
represent the same rotation,
so unit quaternions give a double covering of the
three-dimensional rotation group 
. Composition of rotations corresponds to quaternion
multiplication.
