Slerp

calculating a unit quaternion using a spherical linear interpolation (Slerp)

This routine aims for calculating a unit quaternion, describing a rotation matrix, which lies between two known unit quaternions - q1 and q2, using a spherical linear interpolation - Slerp.
Slerp follow the shortest great arc on a unit sphere, hence, the shortest possible interpolation path.
Consequently, Slerp has constant angular velocity, so it is the optimal interpolation curve between two rotations.