Quaternion Interpolation
Interpolating quaternions produces better results than Euler angles
A quaternion is a point on the 4-D unit sphere
- interpolating rotations requires a unit quaternion at each step - another point on the 4-D sphere
- move with constant angular velocity along the great circle between the two points
- Spherical Linear intERPolation (SLERPing)
Any rotation is given by 2 quaternions, so pick the shortest SLERP
To interpolate more than two points:
- solve a non-linear variational constrained optimization (numerically)
Further information: Ken Schoemake in the Siggraph '85 proceedings (Computer Graphics, V. 19, No. 3, P.245)