A General Construction Scheme for Unit Quaternion Curves

This paper shows that Shoemake's formulation of the spline in SO(3) 
isn't correct in that C2 continuity of a spline curve in R3 doesn't 
carry over to SO(3). They instead show a formulation based on the 
product of simple quaternion curves, each with a fixed angular velocity, 
that transforms a curve in R3 into SO(3). Their resulting Hermite curve 
  has high-order continuity, and so can be used as a torque-minimizing 
curve.

Key ideas: Piecewise linear interpolation doesn't generally produce 
continuous curves in quaternion space. By changing bases to ones more 
suitable for this space, they can produce high-order continuous curves.

Contributions: A way to directly formulate smooth curves in Quaternion 
spaces.