We present an algorithm for generating a twice-differentiable curve on
the rotation group SO(3) that interpolates a given ordered set of rot
ation matrices at their specified knot times. In our approach we regar
d SO(3) as a Lie group with a bi-invariant Riemannian metric, and appl
y the coordinate-invariant methods of Riemannian geometry. The resulti
ng rotation curve is easy to compute, invariant with respect to fixed
and moving reference frames, and also approximately minimizes angular
acceleration.