Smooth interpolation of rotational motions

The authors consider an object is undergoing rotational motions, with orientation known at given times, and wish to interpolate the orientation between those times. If the orientations are represented as unit quaternions, this is equivalent to interpolating among a sequence of points on the three-sphere in four-space. They present an algorithm for doing this smoothly. If the object possesses rotational symmetry, then its orientation is given by its axis, and can be represented as a point on the unit sphere in three-space. The problem of interpolating on the sphere is of interest in its own right, and has other applications. The authors have implemented an algorithm for this, and present graphical results