I have a quaternion class that implements spherical linear interpolation, normalized linear interpolation and spherical cubic interpolation of two quaternions. What I would like to achieve now is a formula to interpolate a series of quaternions defining a sort of quaternion-spline so that the interpolated quaternions pass through the quaternion control points, a bit like catmull-rom splines but with quaternions as control points.
I could of course use normalized quaternion linear interpolation but this does not achieve constant velocity. I have read somewhere that this can be achieved using cubic interpolation but I miss the exact details. I guess that there is a clever formula to smoothly interpolate across a set of quaternions with constant velocity, probably every decent skeletal animation implementation does that… Can anyone point to to a working sample or explanation of how to achieve this?