I devised a manner of solving natural cubic splines in S3. It wasn't torque-minimal like some of the nice papers out there by people who know better. But what it was was a general solution that would work with any arbitrary number of points in the spline. I used it for my work project, the VWRL, which is written in Java. I implemented it here in C++, however amidst all the (few) capabilities of this demo, it never displays the quaternion cubic interpolation in action.

I did develop some documents on how I came up with the formula. It's still in the works. If I find more time I'll post it as well.