I'm trying to implement a program using C++ that could determine a B-spline curve which would represent rational motion between given control positions (following along with Juttler and Wagner's Spatial Rational B-Spline Motion paper, here).
In the paper the authors define the motion curve as being based on three parameters, $v_0(t)$, $v_{0...3}(t)$ and $d_{0...3}(t)$. But where do these parameters come from? Are they simply defined by the transformation from one control point to another, just parameterized with time? I'm really stuck on this, and am having difficulty proceeding forward. Any help would be greatly appreciated!