I have two point $p_1$ and $p_2$. The velocity vectors are $v_1$ and $v_2$ respectively. The length of the velocity vectors are constant.
I want to draw a path from $p_1$ to $p_2$ that enters $p_1$ with velocity $v_1$ and exits $p_2$ with velocity $v_2$. I have functions for quadric and cubic splines to my disposal.
How do I calculate the intermediate points (one or two)?
These points are part of a longer path, but I only know these two points at this time. I cannot wait until I know all the points until I draw the path.