I'm looking for a way to describe movement into $3$-D space and time, in a continuous way, as such that I could manipulate the coordinates later on with transformation matrices. Imagine it as recording a dot moving in $3$-D space and not only keeping it path but also the speed and acceleration of it.
I though about $4$-dimensions NURBS but I'm not exactly sure how this could be possible. I'd like to be able to take that NURBS path and accelerate/slow it down, clamp the movement into $3$-D space or compress it.
I know I could simply use $3$-D positions vector at a fixed time frame and interpolate the position of my dot, but I'd prefer a continuous form.