Oh wait.
The article sais that that would have been the definition of a spline-function of a control-point problem. So that seems to go conform with your explanation.
Since I've got Interpolation/Extrapolation as main topic, I will only need the splines which will go through the control-points. So bezier splines fall out. Is there anywhere a list of all existant splines going through the control points?
Well, the I still need to know in which part of mathematics these problems fall (interpolation with normal polynoms and splines), so I can look for a book! If anybody has a hint, I would be very grateful!
The internet tutorials only focus on how to render curves (mostly bezier), but I need the theory. Have got 5 weeks left. Argh.