thank you for your quick reply. It took me some time and help from people at my university (TU Delft), but I got it right now. I developed a script to do what I asked you for. It solves the polynomial in a different way, by using mldivide. It uses the fact that overdetermined matrices are solved by a least squares fit.
If you are interested, I could mail my script to you.
I am currently searching to minimize influence of different pieces (between the breaks) on one another. I want to have a high degree polynomial (10 and up) but only have the total piecewise polynomial differentiable up to 3rd or 4th order.
I think I only need to change a line or two in the splinebase function, but I wouldn't know which, since I do not understand the fine details of it, in spite the very crisp and clear code you wrote.
I'd really appreciate your help, thank you in advance.