hey Stephan!
I tried out your demo (thanks for putting that together)
it seems to work for me fine. For example:
You're doing a 3rd order fit (i.e. a cubic fit)
But your data input is random
So you're trying to fit a curve surface which is only defined by 10 numbers (triangular bases, 3rd order, 2 inputs) to 25 random points. It just won't be a good fit in that case.
If your points follow a smooth curve like in the image you posted before, then the fit will follow accurately.
You might be looking for something more like a B-Spline mesh which makes itself more complicated as you add more control points. A polyfit is more about finding a global pattern (which then can be defined simply mathematically).