That's a bit different from what I did indeed. I used different Bezier curves between each consecutive points.

So if you have an arbitrary number of points to fit that won't be possible. But I guess under certain conditions you could fit 8 different points (since you use a 7th order curve). That would be a system with 8 unknowns. Unfortunately I don't have a clear answer to give, but if I were you I would try to do this with a 2nd then 3rd order Bezier curve and see if it can be generalized.

I found this very complete online book which might help: https://pomax.github.io/bezierinfo/

Good luck!