Hey umcadop.

The bezier curve is not an interpolation curve: It only is gauranteed to go through the first and last points (if you are using a four point method).

The most basic form of an interpolating curve is the one by Lagrange which just finds the simplest polynomial to go through the points.

You can solve the Lagrange polynomial by setting up a linear system of equations and then finding the coeffecients by reducing the system (or you can use alternative formulas to do what amounts to the same thing).