Maybe you already know this, but it's impossible to convert nurbs to bezier splines exactly because nurbs are rational functions, and bezier splines are polynomials.
I don't understand what it means, and don't yet know if it really means that there is absolutely no way to convert a NURBS curve into a cubic bezier curve (or spline, since I think bezier splines are multiple bezier curves connected together). I get confused because I also read this:
No matter it is Uniform or Non-uniform, NURBS is just made by one or a bunch of Bezier curve; and if you bear with me, what you need to know about NURBS math is just the Bezier-series-equations.
Even just saw this:
NURBS curve can always be converted to piecewise Bézier by repeated knot-insertion.
So some say it's possible, others not.
If it is true that you can't model NURBS with Bezier curves, then I would like to know why rational functions and polynomials can't be morphed into one another, at least at a high level (what is preventing the transformation between the two). In that case I would also like to know if there is a way to approximate a NURBS curve with Bezier curves, even though you lose some precision or the curve changes slightly. I would then just like to know how much you lose when approximating a NURBS curve with a Bezier curve, and what the algorithm or technique is called so I can further explore how to do it. If there is a standard algorithm for accomplishing this, that would be cool to know instead too.