I am building a program where I need to simplify N number of points into a single section of a bezier spline, ie describe them using just 2 end points and 2 control points. Naturally this will lead to some loss of information, but I would like the spline section to be as accurate to the original points as possible.

The input will be points that are already on a reasonably smooth curve.

Any answer is appreciated! (That being said, I'm not very good with equations, so an explanation in words would be even more so).