I have a curve that I know is a (non-periodic) Cubic Bézier Curve (because I constructed it as such). I stored each ordered pair in the curve, but not the control points. Is it mathematically possible, knowing these constraints, to reconstruct the control points that created this curve? If so, how would I do so?
Thank you!
I am assuming that you saved the original interpolation points and not some sampled points. The accuracy of the reconstruction would depend on matching that computer program's choice of parameterization (uniform/chordal) and end point conditions (usually natural end condition).
This paper describes a popular cubic bezier interpolation alorithm, http://www-hagen.informatik.uni-kl.de/~alggeom/pdf/alggeom_script_ws11_03.pdf