1
$\begingroup$

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!

  • 0
    I only posted a comment since what I've written isn't sufficiently elaborate to be an answer, and writing out the solution for this is somewhat of a pain for now. If nobody writes an answer later, I'll try to write one.2012-08-17

1 Answers 1

1

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