title: Reverse engineering a bezier curve
body: <p>Given a few sample points on a <a href="http://www.moshplant.com/direct-or/bezier/index.html" rel="nofollow noreferrer">bézier curve</a>, is it possible to work out the set of possible curves these points may lie on?</p>
  
  <p>In my specific application there is a limited set of endpoints the curve may have, so I want to generate the set of possible curves, enumerate all of them and pick out all the ones which may end on a valid end point.</p>
  
  <p>Some people have asked for more detail.
  I have a set of points which I know are on a <a href="http://en.wikipedia.org/wiki/B%C3%A9zier_curve#Quadratic_B.C3.A9zier_curves" rel="nofollow noreferrer">quadratic</a> bezier curve, I want to calculate the formula of the curve and be able to extrapolate new points on the curve.</p>