Cartesian (non parametric) form of Bezier curves

I needed to find and use the coordinates of the intersection of a cubic Bezier and a straight line. The trouble is that I c开发者_Python百科annot find a non-parametric representation of a Bezier curve which I need for solving with the line.

I do not want to resort to a Newton-Raphson equivalent on the Bezier parametric equation (which can be found here)

Looks like the answer for this SO question might help you out:

Approximating nonparametric cubic Bezier