# Convert Bezier casteljau bezier curve to control point bezier curve

I have a Bezier curve that was constructed using the CastelJau algorithm - if I'm understanding this algorithm correctly, you input 4 points, and it gives you a curve that will roughly pass through those 4 points -

but I want to, using only those 4 input points, recreate the same curve using the control points method (define start and end point of curve, and a control point for each of those points = 4 points total)?

If I can convert the curve to a quadratic (start + end points + only one control point) instead of cubic that would be even better - but the goal is to have the curve I look the same as the original casteljau style one.

How would I do this conversion? Thanks a ton!

Given 4 points and a parameter $$t_0$$, the De Casteljau algorithm allows you to compute the point $$C(t_0)$$ geometrically where $$C(t)$$ is the cubic Bezier curve defined by those 4 points. $$C(t)$$ will only pass the first and last control points. These 4 points will be the control points for $$C(t)$$.