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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!

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1 Answer 1

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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 $C(t)$.

You can use the same De Casteljau algorithm to compute points on a quadratic Bezier curve defined by 3 points.

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  • $\begingroup$ Thanks for the answer - does this mean that you cannot get the control points without t? $\endgroup$
    – Dude
    Aug 11, 2021 at 16:41
  • $\begingroup$ The 4 points with which you apply the De Casteljau algorithm are the control points. The De Casteljau algorithm will give you a single point on the curve at parameter 't'. $\endgroup$
    – fang
    Aug 11, 2021 at 18:31

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