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dslprog

Bezier curves

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I need to draw a Bezier curve with 4 control points, I have 2 fixed control points, the first one and the last one. I need to to calculate the second and third control point so the curve pass (exactly or approximately) through certain points. How can I do this? Thanks.

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hmm, maybe you can just use other spline, spline that passes control points exactly(so called interpolating spline)?
Seems that you just want to make cubic interpolation (aka cubic spline (check Mathworld site)) by specifying parameters to Besier curve.

As about solution for Besier curve... it's long, and i think there's no simpler way at all. You need to make cubic spline that passes control points exactly or least-square approximates points if there's too many points for given degree, then you have to derive formule for additional control points for Besier curve so Besier curve will have same polynomial coefficients as that interpolating spline.(and will produce exactly same results as cubic spline)
(your Besier is also a cubic polynomial)

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