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alexchen

Bezier Curves

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Hi guys,

I need to get some helps for two theoretical questions about Bezier curves.

1 Why control points of Bezier get maximum at t = i/n for t is member of [0,1] (theoretical or mathematical answers please)

2 In general the inner Bezier points do not lie on the curve. I need to construct a cubic Bezier curve such that b1 lies on the curve, and the curve should be of actual degree 3

Thanks in advance

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I don't really understand your first question

As for your second question, in general your control points lie in a 2d plane it is unlikely that just by chance they'll lie on a 1d line like the curve.

One way to force an inner control point to lie on the curve is to place it at an end control point.

Another way is to draw a curve such that the line formed from the end control point and the inner control point cuts the curve (finding such a curve is easy). Then move the inner point linearly towards the end control point and by the intermediate value theorem you should be able to find a point where the inner point lies on the curve.

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