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Is there a way to determine the control points of a bezier curve that passes through 4 points? The points are (0,0), (1,1), (8,2) and (27,3). From the points we can know the curve is y = (x)^(1/3), but how do we plot in Bezier curves? Also the curves must be C1 continuous. I really appreciate any help. thx in advance
Last edited by series100 (2007-08-02 02:20:07)
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The Bézier curve passing through four points is cubic. In this case its
where t ∈ [0,1]
Last edited by JaneFairfax (2007-08-02 19:31:10)
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The Bézier curve passing through four points is cubic. In this case its
where t ∈ [0,1]
The points in the equation above are the control points. That is not what i wanted. I want the curve to pass through the four points and not using the points as control points.
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Okay, I see.
Then suppose the Bézier curve that passes through the four points is the Bézier curve for (0,0), (a[sub]1[/sub],a[sub]2[/sub]), (b[sub]1[/sub],b[sub]2[/sub]), (27,3). Thus
Now suppose the curve passes through (1,1) when t = 1⁄3 and through (8,2) when t = 2⁄3. (I just take these two values of t for convenience.) Then simply put
which will give you four equations in four unknowns. Solve for a[sub]1[/sub], a[sub]2[/sub], b[sub]1[/sub] and b[sub]2[/sub] then.
NB: The Bézier curve you get this way may not be the curve y = x[sup]1⁄3[/sup].
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