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#1 2007-08-02 02:19:40

series100
Member
Registered: 2007-08-02
Posts: 2

Determine Bezier control points

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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#2 2007-08-02 19:28:28

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: Determine Bezier control points

The Bézier curve passing through four points is cubic. In this case it’s

where t ∈ [0,1]

Last edited by JaneFairfax (2007-08-02 19:31:10)

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#3 2007-08-03 02:33:45

series100
Member
Registered: 2007-08-02
Posts: 2

Re: Determine Bezier control points

JaneFairfax wrote:

The Bézier curve passing through four points is cubic. In this case it’s

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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#4 2007-08-03 07:05:41

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: Determine Bezier control points

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. smile

NB: The Bézier curve you get this way may not be the curve y = x[sup]1⁄3[/sup].
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