Re: Getting cartesian values from Bezier curve question
Re: Getting cartesian values from Bezier curve question
- Subject: Re: Getting cartesian values from Bezier curve question
- From: David Blanton <email@hidden>
- Date: Tue, 15 Jun 2004 09:51:58 -0600
On 6/15/04 8:11 AM, "Vince Ackerman" <email@hidden> wrote:
>
Did you get an answer to this? I too need to find this method.
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>
Vince
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>
On Jun 14, 2004, at 16:05, dan donaldson wrote:
>
>
> Hello Wise Ones
>
>
>
> I am considering adding a control to allow users to use a Bezier Path
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> to edit a set of values that change over time. The essentials are a
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> timeline with values determined by keyframes which will be represented
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> by Bezier nodes.
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>
>
> My question is, is there a simple way to derive the y value of a
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> bezier line segment given an x coordinate. Assume that there is no
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> circumstance where more than one y value might exist for a given x
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> value. I don't see anything in the NSBezierPath documentation that
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> indicates that this is supported.
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>
>
> For the purposes I will be putting this to, a close approximation - eg
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> 2% error - would suffice.
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>
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> Anyone?
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>
>
> dan donaldson
Given 4 control points p0,p1,p2,p3 where pi = (xi,yi)
Then the x coordinate for a value of t in [0,1] is
x(t) = Axt^3 + Bxt^2 + Cxt + x0
And the y coordinate is
y(t) = Ayt^3 + Byt^2 + Cyt + y0
Where:
Cx = 3(x1-x0)
Bx = 3(x2-x1)-Cx
Ax = x3-x0-Cx-Bx
Cy, By, Ay are the same form with yi for xi
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