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# Parametric Equations

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What are these and how do they relate to Beizers I would be greatful if someone could provide me with a simple answer. I have read many Beizer tuts but they assume this knowledge and seem complex Thanks Alot ~Steve~

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Let your mind drift back to high school algebra.

Remember functions like y=mx+b, or y=x^2 + 3x - 5? Examine what these functions are. Given any value of x, you can find the corresponding y value. These are non-parametric equations. Parametric equations, in contrast, produce both y and x from a third variable, usually known as t. for instance, this draws a circle:

x(t)=cos(2*pi*t)
y(t)=sin(2*pi*t)

The range of t, for most purposes, is from zero to one.

How do beziers fit into all this? Well, beziers are a prime example of parametric curves.

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What are evaluators and what does the term Domain mean thanks.
If possible could you give me a sample equation for a parametric 2d Beizer curve and explain it.

Thanks Alot for the previous reply it helped alot

~Steve~

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Not sure about domain. But I believe evaluators are simply what calculate the actual coords and do something with it. I may very well be wrong though, I don''t often mess with curves.

A-Tronic Software & Design
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"if you fail in life, you were destined to fail. If you suceed in life, call me."

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The bezier curve is a perfect example of parametric functions. I think the actual function is:

P = C1*t^3 + C2*3t^2*(1 - t) + C3*3t(1 - t)^2 + C4(1 - t)^3

where C1, C2, C3, and C4 are control points, and P is the final point on the bezier curve. By substituting values for t within the range 0 >= t >= 1, you get points along the specific bezier curve moving from C1 to C4.

That''s about as specific as it gets. Check out one of the tutorials on this site. It has a pretty good explanation of bezier curves and bezier patches.

Hope that helps.

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Thanks guys for helping me clear that up. I have been reading about NURBS and Bezier patches in the OpenGL Game Programming book, and it sounded complex maybe I can tackle it easier now.

I know that C1, C2, C3, C4 represent the control points which attract the curve to them like magnets. But what is the value of t used for. I know that it''s in a range of 0 >= t >= 1 but what does it actually define is it the distance between the points or something?

Thanks Alot

~Steve~

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