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# Interpolation Understanding

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float linearInterpolate(float p1,float p2,float mu)
{
return(p1*(1-mu) + (p2*mu));
}

My understanding of this would be that, p1 should be meeting p2''s value at a rate of mu, am I correct? If so, then is my method above right?

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Maybe the form
p(mu) = p1 + (p2-p1)*mu
makes more sense to you. You start from p1 and go towards p2. At mu=1 (mu is the parameter ho far you went) you have reached p2. At 0
Note that p(mu) goes from p1 to p2; p1 and p2 remain static.

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So if mu does not reach 0 within the tick I should go about updating p1 manually?

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p1 and p2 are the endpoints. Neither changes. The interpolated value is always somewhere between p1 and p2. When mu is 0, the interpolated value is p1. When mu is 1, the interpolated value is p2. But, the endpoints do not change.

Athiest has written the more intuitive form. Your point, your interpolated value, is p(mu), a function of the parameter mu. It then, is equal to the linear interpolation between p1 and p2.

Your function is correct, and is equivalent to Athiest''s:

p(mu) = p1*(1-mu) + (p2*mu);

is the same as:

p(mu) = p1 + (p2-p1)*mu

which you can verify by doing some simple algebra.

Graham Rhodes
Principal Scientist
Applied Research Associates, Inc.

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I asked somebody from a mathwebsite how a TI83 does square root, and one of the things mentioned was to perform quadratic interpolation between some values...what does this mean exactly? I understand what linear interpolation is, but I don''t know how you would do quadratic interpolation.

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Maybe something like:

p(mu) = p1 + (p2-p1)*mu*mu

where mu is between 0 and 1?

Just a guess

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I think for a n-order interpolation you need n+1 points given.
So for linear (n=1), you interpolate based on 2 points.
For quadratic (n=2), you should have 3 points to interpolate between them. In this case you get a point on the parabola, which these 3 points define.
For cubic ... and so on

I hope it''s clear.

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that makes sense, but I could have sworn that he said ''interpolate between two values''. I''m trying to find the email but im pretty sure i deleted it.

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What I wrote is Lagrange interpolation. This uses n-1 order polynoms for n points.
Check this out:

http://mathworld.wolfram.com/LagrangeInterpolatingPolynomial.html

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Lagrange sux... very unstable, if your data has a minimal noise it screw up everything.
Try cubic spline: http://www.library.cornell.edu/nr/bookcpdf/c3-3.pdf

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