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Topic: Surface Fitting Coefficients
Replies: 1   Last Post: Oct 17, 2013 9:53 AM

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Torsten Hennig

Posts: 2,419
Registered: 12/6/04
Re: Surface Fitting Coefficients
Posted: Oct 17, 2013 9:53 AM
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> Hi Everyone,
>
> I'm doing surface fitting using MATLAB. It was done
> using fit with the 'poly22' option. The equation of
> the surface is shown below:
>
> zVal = p00 + p10 .* x + p01 .* y + p20 .* x.^2 + p11
> .* x .* y + p02 .* y.^2;
>
> I would like to know how the coefficients
> p00,p10,p01,p20,p11,p02 are derived or calculated.
> Even if its a simple surface fitting algorithm that
> shows how to derive the coefficients, that will be
> very helpful as well.
>
> Thank you.


If (x(i),y(j),zval(i,j)) are your measurement points, the coefficients are determined by minimizing the function
F(p00,p10,p01,p20,p11,p02) = sum_i sum_j (zVal(i,j)-(p00 + p10*x(i) + p01*y(j) + p20*x(i)^2 + p11*x(i)*y(j) + p02*y(j)^2))^2
with respect to p00,p10,p01,p20,p11,p02.

Best wishes
Torsten.



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