# Get equation of the surface from curve fitting

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Gonçalo am 6 Feb. 2024
Bearbeitet: Walter Roberson am 6 Feb. 2024
Hello,
I have a variable A that is depedent on two other variables N and phi.
I would like to get a mathematical function that describes the surface of the 3D space, so I can, given a N and phi, get a value for A.
From here there's any way to get the surface function?
If not, which other method can I use to get a function that describes the surface (can be without the toolboox)?
Thanks.
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Cris LaPierre am 6 Feb. 2024
Bearbeitet: Cris LaPierre am 6 Feb. 2024
In curve fitting, you need to supply the equation. The fitting is accomplished by adjusting the coefficients of the equation to minimize error. Without the equation, you can't curve fit.
This looks like a response surface model. If there is not already an equation used by others in this space, you might consider looking into adapting the greco, minto, or hierarchy model for your use case.
Dyuman Joshi am 6 Feb. 2024
Bearbeitet: Dyuman Joshi am 6 Feb. 2024
How did you get the surface you showed?
"I would like to get a mathematical function that describes the surface of the 3D space, so I can, given a N and phi, get a value for A."
"If not, which other method can I use to get a function that describes the surface (can be without the toolboox)?"
I can only think of interpolation for this. See scatteredInterpolant.
Other contributers might have a better idea.

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### Antworten (2)

Catalytic am 6 Feb. 2024
I would like to get a mathematical function that describes the surface of the 3D space, so I can, given a N and phi, get a value for A.
Just use interp2 -
A=interp2(NData,phiData, N,phi)
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Sam Chak am 6 Feb. 2024
Please address the previous inquiries in the comments. It will assist others in providing you with the necessary help.
If your objective is to have a surface equation that predicts the points within the given intervals, you can consider fitting the following equation:
Matt J am 6 Feb. 2024
I would like the equation in is mathematical form so that I'm no depended on MatLab
How will you do the mathematical operations needed to evaluate the equation at different (N,phi)? If you'll be doing that with alternative software, the software can probably do interpolation as well. There's no need to go through Matlab at all.

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Joe Vinciguerra am 6 Feb. 2024
Bearbeitet: Walter Roberson am 6 Feb. 2024
To my knowledge you can't extract fit parameters from nonparametric fitting methods such as Lowess ( https://www.mathworks.com/help/curvefit/nonparametric-fitting.html )
If you want to extract the equation, you need to define an equation; instead of using Lowess, try Polynomial or Custom Equation ( https://www.mathworks.com/help/curvefit/fit.html )
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