How to interpolate with a polynom in 3D?

Hi all, I am working on a project and I need to obtain the polynom for a 3D table. Why? Because my idea is to use that polynom in Excel for calculus since I think it will be faster for iterations rathen than looking for values in a table, specially if the values are not in the table and an interpolation would be needed.

The table is in the images.

I found that with polyfit or polyfitn I could get the coefficients of a polynom. But I don't know how to insert the table in the Z.

Thank you very much,

Agustin.

Answer 1

[Cameron]

Use interp2. Here's an example

x = 0.1:0.1:1; %sample x data
y = transpose(1:10); %sample y data
z = sin(x) - y.^x; %sample z data
interpX = 0.15; %your interpolated x value
interpY = 2.2; %your interpolated y value
interpZ = interp2(x,y,z,interpX,interpY); %interpolated value at that point

[Agustin Garzon]

Thank you Cameron for your answer. I tried, and I can get de z value, but I need the polynom in order to use it in excel.

[Cameron]

Are you looking to get a parametric equation from the values in this table?

[Agustin Garzon]

Exactly, thats what I am looking for

[Torsten]

@Agustin Garzon

Take a look at the example

"Fit a polynomial surface"

under

https://de.mathworks.com/help/curvefit/fit.html

I don't know the quality of the fit you will obtain for your data, but I still would advice you to use 2d-interpolation as suggested.

[Agustin Garzon]

Thank you very much, I will try that.