How can I get the equation of 3D interpolation?

I'm trying to get the equation of 3D interpolation but i don't know how to do it. ¿How can I get the equation?

Currently I'm getting the values putting F(x,y) in the command window.

x = [470;470;470; 1000; 1000; 1000;];
y = [1;2;3; 1;2;3];
z = [-2.68;-0.98;-0.55;-1.42;0.36;0.8];

scatter3(x,y,z)

F = scatteredInterpolant(x,y,z);

[xq,yq] = meshgrid(470:1000,1:3);


vq1 = F(xq,yq);
plot3(x,y,z,'mo')
hold on
mesh(xq,yq,vq1)
legend('Sample Points','Interpolated Surface','Location','NorthWest')

[Star Strider]

With only 6 data points (triples), what you have is the best you can do.

[Izan Segarra]

I have vectors with more than 6 points (I read data from a file) but I am trying to get it with 6 points and then apply it to a larger number. You know how to do it?

[Matt J]

The equation is a very complicated piecewise linear surface. How would it help you to have an equation? Why isn't

vq=F(xq,yq);

sufficient to evaluate the surface wherever you want?

[Izan Segarra]

I am making some measurements with differential probes. The results that we are obtaining are generating a lot of error of noise of the electrical installation. Then a study of these results has been made and it is possible to make a compensation to eliminate the noise, but it is necessary to interpolate all the obtained measurements and find an equation for its correction.

I have 4 data vectors:

• Current vector = [1 2 3]
• Impezanze vector = [470 1000]
• Frequency vector = [8 9 10 11 12 15 16]
• Error vector

The error vector contains the error for each impedance at each frequency and for each current, so I need to perform a 4D interpolation and get the equation to correct the measurement error.

I had started with a 3D interpolation and 6 points to understand how to perform the process. Could you help me get the equation?

Answer 1

[Matt J]

I think you want griddedInterpolant instead:

F=griddedInterpolant({current,impedance,frequency}, Error);

Now just use it to evaluate the error at any combination of current, impedance, and frequency of interest,

 error_q=F(current_q,impedance_q,frequency_q);

You do not need to fit an equation to your original data.

Answer 2

[darova]

Try interp2 or fit

[Izan Segarra]

I will try to use fit. Thanks you!