How to find an equation to fitting surface?

I have a 100x100 matrix, which contains 10000 different values

Use of imagec instruction drawing as follows

http://ppt.cc/hSzU

I want to find an equation to fitting this surface

How to do?

Thanks~!!

[Matt J]

The surface doesn't look like a plane to me. Are you sure that's how you want the fit to model it. If not, why does your title say that you're fitting a plane?

[BB]

sorry, I change my title as fitting a surface.

Answer 1

[Matt J]

If you have the Curve Fitting Toolbox, you should probably look at CFTOOL.

[BB]

I have been try to use CFTOOL

But I don't know how to put my starting value

Is X data put [1 100], Y data put [1 100], Z data put this matrix?

[Matt J]

No, length(X) must be the same as size(Z,2) and length(Y) must be the same as size(Z,1)

Answer 2

[Valter Zöldhegyi]

Without toolbox: you can use the polyfitn function by John D'Errico: https://www.mathworks.com/matlabcentral/fileexchange/34765-polyfitn

Considering your example:

myIn = NaN(10000, 3);
myIn(:,1) = repmat((0:1:99, 1, 100); %x
myIn(:,2) = repelem(0:1:99, 100); %y
myIn(:,3) = myData(:); % z, myData is the 100x100 matrix you have
myModel = polyfitn([myIn(:,1),myIn(:,2)],myIn(:,3),4); % x and y is the depending variable, z is the independant variable, 4 is the degree of the polynom

In the myModel struct you will have the ModelTerms and the Coefficients fields. ModelTerms matrix defines the term used (eg. a row with [0 0] means a constant; row [1 1] is a x*y term). The coefficients for each term can be found in the Coefficients vector.