How can I find integral of a 3-D mesh field?

For example, there is a mesh field for 2-D data.

I want to find the integration for the mesh graph that consist of the data value. The values are all positive,

How can I find it?

[darova]

Is your dx and dy steps equal? Can you show the surface from the top?

[Han]

I don't know what you say about dx and dy. the surface from the top, different from the above figure, can be shown as follows.

The points on the surface are grid points.

x and y range are [0 5000], respectively.

Answer 1

[Star Strider]

See if using trapz on one or both dimensions of your matrix will do what you want.

Answer 2

[darova]

Volume under the surface can be found as

s = 0;
for i = 1:size(A,1)-1
    for j = 1:size(A,2)-1
        s = s + A(i:i+1,j:j+1);     % sum each rectangle points
    end
end
s = sum(s(:))/4*dx*dy;              % division by 4 - averaging points

See my answer here for more explanations: LINK