# How to integrate a vector over a surface of x,y-coordinate vectors

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Jakob Aberhan on 18 Jul 2023
Commented: Jakob Aberhan on 21 Jul 2023
Hello,
I have 3 vectors. One x vector with x-coordinates, one y vector with y-coordinates and a vector z with values to this x,y-coordinates. Now I need to integrate the values of the z vecotor over the x,y-surface.
I tried to first make a 2D-Mesh with
[X,Y] = meshgrid(x,y)
and then resape the vector z on to this mesh with
Z = griddata(x, y, z, X(:,1), Y(1,:));
this didnt work.
Can anyone tell me what I am doing wrong or can tell me how I can integrate one verctor over the x,y-coordinates of vector x and y ?
I am using matlab R2022b
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Jakob Aberhan on 18 Jul 2023
Hey,
My Data is quiet big so I cant attach the original. I have a velocity field. The Data is stored in 3 vectors with same length.
x giving the x-coordinates, y the y-coordinates and z is the magnitude of the velocity at the point (x,y). The spacing bewteen the coordinates is irregular. So now I want to integrate the velocity over x and y. To do so my idea was to create a mesh with [X,Y]=meshgrid(x,y). Then interpolate z on that mesh with Z = griddata(x,y,z,X,Y) . And then integrate over x and y.
Jakob Aberhan on 18 Jul 2023
My problem is I dont know how to interpolate correctly and how to integrate then over the x,y-Mesh with Data in it.

KSSV on 19 Jul 2023
Edited: KSSV on 19 Jul 2023
You need to find out whether your data is structured is unstructured. Depedning on that, you need to proceed.
%%structured
xi = unique(x) ; yi = unique(y) ;
[X,Y] = meshgrid(xi,yi) ;
Z = reshape(z,size(X)) ;
figure
surf(X,Y,Z)
%%unstructured
m = 100 ; n = 100 ;
xi = linspace(min(x),max(x),m) ;
yi = linspace(min(y),max(y),n) ;
[X,Y] = meshgrid(xi,yi) ;
Z = griddata(x,y,z,X,Y) ;
figure
surf(X,Y,Z)
To integrate have have look on trapz
KSSV on 19 Jul 2023
Need not to use that line. You may remove it. Edited the code.
Jakob Aberhan on 21 Jul 2023
Ok so I could solve my problem. Thanks a lot, you really helped me with your answer.

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