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

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

Thank you in advance :)

[Dyuman Joshi]

Can you attach the data of the arrays - x, y and z? Use the paperclip button to do so.

"this didnt work."

I assume you did not get the intended result?

Also, note that griddata performs interpolation, and not integration.

[Jakob Aberhan]

Hey,

thank you for your reply.

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]

My problem is I dont know how to interpolate correctly and how to integrate then over the x,y-Mesh with Data in it.

Answer 1

[KSSV]

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

[Torsten]

Surface integrals are more complicated to handle as to just take "trapz".

[Jakob Aberhan]

Hello,

so I have a unstructured data. Your code is working but the command tri = dt.ConnectivityList matlab gives me an the error: Unable to resolve the name 'dt.ConnectivityList'.

What does this command aims to do ?

And can you help me how to integrate now the Z over the X,Y-surface ?

Thanks a lot

[KSSV]

Need not to use that line. You may remove it. Edited the code.

[Jakob Aberhan]

Ok so I could solve my problem. Thanks a lot, you really helped me with your answer.