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

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Jakob Aberhan 2023-7-18

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评论： Jakob Aberhan 2023-7-21

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 :)

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Jakob Aberhan 2023-7-18

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 2023-7-18

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

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采纳的回答

KSSV 2023-7-19

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此回答的直接链接

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编辑：KSSV 2023-7-19

在 MATLAB Online 中打开

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

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KSSV 2023-7-19

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

Jakob Aberhan 2023-7-21

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

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MATLAB Mathematics Numerical Integration and Differential Equations Numerical Integration and Differentiation

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