Creating a grid from a 2D scatter plot of vectors

So I have a list of x positions, y positions, x velocity and y velocity, I want to turn this in to 4 grid matrices with (i,j) from each of the 4 matrices corresponding to the values for x,y,u,v from the list above with the x, y values being in order in terms of their physical position. I have tried to just reshape the matrices but this isnt working and tried griddata but as I have two values for the velocity it wont work as v needs to be just a single value, and the velocity values are essentially random, so i can't create a fucntion that defines them over the domain, and if I get the resultant velocity vector this only defines the magnitude and not the direction.

I need to do this so I can do partial differentiation using the finite difference scheme. Does anyone have any suggestions as to how I might do this?

[KSSV]

Attach your data. Along with code you have tried.

[Dhruv G]

Why exactly does v have 2 values?

[Roisin Coveney]

I have values from a velocity field, so the velocity at each point in x and y is defined by the x velocity and the y velocity.

[Dhruv G]

yeah, so that's u and v, each with 1 value...

[Roisin Coveney]

Sorry so I think I was a bit unclear there. I was trying to use this fucntion vq = griddata(x,y,v,xq,yq). where v = f(x,y). When I say my V has two values I mean that the values that I am trying to define along each x and y position are velcoities say, ux and uy, instead of u and v to avoid confusion. In this fucntion though v can only have one value, and I cant define my velocity only in terms of its magnitude as I los the information about the direction of the veloicty vector.

Maybe I should use a different method than griddata, I just need to create 4 matrices where the (i, j) value from each matrix corresponds to eachother in the velcoity field. I just wanted the x and y values in the matrix to corrspond to their positions reative to each other so that I can make a for loop which calculates du/dx, dv/dy etc for each vector using finite difference scheme, I know there are functions to do partial differentiation in matlab but it seems that they are based on differentiatng a function and not discrete values. The velocity values are essentially random as they are velocity vectors obtained using PIV.

Answer 1

[KSSV]

Let x, y, xvel, yvel be your data.

m = 100 ; n = 100;
x = linspace(min(x),max(x),m) ; 
y = linspace(min(y),max(y),n) ; 
[X,Y] = meshgrid(x,y) ; 

u = griddata(x,y,xvel,X,Y) ; 
v = griddata(x,y,yvel,X,Y) ;
quiver(X,Y,u,v)

[Roisin Coveney]

Thank you! Does quiver create a matrix from the list of vectors or is it just a plot? I actually just used meshgrid twice once for the x velocity and once for the y velocity and now I think I have the 4 matrices for FDS.

%Imports vector field
T = readmatrix('VectorField.txt');
%Removes last column of vector as it is not applicable
R = T(:,1:4);
%Removes NaN values
R2 = rmmissing(R);
%seperates each vector column in to x,y, vx, vy
xq = R2(:,1);
yq = R2(:,2);
u1= R2(:,3);
v1= R2(:,4);
spacing = xq(2,1)-xq(1,1);

X = min(xq):spacing:max(xq);
Y = min(yq):spacing:max(yq);
[x,y] = meshgrid(X,Y);

%Creates Meshgrid for x, y and u and v values
vv1 = griddata(xq, yq, u1, x,y );
vv2 = griddata(xq, yq, v1, x,y );

[KSSV]

quiver is just a plot. It takes the data and plots the velocities in arrows.

[Roisin Coveney]

Yes I thought so, thank you!

[KSSV]

Thanks is accepting/ voting the answer. :)

[Roisin Coveney]

Sorry will do that now, my first time asking a question so I didn't know!