Combining and sorting two meshgrids

Say I have four meshgrids with values that are offset by a constant value along, x, y and both x and y:

% Grid No. 1
x1 = 1:1:10;
y1 = 1:1:10;
[X1,Y1] = meshgrid(x1,y1);

offset = 0.5;

% Grid No. 2
x2 = x1 + offset;
y2 = y1;
[X2,Y2] = meshgrid(x2,y2);

% Grid No. 3
x3 = x1;
y3 = y1 + offset;
[X3,Y3] = meshgrid(x3,y3);

% Grid No. 4
x4 = x1 + offset;
y4 = y1 + offset;
[X4,Y4] = meshgrid(x4,y4);

Corresponding to these four different grids are discrete data-sets that represent say velocity, for example:

v1 = rand(10,10); % Velocity corresponding to x1,y1
v2 = rand(10,10); % Velocity corresponding to x2,y2
v3 = rand(10,10); % Velocity corresponding to x3,y3
v4 = rand(10,10); % Velocity corresponding to x4,y4

How can you combine and sort the four velocity matrces into a single matrix based on a combination of the four x,y grids? I believe in the elementary example I listed above, the results would be a velocity matrix that is 20x20. The velocity values would correspond to position:

x = 1:offset:10;
y = 1:offset:10;
[X,Y] = meshgrid(x,y);

Answer 1

[Akira Agata]

How about the following?

Xall = [X1(:); X2(:); X3(:); X4(:)];
Yall = [Y1(:); Y2(:); Y3(:); Y4(:)];
vall = [v1(:); v2(:); v3(:); v4(:)];

[~, loc] = ismember([X(:), Y(:)], [Xall, Yall], 'rows');

Z = vall(loc);
Z = reshape(Z,size(X));

[Lucas Warwaruk]

It works. Thank you sir!