interp2 from 6x6 map to 500x500 map

I have this matrix which represents a profile of velocity which my model gave as an output:

V =  [55.4710   58.8408   64.2922   64.3100   58.8997   55.4584;...
    31.4855   33.5256   39.2656   39.2657   33.5190   31.4851;...
    32.2817   38.7198   44.8627   44.8602   38.7216   32.2812;...
    32.3167   38.7370   44.8789   44.8765   38.7389   32.3162;...
    31.5531   33.4961   39.2318   39.2320   33.4895   31.5529;...
    55.7294   59.0097   64.4591   64.4769   59.0688   55.7165];

which physically represents nodal values in a mesh, which visualized is :

the coordinates of the vertical and horizontal line forming the mesh are:

N_mesh = 6;

dx = 1*(0:1/N_mesh:1);
dy = 1*(0:1/N_mesh:1);

I want to use the interpolation "interp2" with the "nearest" option, to create a map for example 500x500.

I looked for documentation but can't seem to use the correct things to successfully do what I have in mind.

For example I tried using 'meshgrid', but since the dx has 7 points, and the map has 6 points the image is not centered...

I tried this:

dx = 1*(0:1/(N_mesh-1):1); %defining nodal points
dy = 1*(0:1/(N_mesh-1):1);
[X,Y] = meshgrid(dx,dy);

Xq = linspace(0,1,500); %defining points for the bigger map
Yq = linspace(0,1,500);
[Xq,Yq] = meshgrid(Xq,Yq);

V_500x500 = interp2(X,Y,V,Xq,Yq,"nearest"); %interpolating

figure() %visualizing the result
contourf(V_500x500)
colorbar
title('interp2 output')

But the image is not centered at the extremes...

the problem is that the original dx are dx = 1*(0:1/N_mesh:1); , but for using meshgrid I have to use dx = 1*(0:1/(N_mesh-1):1);

I just wanted the first image I attached being in the bigger map.

Does anybody know how to get the centered image with interp2?

Any help would be greatly appreciated.

Answer 1

[Jan]

Of course, 1*(0:1/N_mesh:1) has N_mesh+1 points.

"But the image is not centered at the extremes..." - What does this mean?

By the way, you can omit meshgrid and work with index vectors directly:

V =  [55.4710   58.8408   64.2922   64.3100   58.8997   55.4584;...
    31.4855   33.5256   39.2656   39.2657   33.5190   31.4851;...
    32.2817   38.7198   44.8627   44.8602   38.7216   32.2812;...
    32.3167   38.7370   44.8789   44.8765   38.7389   32.3162;...
    31.5531   33.4961   39.2318   39.2320   33.4895   31.5529;...
    55.7294   59.0097   64.4591   64.4769   59.0688   55.7165];

vx = 1:6;
wx = linspace(1, 7, 501);
wx = floor(wx(1:end-1));

W = interp2(vx, vx.', V, wx, wx.');

figure;
vy = linspace(0, 1, numel(vx));
imagesc(vy, vy.', V);

figure;
wy = linspace(0, 1, numel(wx));
imagesc(wy, wy, W);

[anto]

OK, yes I needed the matrix which you called W, a "centered" (in the sense of properly rescale the 6x6 map) 500x500 matrix in which I can use it for further analysys. Thanks a lot