Texture map for a 2D grid

Question

I have a set of points `[x,y]=meshgrid(1:N,1:M)` defined on a regular 2D, `N x M` grid. I have another set of points `[u,v]` that are some deformation of the original grid, i.e `[u,v]=f(x,y)'` (however I do not have the actual `f` that caused the deformation). How can I map a texture to the "deformed" grid defined by `u,v`? i.e., given an image with aspect-ratio `N/M` how can I map it to the deformed grid?

Accepted Answer

I think you are asking to get samples of the original texture at `[u,v]`. You can use interp2.

Let's say that the texture samples are in `z` and you want new samples `z2`. To interpolate the original texture at `[u,v]`, use:

```
z2 = interp2(x,y,z,u,v);
```

On the other hand, if you want to map the "deformed" texture back to a regularly spaced grid `[x2,y2]`, use griddata:

```
[x2,y2] = meshgrid(1:N2,1:M2);
z2 = griddata(u,v,z,x2,y2);
```

Update:

Here's some example code showing how to do this with real data. Using normalized coordinates makes it easier.

```
% get texture data
load penny
z = P;

% define original grid based on image size
[m,n] = size(z);
[a,b] = meshgrid(linspace(0,1,n), linspace(0,1,m));

% define new, differently sized grid
m2 = 256;
n2 = 256;
[x,y] = meshgrid(linspace(0,1,n2), linspace(0,1,m2));

% define deformed grid
u = sqrt(x);
v = y.^2;

% sample the texture on the deformed grid
z2 = interp2(a,b,z,u,v);

% plot original and deformed texture
figure
subplot(2,1,1)
surface(a,b,z,'EdgeColor','none')
axis ij image off
colormap gray
title('original')
subplot(2,1,2)
surface(x,y,z2,'EdgeColor','none')
axis ij image off
colormap gray
title('deformed')
```

And this is the result:

Texture map for a 2D grid

Solution

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