Converting rectangular grids to an array

I'm using ndgrid to create a series of rectangular grids. For example :

nx = [1 2 3];
ny = [4 5 6];
nz = [7 8 9];

 [x_mesh, y_mesh, z_mesh] = ndgrid(nx, ny, nz);

Is there a simple way to convert the coordinates of the rectangular grids to a NxM array (in this case 27x3)? The result should look like this:

[1,4,7;
 1,4,8;
 1,4,9;
 1,5,7;
 1,5,8;
 1,5,9;
 1,6,7;
 1,6,8;
 1,6,9;
 ...
 3,6,7;
 3,6,8;
 3,6,9]

If possible, I'd like to specify the direction in which to compile the coordinates in the array. For example, the above moves along z, then y, then x. It'd be nice if one could specify to move in the order x, then y, then z instead.

Answer 1

[David Goodmanson]

Hi Alex,

The concatenation

m = [x_mesh(:) y_mesh(:) z_mesh(:)]

gives a 27x3 list of all the points, but not in the order you prefer. Doing some permutations on indices works:

xx = permute(x_mesh,[3 2 1]);
zz = permute(z_mesh,[3 2 1]);
m = [xx(:) y_mesh(:) zz(:)]

[Alex]

Thanks David ... ended up with a very similar solution

 order = [1 3 2];
 grid = reshape(permute(cat(4,x_mesh,y_mesh,z_mesh),[order 4]),[],3)

[Stephen23]

Why so pointlessly complex? See my answer to know how simple this really is.

Answer 2

[Stephen23]

All you really need to do is use the correct order of arguments to ndgrid:

>> nx = [1 2 3];
>> ny = [4 5 6];
>> nz = [7 8 9];
>> [z_mesh,y_mesh,x_mesh] = ndgrid(nz,ny,nx);
>> m = [x_mesh(:),y_mesh(:),z_mesh(:)]
m =
     1     4     7
     1     4     8
     1     4     9
     1     5     7
     1     5     8
     1     5     9
     1     6     7
     1     6     8
     1     6     9
     2     4     7
     2     4     8
     2     4     9
     2     5     7
     2     5     8
     2     5     9
     2     6     7
     2     6     8
     2     6     9
     3     4     7
     3     4     8
     3     4     9
     3     5     7
     3     5     8
     3     5     9
     3     6     7
     3     6     8
     3     6     9
>>