# Converting rectangular grids to an array

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Alex on 24 Aug 2017
Edited: Stephen23 on 25 Aug 2017
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.

David Goodmanson on 24 Aug 2017
Edited: David Goodmanson on 24 Aug 2017
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(:)]
##### 2 CommentsShowHide 1 older comment
Stephen23 on 24 Aug 2017
Why so pointlessly complex? See my answer to know how simple this really is.

Stephen23 on 24 Aug 2017
Edited: Stephen23 on 25 Aug 2017
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
>>

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