Meshgrid function different order

I have this code:

x = 0:1:5;
y = 0:1:5;
z = 0:1:5;
meshgrid(x, y, z); 
[x_a, y_a, z_a] = meshgrid(x, y, z);
Mesh = [x_a(:), y_a(:), z_a(:)];

Mesh =

0 0 0

0 1 0

... ... ...

0 5 0

1 0 0

1 1 0

... ... ...

1 5 0

2 0 0

2 1 0

... ... ...

0 0 1

0 1 1

... ... ...

But I wish Mesh was:

0 0 0

0 0 1

... ... ...

0 0 5

0 1 0

0 1 1

... ... ...

0 1 5

0 2 0

0 2 1

... ... ...

5 5 0

5 5 1

... ... ...

It seems that, with meshgrid function, x and y change first while z is constant, but what I mean is the opposite, x and y are constant first and z change. Is it possible with meshgrid function?

Answer 1

[Neuropragmatist]

x = 0:1:5;
y = 0:1:5;
z = 0:1:5;
[y_a, z_a, x_a] = meshgrid(y,z,x);
Mesh = [x_a(:),y_a(:),z_a(:)]

Or probably better:

x = 0:1:5;
y = 0:1:5;
z = 0:1:5;
[x_a,y_a,z_a] = meshgrid(x,y,z);
Mesh = sortrows(sortrows([x_a(:),y_a(:),z_a(:)],2),1)

Hope this helps,

M.

[madhan ravi]

Last line can be deduced to:

Mesh = sortrows([x_a(:),y_a(:),z_a(:)],[1,2])

[Neuropragmatist]

Yea, you are right. I played around with this and didn't get the results I expected so I settled on wrapping it. Do you know why the order of the columns is reversed between the two?

[Rafael Luque]

Thank you very much!

Answer 2

[Guillaume]

Personally, I think meshgrid is an abomination as it doesn't really makes its mind what order the dimensions are in. It iterates over the dimensions in the order [2, 1, 3] (and doesn't do more than 3).

ndgrid on the other hand iterates in a logical order, [1, 2, 3, ...] and works for as many dimensions as you want (or your computer can manage).

So, I'd recommend using ndgrid. With either, you can of course swap the order of the input to get them to iterate in the order you want.

[Adam Danz]

+1 meshgrid has caused so much confusion.

[Steven Lord]

meshgrid predates ndgrid, which I believe was only introduced when N-dimensional (N > 2) arrays were introduced to MATLAB in MATLAB 5.0 (December 1996 according to Wikipedia.)

I believe meshgrid was introduced in MATLAB 4.0 (1994) but there appears to be an older function named meshdom that looks very similar in MATLAB 3.5 (1990). I haven't gone any further back than that.

Of course, all those dates predate the start of my tenure at MathWorks by at least a couple years.