meshgrid provides wrong dimensions

Hello,

I am using the meshgrid function to try and make a grid for my surface plots. My x,y, and z arrays are length 102, 42, and 102 respectively. But when I run [X,Y,Z] = meshgrid(x,y,z) the output has the wrong dimensions. X, Y and Z are 42 x 102 x 102 not 102 x 42 x 102. Can someone help me understand what is going wrong with this?

I tried playing around with the order and if I have [X,Y,Z] = meshgrid(y,x,z) it gives the correct output size of 102 x 42 x 102. For now I can run the code using this alternative order but I would like to know why it is making the wrong size.

Thanks

[Stephen23]

That is the correct behavior of meshgrid. You should be using ndgrid instead.

(And learn to navigate to the bottom of the help page, where you will find a list of "See Also" functions. You would have found ndgrid yourself quite simply by scrolling to the bottom of the page)

Answer 1

[Jan]

Why do you assume that the output is "wrong"? It is exactly how defined in the documentation:

 [X,Y,Z] = meshgrid(x,y,z) returns 3-D grid coordinates defined by the
 vectors x, y, and z. The grid represented by X, Y, and Z has size
 length(y)-by-length(x)-by-length(z).

See: doc meshgrid.

Well, length(y)-by-length(x)-by-length(z) sounds strange, I agree. But the function works as advertised. Note: Never trust your expectations, what a function returns, but trust only the documentation. Intuition is fine, but programming languages have been designed by human. ;-)

A similar problem is gradient:

[FX,FY] = gradient(F)

Now FX is along the "horizontal direction", FY the "vertical direction". Sounds okay. But in

[FX,FY,FZ] = gradient(F)

the 1st output concerns the 2nd dimension, the 2nd output the 1st one and the 3rd output the 3rd one. Brrr.

[Steven Lord]

Consider using ndgrid for this type of operation instead. See the Tips section on that page.

[Gabriele Curcio]

but why that "strange" output and not a "normal" one? just for curiosity

[Steven Lord]

I wouldn't call either meshgrid or ndgrid "strange" or "normal". They simply use different conventions for how they arrange their data. See this Answers post for more information.

[Stephen23]

"but why that "strange" output and not a "normal" one? just for curiosity"

The reason is due to humans and the graphics they like to look at: when given a matrix of data, many use-cases interpret the horizontal direction as the horizontal axes... and the vertical direction as the vertical axes. This is most likely what you would expect when you display a matrix as an image (otherwise displaying a matrix of data in the command window would be transposed to how it would look when displayed as an image... ouch!). But consider this: the horizontal axes is mathematically defined as the 2nd matrix dimension, while the vertical axes as the 1st matrix dimension. So humans get the first two dimensions mixed up: they prefer the independent-axes as the X-axes and the dependent-axes as the Y-axes... but note that this means the 2nd and 1st matrix dimensions respectively. Ouch.

In essence it is due to an inconsistency between the mathematical definition of matrices/arrays (i.e. NDGRID) and graphics/image/plotting expectations (i.e. MESHGRID). Note that this is not specific to MATLAB: it applies to all graphics apps/libraries and all mathematical apps/libraries.

You can find some explanations here:

https://blogs.mathworks.com/loren/2007/06/21/indexing-terminology/

https://www.mathworks.com/matlabcentral/answers/402941-do-matlabs-3d-plots-swap-axes

This not just something that MATLAB has to contend with, see the indexing option here:

https://numpy.org/doc/stable/reference/generated/numpy.meshgrid.html

and another blog, apparently written by someone with a graphics background:

https://eli.thegreenplace.net/2014/meshgrids-and-disambiguating-rows-and-columns-from-cartesian-coordinates/

This has been discussed many times before:

https://www.mathworks.com/matlabcentral/answers/521908-why-does-gradient-function-calculate-wrong-dimensions-1-and-2#answer_429332

https://www.mathworks.com/matlabcentral/answers/99720-what-is-the-difference-between-the-ndgrid-and-meshgrid-functions-in-matlab

[Dyuman Joshi]

Nice explaination, @Stephen23!