CODEWITHSUNDEEP
matlabgrid
phdstudent
phdstudent

Reputation: 1144

4 Dimensional Meshgrid - matlab

I want to create a 4 dimensional meshgrid. I know I need to use the ngrid function. However, the output of meshgrid and ngrid is not exactly the same unless one permutes dimensions.

To illustrate, a three dimensional meshgrid seems to be equivalent to a three dimensional ngrid if the following permutations are done:

[X_ndgrid,Y_ndgrid,Z_ndgrid] = ndgrid(1:3,4:6,7:9)
X_meshgrid = permute(X_ndgrid,[2,1,3]);
Y_meshgrid = permute(Y_ndgrid,[2,1,3]);
Z_meshgrid = permute(Z_ndgrid,[2,1,3]);
sum(sum(sum(X == X_meshgrid))) == 27
sum(sum(sum(Y == Y_meshgrid))) == 27
sum(sum(sum(Z == Z_meshgrid))) == 27

I was wondering what are the right permutations for a 4-D meshgrid. 

[X_ndgrid,Y_ndgrid,Z_ndgrid, K_ndgrid] = ndgrid(1:3,4:6,7:9,10:12 )

Edit: EBH, thanks for your answer below. Just one more quick question. If the endgoal is to create a grid in order to use interpn, what would be the difference between creating a grid with meshgrid or with ndgrid (assuming a 3 dimensional problem?)

Upvotes: 2

Views: 2055

Answers (1)

EBH
EBH

Reputation: 10440

The difference between meshgrid and ndgrid is that meshgrid order the first input vector by the columns, and the second by the rows, so:

>> [X,Y] = meshgrid(1:3,4:6)
X =
     1     2     3
     1     2     3
     1     2     3
Y =
     4     4     4
     5     5     5
     6     6     6

while ndgrid order them the other way arround, like:

>> [X,Y] = ndgrid(1:3,4:6)
X =
     1     1     1
     2     2     2
     3     3     3
Y =
     4     5     6
     4     5     6
     4     5     6

After the first 2 dimensions, there is no difference between them, so using permute only on the first 2 dimensions should be enough. So for 4 dimensions you just write:

[X_ndgrid,Y_ndgrid,Z_ndgrid,K_ndgrid] = ndgrid(1:3,4:6,7:9,10:12);
[X_meshgrid,Y_meshgrid,Z_meshgrid] = meshgrid(1:3,4:6,7:9);
X_meshgrid_p = permute(X_meshgrid,[2,1,3]);
Y_meshgrid_p = permute(Y_meshgrid,[2,1,3]);
all(X_ndgrid(1:27).' == X_meshgrid_p(:)) % the transpose is only relevant for this comparison, not for the result.
all(Y_ndgrid(1:27).' == Y_meshgrid_p(:)) % the transpose is only relevant for this comparison, not for the result.
all(Z_ndgrid(1:27).' == Z_meshgrid(:)) % the transpose is only relevant for this comparison, not for the result.

and it will return:

ans =
     1
ans =
     1
ans =
     1

If you want to use it as an input for interpn, you should use the ndgrid format.

Upvotes: 2

Related Questions