The difference between ndgrid and meshgrid is how they treat the first two dimensions.
size_x = 3;
size_y = 4;
size_z = 2;
mag=5;
U=linspace(-mag,mag,size_x);
V=linspace(-mag,mag,size_y);
W=linspace(-mag,mag,size_z);
X=1:size_x; %256
Y=1:size_y; %256
Z=1:size_z; %75
ndgrid varies things in order (vector one along first dimension, vector 2 along the second dimension, etc):
[u1,v1,w1]=ndgrid(U,V,W);
[x1,y1,z1]=ndgrid(X,Y,Z);
>> x1
x1(:,:,1) =
1 1 1 1
2 2 2 2
3 3 3 3
x1(:,:,2) =
1 1 1 1
2 2 2 2
3 3 3 3
>> y1
y1(:,:,1) =
1 2 3 4
1 2 3 4
1 2 3 4
y1(:,:,2) =
1 2 3 4
1 2 3 4
1 2 3 4
while meshgrid flips the first two dimensions (to sort of match x/y conventions when plotting):
[u2,v2,w2]=meshgrid(U,V,W);
[x2,y2,z2]=meshgrid(X,Y,Z);
>> x2
x2(:,:,1) =
1 2 3
1 2 3
1 2 3
1 2 3
x2(:,:,2) =
1 2 3
1 2 3
1 2 3
1 2 3
>> y2
y2(:,:,1) =
1 1 1
2 2 2
3 3 3
4 4 4
y2(:,:,2) =
1 1 1
2 2 2
3 3 3
4 4 4
Most plotting functions, such as quiver3, will accept either of these, as long as the input matrices all have the same input order. And when dealing with more than two dimensions, I definitely prefer to use ndgrid. However, several of the interpolation functions (namely, griddedInterpolant, which underlies interp3), very annoyingly insist on using the meshgrid-style input only.
You can either use the meshgrid setup (but make sure to keep your input and output variables in the same order!), or use ndgrid for setup and then permute the values when interpolating:
x3 = rand(10,1)*(size_x-1) + 1;
y3 = rand(10,1)*(size_y-1) + 1;
z3 = rand(10,1)*(size_z-1) + 1;
u3 = interp3(permute(x1,[2 1 3]), ...
permute(y1,[2 1 3]), ...
permute(z1,[2 1 3]), ...
permute(u1,[2 1 3]), x3,y3,z3);
v3 = interp3(permute(x1,[2 1 3]), ...
permute(y1,[2 1 3]), ...
permute(z1,[2 1 3]), ...
permute(v1,[2 1 3]), x3,y3,z3);
w3 = interp3(permute(x1,[2 1 3]), ...
permute(y1,[2 1 3]), ...
permute(z1,[2 1 3]), ...
permute(w1,[2 1 3]), x3,y3,z3);
u4 = interp3(x2,y2,z2,u2, x3,y3,z3);
v4 = interp3(x2,y2,z2,v2, x3,y3,z3);
z4 = interp3(x2,y2,z2,w2, x3,y3,z3);
>> isequal(u3,u4)
ans =
1
