accessing indexed values in a 3D array

I have a 3D array of temperature data that looks like this:

Z = rand(3,4,8);

It contains 8 slices of data on a 3x4 grid. For each point in the 3x4 grid I have an index that correspond to a slice the third dimension:

ind = randi(8,[3 4])

How do I create a 3x4 surface of values in Z given by the indices ind? I could do it manually like this:

s(1,1) = Z(1,1,ind(1,1)); 
s(1,2) = Z(1,2,ind(1,2)); 
s(1,3) = Z(1,3,ind(1,3)); 
...
s(3,4) = Z(3,4,ind(3,4));

But my Z matrix is 500x500x100, so doing it manually is out of the question. I'm sure I can avoid a loop here somehow.

Answer 1

[David Young]

[rows, cols] = ndgrid(1:size(Z,1), 1:size(Z,2));
Zindex = sub2ind(size(Z), rows, cols, ind);
s = Z(Zindex);

[Chad Greene]

This is perfect, thank you!

Answer 2

[Walter Roberson]

Zs = size(Z);
S = zeros(Zs(1), Zs(2));
ind_offset = (ind - 1) * Zs(1) * Zs(2) + (1:numel(S));
S(1:numel(S)) = Z(ind_offset);

[Walter Roberson]

I made a mistake in the above. Also after seeing David's perfectly workable answer I would improve mine:

Zs = size(Z);
ind_offset = (ind - 1) * Zs(1) * Zs(2) + reshape(1:Zs(1)*Zs(2),Zs(1),Zs(2));
S = Z(ind_offset);

[Chad Greene]

Thanks Walter!