Generation of cubic grid

I am trying to generate a cubic grid in Matlab so that I can produce a grid of M x N x Q cubes with M, N and Q being integer numbers. I don't need to plot it but rather to produce a B-Rep of the grid (vertex matrix and faces matrix - with no duplicate internal faces). I have tried two approaches:

Copy and translate points in the X, Y, Z direction, eliminate duplicate points and try to generate the new topology (I have no idea how).
Use the Matlab Neuronal Neural Network toolbox, specifically the gridplot function that produces a 3D grid of points but the faces matrix cannot be generated from this function.

Any suggestions?

Thank you.

Update The vertex matrix contains all 8 points of each cube and the faces matrix all 6 faces of each cube. I can generate that with the following code: clc clear

fac = [1 2 3 4; 
        4 3 5 6; 
        6 7 8 5; 
        1 2 8 7; 
        6 7 1 4; 
        2 3 5 8];      
vert_total = [];
face_total = fac;

for x = 0 : 1
for y = 0 : 1
for z = 0 : 1
  vert = [1 1 0; 
         0 1 0; 
         0 1 1; 
         1 1 1; 
         0 0 1;
         1 0 1; 
         1 0 0;
         0 0 0];
 vert(:,1) = vert(:,1) + x;
 vert(:,2) = vert(:,2) + y;
 vert(:,3) = vert(:,3) + z;
 vert_total = [vert_total; vert];

 face = face_total(end-5:end,:);
 face_total = [face_total; face+8];

end
end
end

The problem with this code is that it contains duplicate vertex and duplicate faces. Eliminating the repeated vertex is pretty straightforward using the unique function, but I don't know how to handle the topology (faces matrix) when I eliminate the repeated points (obviously, some of the faces should be eliminated as well).

Any sugestions with that?

Solution

You can create the 3D grid, and then keep only those at 6 faces. Someone else may point a better way than this.

M = 5; N = 6; Q = 7;
[X, Y, Z] = ndgrid(1:M, 1:N, 1:Q); % 3D
faces = X==1 | X==M | Y==1 | Y==N | Z==1 | Z==Q;
X = X(faces);
Y = Y(faces);
Z = Z(faces);

Now [X Y Z] are coordinates for faces.