Visualize a three-dimensional array like cubic lattice using MATLAB

Question

I want to visualize a three-dimensional array just like cubic lattice using MATLAB.

I have read How to plot 3D grid (cube) in Matlab, and Simple cubic lattice using three-dimensional array

If element in the array is only 0 and 1, I know how to use a three-dimensional array to draw a simple cubic lattice, the small cube has the same size.

However, Now I have a three-dimensional array like this,

cube(:,:,1) =
 1     0     1
 0     1     1
 2    1     0
cube(:,:,2) =

 0     0     1
 1     5     1
 0     1     0

cube(:,:,3) =

 1     1     1
 0     1     1
 2    0     1

The array cube have value except 0 and 1. I want to visualize the array like cubic lattice, in which cube(:,:,1) denotes the first floor of the cubic lattice,

 cube(:,:,2) denotes the second floor, and 
 cube(:,:,3) the third floor.

The value 0 denotes nothing, while value 1 denotes a small blue cube.

Value greater than 1 denotes sphere, the diameter of sphere varies according to the value. The desired result is something like this:

Visualization of a three-dimensional array, 1 denotes a small green cube，0 denotes nothing，Value greater than 1 denotes white sphere, the diameter of sphere varies according to the value.

To explain my question more clear, show one visualization of two-dimensional array

1 denotes a small black sphere，0 denotes nothing，Value greater than 1 denotes white sphere, the diameter of sphere varies according to the value.

The desired effect drawing

it is Ok, when side length of cube is 1

when set side length as 2, drawCube([ix,iy,iz],2,Royal_Blue). The problem occurs, cubes is overlapping,

Answer 1

Let me show you my attempt. It is based into drawing each cube and circle independently. This will be slow in if A is big.

Result:

The code should be self explanatory.

% Create some data. This piece of code just creates some matrix A with
% some 1s and 0s and inserts a 2 and a 3 to specific positions. Subsitute
% this with your own data matrix.
th=0.2;
A=double(rand(10,10,10)<th);
A(1,1,1)=2;
A(5,5,5)=3;

% A nice color. I just dont like the standard blue so I picked another one.
Royal_Blue=[65 105 225]/255; 

%%%%%%%%%%%%%%%%%%%%%%
%% Draw cubes

% Obtain all the linear indexes (search mathworks for help between  
% subscripts vs linear indices) of the locations where a cube is wanted 
% (A==1)

ind=find(A==1);

% Create a figure
fig=figure();
hold on

% Draw the cubes one by one

for ii=1:length(ind)

    % For each linear index get its subscript (that also 
    % will be x,y,z position)
    [ix,iy,iz]=ind2sub(size(A),ind(ii));

    % Use the drawcube function to draw a single cube in the
    % desired position with the desired size (1) and colour.
    drawCube([ix,iy,iz],1,Royal_Blue);
end

% Nice plotting code. This just makes the drawing nicer. 

camlight left
lighting gouraud
axis equal
axis off
view(-50,25)

%%%%%%%%%%%%%%%
%% Now draw the spheres

% This code is the same as the previous one but I just draw
% spheres instead of cubes.
ind=find(A>1);
% create an sphere
[X,Y,Z] = sphere;
for ii=1:length(ind)
    [ix,iy,iz]=ind2sub(size(A),ind(ii));
    % scale sphere
    Xs=X*A(ix,iy,iz)/2;
    Ys=Y*A(ix,iy,iz)/2;
    Zs=Z*A(ix,iy,iz)/2;
    surf(Xs+ix,Ys+iy,Zs+iz,'edgecolor','none','facecolor',[1 1 1]);

end

% Change the background colour to black
whitebg(fig,'k')
% MAke sure it stays black
set(gcf, 'InvertHardCopy', 'off');

Function drawCube is as follows:

function drawCube( origin, size,color)
% From
% http://www.mathworks.com/matlabcentral/newsreader/view_thread/235581

if nargin<3
    color='b';

end
x=([0 1 1 0 0 0;1 1 0 0 1 1;1 1 0 0 1 1;0 1 1 0 0 0]-0.5)*size+origin(1);
y=([0 0 1 1 0 0;0 1 1 0 0 0;0 1 1 0 1 1;0 0 1 1 1 1]-0.5)*size+origin(2);
z=([0 0 0 0 0 1;0 0 0 0 0 1;1 1 1 1 0 1;1 1 1 1 0 1]-0.5)*size+origin(3);
for i=1:6
    h=patch(x(:,i),y(:,i),z(:,i),color);

    set(h,'edgecolor','none')

end

end