How can I plot a 3D matrix as a cube with different transparent colors for the values?

Hello,

I have a 3D-Matrix consisting only of values 0,1,2 and 3. Is it possible to plot the matrix so it looks like a big, transparent rubic´s cube, where every value gets its own colour? Like imagesc(...) but only in 3D.

Thanks a lot!

[darova]

Did you try scatter3()?

[BananaBandana]

Hey,

But scatter3() uses vectors as inputs, right?

But I have a (n x n x n) Matrix. This wouldn't work I guess, would it?

[darova]

You have only one matrix 3D?

[BananaBandana]

yes, one threedimensional Matrix

[Korosh Agha Mohammad Ghasemi]

Steps:

1. Use patch to create colored and semi-transparent cubes for each element in the 3D matrix.
2. Assign colors based on the values in the matrix.
3. Use transparency to visualize overlapping cubes.

% Example 3D matrix
matrix = randi([0, 3], 5, 5, 5); % Replace with your matrix

% Define colors for each value
colors = [
    1, 1, 1;    % White for 0
    1, 0, 0;    % Red for 1
    0, 1, 0;    % Green for 2
    0, 0, 1     % Blue for 3
];

% Create figure
figure;
hold on;
axis equal;
xlabel('X'); ylabel('Y'); zlabel('Z');
view(3);

% Iterate over matrix
[nx, ny, nz] = size(matrix);
for x = 1:nx
    for y = 1:ny
        for z = 1:nz
            value = matrix(x, y, z);
            if value >= 0 && value <= 3
                % Draw cube with specified color
                drawCube([x-0.5, y-0.5, z-0.5], colors(value+1, :), 0.5);
            end
        end
    end
end

hold off;

% Function to draw a single cube
function drawCube(center, color, alpha)
    % Define cube vertices
    vertices = [
        0 0 0; 1 0 0; 1 1 0; 0 1 0; % Bottom face
        0 0 1; 1 0 1; 1 1 1; 0 1 1  % Top face
    ];
    vertices = vertices - 0.5; % Center around (0,0,0)
    vertices = vertices + center; % Shift to desired center
    
    % Define cube faces
    faces = [
        1 2 6 5; % Bottom
        2 3 7 6; % Right
        3 4 8 7; % Top
        4 1 5 8; % Left
        1 2 3 4; % Front
        5 6 7 8  % Back
    ];
    
    % Draw cube
    patch('Vertices', vertices, 'Faces', faces, ...
          'FaceColor', color, 'FaceAlpha', alpha, ...
          'EdgeColor', 'black');
end

Explanation:

1. Matrix values to colors: Each value (0, 1, 2, 3) is mapped to a specific RGB color.
2. Transparent cubes: The FaceAlpha property in the patch function sets transparency.
3. Cubic layout: The cubes are centered at the (x, y, z) indices of the matrix.

The script creates a 3D plot with a cube for each matrix element, colored based on its value, and transparent enough to see overlapping layers.

Answer 1

[darova]

Since you have matrix of 0,1,2,3 and don't have coordinates you can create them

Assume A - is you matrix (N x N x N)

% (:) - colon operator (make vector from matrix of length N*N*N)
[X,Y,Z] = meshgrid(1:N);
scatter3(X(:),Y(:),Z(:),5,A(:))

[BananaBandana]

Ah, this goes into the right direction. But if I do it like you did it, then I get a marker at the nodes of the matrix. But I wanted to get a big cube consisting of (N x N x N) smaller cubes, where every cube resembles the equivalent matrix value with a color. Similar to this picture

I could not find a way to do it like this.

Thanks!

[darova]

Create one cube using patch() (or fill3()) then copy it using for loop

clear,clc,cla

x1 = [1 1 1 1]'/2;       % right wall
y1 = [1 1 -1 -1]'/2;
z1 = [1 -1 -1 1]'/2;

x2 = [1 1 -1 -1]'/2;     % top wall
y2 = [-1 1 1 -1]'/2;
z2 = [1 1 1 1]'/2;

x3 = x2;                 % bottom wall
y3 = y2;
z3 = -z2;

X = [x1 x2 x3];
Y = [y1 y2 y3];
Z = [z1 z2 z3];

patch(X,Y,Z,'b')
alpha(0.5)
axis equal

I succeded

[BananaBandana]

Thanks!

it worked! But I realized that it takes a lot of time to process for a bigger matrix and therefore is probably is not useable for my case :( I will probably have to think of a different way to visualize it... but thats a different question