3D Visualization of Items Arrangement

How do I get the 3D visualization of items in the bin from this algorithm?

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% Copyright (c) 2015, Yarpiz (www.yarpiz.com)
% All rights reserved. Please read the "license.txt" for license terms.
%
% Project Code: YPAP105
% Project Title: Solving Bin Packing Problem using PSO, FA and IWO
% Publisher: Yarpiz (www.yarpiz.com)
% 
% Developer: S. Mostapha Kalami Heris (Member of Yarpiz Team)
% 
% Contact Info: [e-mail], [e-mail]
%

clc;
clear;
close all;

%% Problem Definition

model = CreateModel();  % Create Bin Packing Model

CostFunction = @(x) BinPackingCost(x, model);  % Objective Function

nVar = 2*model.n-1;     % Number of Decision Variables
VarSize = [1 nVar];     % Decision Variables Matrix Size

VarMin = 0;     % Lower Bound of Decision Variables
VarMax = 1;     % Upper Bound of Decision Variables


%% PSO Parameters

MaxIt=50;      % Maximum Number of Iterations

nPop=20;        % Population Size (Swarm Size)

% PSO Parameters
w=1;            % Inertia Weight
wdamp=0.99;     % Inertia Weight Damping Ratio
c1=1.5;         % Personal Learning Coefficient
c2=2.0;         % Global Learning Coefficient

% If you would like to use Constriction Coefficients for PSO,
% uncomment the following block and comment the above set of parameters.

% % Constriction Coefficients
% phi1=2.05;
% phi2=2.05;
% phi=phi1+phi2;
% chi=2/(phi-2+sqrt(phi^2-4*phi));
% w=chi;          % Inertia Weight
% wdamp=1;        % Inertia Weight Damping Ratio
% c1=chi*phi1;    % Personal Learning Coefficient
% c2=chi*phi2;    % Global Learning Coefficient

% Velocity Limits
VelMax=0.1*(VarMax-VarMin);
VelMin=-VelMax;

nParticleMutation = 2;      % Number of Mutations Performed on Each Particle
nGlobalBestMutation = 5;    % Number of Mutations Performed on Global Best

%% Initialization

empty_particle.Position=[];
empty_particle.Cost=[];
empty_particle.Sol=[];
empty_particle.Velocity=[];
empty_particle.Best.Position=[];
empty_particle.Best.Cost=[];
empty_particle.Best.Sol=[];

particle=repmat(empty_particle,nPop,1);

GlobalBest.Cost=inf;

for i=1:nPop
    
    % Initialize Position
    particle(i).Position=unifrnd(VarMin,VarMax,VarSize);
    
    % Initialize Velocity
    particle(i).Velocity=zeros(VarSize);
    
    % Evaluation
    [particle(i).Cost, particle(i).Sol]=CostFunction(particle(i).Position);
    
    % Update Personal Best
    particle(i).Best.Position=particle(i).Position;
    particle(i).Best.Cost=particle(i).Cost;
    particle(i).Best.Sol=particle(i).Sol;
    
    % Update Global Best
    if particle(i).Best.Cost<GlobalBest.Cost
        GlobalBest=particle(i).Best;
    end
    
end

BestCost=zeros(MaxIt,1);

%% PSO Main Loop

for it=1:MaxIt
    
    for i=1:nPop
        
        % Update Velocity
        particle(i).Velocity = w*particle(i).Velocity ...
            +c1*rand(VarSize).*(particle(i).Best.Position-particle(i).Position) ...
            +c2*rand(VarSize).*(GlobalBest.Position-particle(i).Position);
        
        % Apply Velocity Limits
        particle(i).Velocity = max(particle(i).Velocity,VelMin);
        particle(i).Velocity = min(particle(i).Velocity,VelMax);
        
        % Update Position
        particle(i).Position = particle(i).Position + particle(i).Velocity;
        
        % Velocity Mirror Effect
        IsOutside=(particle(i).Position<VarMin | particle(i).Position>VarMax);
        particle(i).Velocity(IsOutside)=-particle(i).Velocity(IsOutside);
        
        % Apply Position Limits
        particle(i).Position = max(particle(i).Position,VarMin);
        particle(i).Position = min(particle(i).Position,VarMax);
        
        % Evaluation
        [particle(i).Cost, particle(i).Sol] = CostFunction(particle(i).Position);
        
        % Perform Mutation
        for j=1:nParticleMutation
            NewParticle = particle(i);
            NewParticle.Position = Mutate(particle(i).Position);
            [NewParticle.Cost, NewParticle.Sol] = CostFunction(NewParticle.Position);
            if NewParticle.Cost <= particle(i).Cost
                particle(i) = NewParticle;
            end
        end
        
        % Update Personal Best
        if particle(i).Cost<particle(i).Best.Cost
            
            particle(i).Best.Position=particle(i).Position;
            particle(i).Best.Cost=particle(i).Cost;
            particle(i).Best.Sol=particle(i).Sol;
            
            % Update Global Best
            if particle(i).Best.Cost<GlobalBest.Cost
                GlobalBest=particle(i).Best;
            end
            
        end
        
    end
    
    % Perform Mutation on Global Best
    for i=1:nGlobalBestMutation
        NewParticle = GlobalBest;
        NewParticle.Position = Mutate(GlobalBest.Position);
        [NewParticle.Cost, NewParticle.Sol] = CostFunction(NewParticle.Position);
        if NewParticle.Cost <= GlobalBest.Cost
            GlobalBest = NewParticle;
        end
    end
    
    
    BestCost(it)=GlobalBest.Cost;
    
    disp(['Iteration ' num2str(it) ': Best Cost = ' num2str(BestCost(it))]);
    
    w=w*wdamp;
    
end

BestSol = GlobalBest;

%% Results

figure;
plot(BestCost,'LineWidth',2);
xlabel('Iteration');
ylabel('Best Cost');
grid on;

i got this algorithm from https://www.mathworks.com/matlabcentral/fileexchange/53111-bin-packing-problem-using-ga-pso-fa-and-iwo

Answer 1

[Yatharth]

Hi Thulasy,

You can use the "patch" function to draw each item as a 3D box. You'll need to calculate the vertices of each box based on it's position and dimensions.

Initial step to extract item positions and dimensions : You need to have coordinates of bottom-left-corner and dimensions (length , width, height) of each item. This information you'll need to extract from the solution structure.

Here is a basic framework on how to implement the visualization.

Note: that you'll need to adapt this code to fit the structure of your solution.

Code for defining vertices and using patch function

items = [2, 2, 1, 0, 0, 0;
            2, 1, 2, 0, 0, 0;
             1, 2, 2, 0, 0, 0;
             1, 1, 1, 0, 0, 0;
             3, 2, 1, 0, 0, 0;
             2, 2, 2, 0, 0, 0;
             1, 3, 2, 0, 0, 0;
             2, 1, 1, 0, 0, 0;
             1, 2, 1, 0, 0, 0;
             1, 1, 2, 0, 0, 0];
figure;
hold on;
for i = 1:size(items, 1)
    % Extract position and dimensions here I am using items matrix but you
    % will have to extract it from your solution structure.
    l = items(i, 1);
    w = items(i, 2);
    h = items(i, 3);
    x = items(i, 4);
    y = items(i, 5);
    z = items(i, 6);
    
    % Define vertices of the 3D box
    vertices = [x, y, z; 
                x+l, y, z; 
                x+l, y+w, z; 
                x, y+w, z; 
                x, y, z+h; 
                x+l, y, z+h; 
                x+l, y+w, z+h; 
                x, y+w, z+h];
    
    % Define faces of the box
    faces = [1, 2, 3, 4; % Bottom
             5, 6, 7, 8; % Top
             1, 2, 6, 5; % Side 1
             2, 3, 7, 6; % Side 2
             3, 4, 8, 7; % Side 3
             4, 1, 5, 8];% Side 4
    
    % Plot the box
    patch('Vertices', vertices, 'Faces', faces, 'FaceColor', rand(1,3), 'EdgeColor', 'k', 'FaceAlpha', 0.5);
end

xlabel('X');
ylabel('Y');
zlabel('Z');
title('3D Visualization of Bin Packing');
axis equal;
grid on;
view(3); % Set the view to 3D
hold off;

Here is the documentation for the patch function : https://www.mathworks.com/help/matlab/ref/patch.html#:~:text=example-,patch(%27Faces%27%2CF%2C%27Vertices%27%2CV),-creates%20one%20or

[Thulasy Chandran]

if i want to plot the bounding box according to the box arrangement, how do i do that?

For example, something like this?

[Yatharth]

Hi @Thulasy Chandran,

You can plot the bounding box using this custom function

function plotBoxes(boxPosition, boxSize)
    % figure;
    hold on;
    axis equal;
    xlabel('X');
    ylabel('Y');
    zlabel('Z');
    view(3); % Set the view to 3D
    
    numBoxes = size(boxPosition, 2);
    
    for i = 1:numBoxes
        pos = boxPosition(:, i);
        sz = boxSize(:, i);
        
        % Calculate the vertices of the box
        vertices = [pos(1), pos(2), pos(3); 
                    pos(1) + sz(1), pos(2), pos(3);
                    pos(1) + sz(1), pos(2) + sz(2), pos(3);
                    pos(1), pos(2) + sz(2), pos(3);
                    pos(1), pos(2), pos(3) + sz(3);
                    pos(1) + sz(1), pos(2), pos(3) + sz(3);
                    pos(1) + sz(1), pos(2) + sz(2), pos(3) + sz(3);
                    pos(1), pos(2) + sz(2), pos(3) + sz(3)];
                
        % Define the faces of the box
        faces = [1, 2, 3, 4; % bottom
                 5, 6, 7, 8; % top
                 1, 2, 6, 5; % front
                 2, 3, 7, 6; % right
                 3, 4, 8, 7; % back
                 4, 1, 5, 8]; % left
                 
        % Plot the box
        patch('Vertices', vertices, 'Faces', faces, 'FaceColor', 'none', 'EdgeColor', 'r');
    end
    
    hold off;
end

Here is how you can use this function at the end of your code.

clear;
items = [2, 2, 1, 0, 0, 0;
            2, 1, 2, 0, 0, 0;
             1, 2, 2, 0, 0, 0;
             1, 1, 1, 0, 0, 0;
             3, 2, 1, 0, 0, 0;
             2, 2, 2, 0, 0, 0;
             1, 3, 2, 0, 0, 0;
             2, 1, 1, 0, 0, 0;
             1, 2, 1, 0, 0, 0;
             1, 1, 2, 0, 0, 0];
figure;
hold on;
for i = 1:size(items, 1)
    % Extract position and dimensions here I am using items matrix but you
    % will have to extract it from your solution structure.
    l = items(i, 1);
    w = items(i, 2);
    h = items(i, 3);
    x = items(i, 4);
    y = items(i, 5);
    z = items(i, 6);
    
    % Define vertices of the 3D box
    vertices = [x, y, z; 
                x+l, y, z; 
                x+l, y+w, z; 
                x, y+w, z; 
                x, y, z+h; 
                x+l, y, z+h; 
                x+l, y+w, z+h; 
                x, y+w, z+h];
    
    % Define faces of the box
    faces = [1, 2, 3, 4; % Bottom
             5, 6, 7, 8; % Top
             1, 2, 6, 5; % Side 1
             2, 3, 7, 6; % Side 2
             3, 4, 8, 7; % Side 3
             4, 1, 5, 8];% Side 4
    
    % Plot the box
    patch('Vertices', vertices, 'Faces', faces, 'FaceColor', rand(1,3), 'EdgeColor', 'k', 'FaceAlpha', 0.5);
end
xlabel('X');
ylabel('Y');
zlabel('Z');
title('3D Visualization of Bin Packing');
axis equal;
grid on;
view(3); % Set the view to 3D

boxPosition = [0, 0, 0; 2, 0, 0; 0, 2, 0]; % 3 boxes positioned at the origin
boxSize = [1, 1, 3; 1, 1, 3; 1, 1, 3]; % All boxes are 1x1x1 cubes

% Plot the boxes
plotBoxes(boxPosition, boxSize); %calling the custom function here

hold off;

[Thulasy Chandran]

i want to plot the boundary box around the arrangment of items where we can calculate the minimum space left. this looks more like the the boundary box plotted at the maximum size of the bin.