3D plotting of boxes using coordinates in CSV file

hi,

i need help on how to plot the coordinates stored in csv file in a 3D visual.

input CSV file:

expected visual:

the code im working on which is not giving th eexpected output:

Answer 1

[Voss]

solutionData = [ ...
    4 0 0 0 0 15 0 0 0 20 0 15 20 25 0 0 25 15 0 25 0 20 25 15 20; ...
    2 25 0 0 25 18 0 25 0 12 25 18 12 33 0 0 33 18 0 33 0 12 33 18 12; ...
    3 25 18 0 25 23 0 25 18 14 25 23 14 35 18 0 35 23 0 35 18 14 35 23 14; ...
    5 25 0 12 25 12 12 25 0 30 25 12 30 47 0 12 47 12 12 47 0 30 47 12 30; ...
    1 25 12 12 25 32 12 25 12 22 25 32 22 40 12 12 40 32 12 40 12 22 40 32 22];

coordinates = solutionData(:, 2:end);

N = size(coordinates,1);
colors = [0 1 0; 0 0 1; 1 0 0; 1 1 0; 1 0 1];
colors = repmat(colors,ceil(N/size(colors,1)),1);

figure

F = [1 2 4 3; 5 6 8 7; 1 2 6 5; 4 3 7 8; 2 6 8 4; 1 5 7 3];

for ii = 1:N
    C = reshape(coordinates(ii, :), 3, []).';
    patch( ...
        'Vertices',C, ...
        'Faces',F, ...
        'FaceColor','flat', ...
        'FaceVertexCData',colors(ii,:), ...
        'FaceAlpha',0.5);
end

view(3)

xlabel('X-axis');
ylabel('Y-axis');
zlabel('Z-axis');
title('Visualization of Boxes');
grid on;

[Thulasy Chandran]

is there any way to attach the csv file directly rather than listing the coordinates?

[Voss]

To attach the csv file here, use the paperclip button.

To read the file in your code, use readmatrix, readcell, or readtable.

I only listed the coordinates because I didn't have the file.

[Thulasy Chandran]

i have attached the file here. is it possible to do a bounding box for this?

[Voss]

Yes, you would calculate the coordinates of the bounding box and then plot it like the individual boxes are plotted.

[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?

[Voss]

solutionFile = '0 - GA (20-Dec-2023 06.09.07).csv';
solutionData = readmatrix(solutionFile);

% get the two bounding box corners (min(x),min(y),min(z)) and (max(x),max(y),max(z))
p1 = min(reshape(min(solutionData(:,2:end),[],1),3,[]).',[],1);
p8 = max(reshape(max(solutionData(:,2:end),[],1),3,[]).',[],1);

coordinates = solutionData(:, 2:end);

% append the bounding box coordinates to the end of the coordinates matrix:
p_bb = [p1,p1,p1,p8,p1,p8,p8,p8];
p_bb([5 9 13]) = p8([2 3 1]);
p_bb([10 18 20]) = p1([1 3 2]);
coordinates(end+1,:) = p_bb;

N = size(coordinates,1);
colors = [0 1 0; 0 0 1; 1 0 0; 1 1 0; 1 0 1];
colors = repmat(colors,ceil(N/size(colors,1)),1);
% make the bounding box a special color:
colors(N,:) = [0.8 0.8 0.8];

figure

F = [1 2 4 3; 5 6 8 7; 1 2 6 5; 4 3 7 8; 2 6 8 4; 1 5 7 3];

for ii = 1:N
    C = reshape(coordinates(ii, :), 3, []).';
    patch( ...
        'Vertices',C, ...
        'Faces',F, ...
        'FaceColor','flat', ...
        'FaceVertexCData',colors(ii,:), ...
        'FaceAlpha',0.5);
end

view(3)

xlabel('X-axis');
ylabel('Y-axis');
zlabel('Z-axis');
title('Visualization of Boxes');
grid on;

[Thulasy Chandran]

how do i calculate the volume of the outer container and total boxes volume?

and how to calculate the middle point of container and middle point of the box as the formula below?

distance to outer middle = Ʃ (middle point of container – middle point of box)

[Voss]

Volume is length times width times height, where length, width, and height are found by taking differences of coordinates. Middle point is average of coordinates.

[Thulasy Chandran]

may i know how to point each row by separating x,y and z coordinates to get the average coordinates?

[Voss]

solutionFile = '0 - GA (20-Dec-2023 06.09.07).csv';
T = readtable(solutionFile)

T = 5×25 table
    PresentId    x1    y1    z1    x2    y2    z2    x3    y3    z3    x4    y4    z4    x5    y5    z5    x6    y6    z6    x7    y7    z7    x8    y8    z8
    _________    __    __    __    __    __    __    __    __    __    __    __    __    __    __    __    __    __    __    __    __    __    __    __    __

        4         0     0     0     0    15     0     0     0    20     0    15    20    25     0     0    25    15     0    25     0    20    25    15    20
        2        25     0     0    25    18     0    25     0    12    25    18    12    33     0     0    33    18     0    33     0    12    33    18    12
        3        25    18     0    25    23     0    25    18    14    25    23    14    35    18     0    35    23     0    35    18    14    35    23    14
        5        25     0    12    25    12    12    25     0    30    25    12    30    47     0    12    47    12    12    47     0    30    47    12    30
        1        25    12    12    25    32    12    25    12    22    25    32    22    40    12    12    40    32    12    40    12    22    40    32    22

vars = T.Properties.VariableNames;

x = T{:,startsWith(vars,'x')}

x = 5×8

0 0 0 0 25 25 25 25 25 25 25 25 33 33 33 33 25 25 25 25 35 35 35 35 25 25 25 25 47 47 47 47 25 25 25 25 40 40 40 40

y = T{:,startsWith(vars,'y')}

y = 5×8

0 15 0 15 0 15 0 15 0 18 0 18 0 18 0 18 18 23 18 23 18 23 18 23 0 12 0 12 0 12 0 12 12 32 12 32 12 32 12 32

z = T{:,startsWith(vars,'z')}

z = 5×8

0 0 20 20 0 0 20 20 0 0 12 12 0 0 12 12 0 0 14 14 0 0 14 14 12 12 30 30 12 12 30 30 12 12 22 22 12 12 22 22

avg_x = mean(x,2)

avg_x = 5×1

12.5000 29.0000 30.0000 36.0000 32.5000

avg_y = mean(y,2)

avg_y = 5×1

7.5000 9.0000 20.5000 6.0000 22.0000

avg_z = mean(z,2)

avg_z = 5×1

10 6 7 21 17

[Thulasy Chandran]

can you help me with the calculation of space left and distance to outer middle as well? im finding hard to do it.

[Voss]

What is space left and distance to outer middle?

[Thulasy Chandran]

space left = outer container volume – total boxes volume

distance to outer middle = Ʃ (middle point of container – middle point of box)

[Voss]

solutionFile = '0 - GA (20-Dec-2023 06.09.07).csv';
T = readtable(solutionFile)

T = 5×25 table
    PresentId    x1    y1    z1    x2    y2    z2    x3    y3    z3    x4    y4    z4    x5    y5    z5    x6    y6    z6    x7    y7    z7    x8    y8    z8
    _________    __    __    __    __    __    __    __    __    __    __    __    __    __    __    __    __    __    __    __    __    __    __    __    __

        4         0     0     0     0    15     0     0     0    20     0    15    20    25     0     0    25    15     0    25     0    20    25    15    20
        2        25     0     0    25    18     0    25     0    12    25    18    12    33     0     0    33    18     0    33     0    12    33    18    12
        3        25    18     0    25    23     0    25    18    14    25    23    14    35    18     0    35    23     0    35    18    14    35    23    14
        5        25     0    12    25    12    12    25     0    30    25    12    30    47     0    12    47    12    12    47     0    30    47    12    30
        1        25    12    12    25    32    12    25    12    22    25    32    22    40    12    12    40    32    12    40    12    22    40    32    22

vars = T.Properties.VariableNames;

x = T{:,startsWith(vars,'x')};
y = T{:,startsWith(vars,'y')};
z = T{:,startsWith(vars,'z')};

dx = max(x,[],2)-min(x,[],2);
dy = max(y,[],2)-min(y,[],2);
dz = max(z,[],2)-min(z,[],2);

DX = max(x(:))-min(x(:));
DY = max(y(:))-min(y(:));
DZ = max(z(:))-min(z(:));

v = dx.*dy.*dz;
V = DX*DY*DZ;
space_left = V-sum(v)

space_left = 27440

avg_x = (max(x,[],2)+min(x,[],2))/2;
avg_y = (max(y,[],2)+min(y,[],2))/2;
avg_z = (max(z,[],2)+min(z,[],2))/2;

AVG_X = (max(x(:))+min(x(:)))/2;
AVG_Y = (max(y(:))+min(y(:)))/2;
AVG_Z = (max(z(:))+min(z(:)))/2;

D = [avg_x avg_y avg_z]-[AVG_X AVG_Y AVG_Z];
distance_to_centers = sqrt(sum(D.^2,2))

distance_to_centers = 5×1

14.7733 12.6590 11.2472 17.0953 11.0000

[Voss]

If I have answered all your questions, please Accept This Answer.

[Thulasy Chandran]

hi, i have question regarding the distance to centre.

avg_x avg_y avg_z - is the average coordinates of the points along the x, y, and z axes, respectively?

AVG_X AVG_Y AVG_Z - is the global center in 3D space or the centre of the outer container?

[Voss]

Yes avg_* is the center of each small box and also the average of x, y, z for each box.

Yes AVG_* is the center of the outer box and also the average of x, y, z for the outer box.

[Thulasy Chandran]

for the distance to outer middle, need to find for a box and deduct it with the middle point of the outer container. This need to be done for all 5 boxes and then sum it all in the end.

distance to outer middle = Ʃ (middle point of container – middle point of box)

i tried to simulate the output for first and last generation of genetic algorithm. supposedly, the distance to centers should be lower for last generation based on the space left value but its higher.

First:

space_left =

27440

distance_to_centers =

14.7733

12.6590

11.2472

17.0953

11.0000

Last:

space_left =

24460

distance_to_centers =

19.2354

19.0066

11.6082

12.6293

22.3495

1. based on the code provided, is it taking the middle point of all the boxes?
2. is it possible to display the centre of the outer container and centre of one of the boxes in the visualization plot?

[Voss]

1. My code is there; you can see what it does.

If you want to sum the distances, do this:

sum(distance_to_centers)

2. Yes, add some plot call(s) where you plot the points. I'm gonna let you figure that out.

[Thulasy Chandran]

thank you so much. helped me alot!

[Voss]

You're welcome!

[Thulasy Chandran]

hi, how do we change this according to the datasets?

% append the bounding box coordinates to the end of the coordinates matrix:
p_bb = [p1,p1,p1,p8,p1,p8,p8,p8];
p_bb([5 9 13]) = p8([2 3 1]);
p_bb([10 18 20]) = p1([1 3 2]);
coordinates(end+1,:) = p_bb;

[Voss]

What's wrong with it?

[Thulasy Chandran]

i would like to expand my datasets. i would like to know how can change the boundary box plotting according to it.

dataset 1:

BoxID	containerWidth	containerLength	containerHeight
1	26	34	45
2	28	32	40
3	30	36	44
4	25	35	42
5	32	33	41
6	27	38	46
7	29	39	48
8	31	37	47
9	34	40	43
10	33	31	49

dataset 2:

BoxID	containerWidth	containerLength	containerHeight
1	51	60	70
2	55	62	65
3	53	68	72
4	50	61	66
5	59	64	67
6	57	65	71
7	56	69	74
8	60	66	73
9	54	63	68
10	52	70	75
11	61	67	64
12	58	59	69
13	62	71	63
14	63	72	61
15	64	73	62