Random deposition of balls in a 2D grayscale image with avoiding the overlap as much as I can

I have a code to generate balls ( one size or different sizes ). the balls have to be deposited in a random way, but at the same time I coud'nt avoid the overlap between the balls. How can I modified this code so I can generate randome packing balls avoiding the balls overlap as much as I can? Here is the code:

% Seed the random number generator for reproducibility

rng(42);

t1 = cputime;

Kbn = 1.2; % Lowball number estimate

smallColor = 0; % Four different colors: 0, 0.3, 0.6, 1

imageCut = 2048; % Image size we need, 2048x2048 pixels

BoxSize = ceil(imageCut * 1.2); % Model size, 1.2 times the image size

x_min = 1;

z_min = 1;

x_max = BoxSize;

z_max = BoxSize;

R_small = 90; % Radius of the small ball

ballNum = ceil((x_max/R_small/2)^2*Kbn); % Lowball number estimate

ballNum2 = ballNum; % Real ball number needed

% Generate ball positions

list = zeros(ballNum, 3);

for i = 1:ballNum

x_pos = x_min + (x_max - x_min) * rand; % Random x position within the container boundaries

z_pos = z_min + (z_max - z_min) * rand; % Random z position within the container boundaries

% Update the list matrix with the calculated x and z positions.

list(i, 1) = x_pos;

list(i, 2) = z_pos;

list(i, 3) = R_small; % Using only one ball size.

end

% Adjust positions to reduce overlaps

minSeparation = R_small * 2.3; % Minimum separation between ball centers

list = adjustBallPositions(list, minSeparation);

% Create the image with balls placed randomly

A1 = ones(x_max, z_max); % Create a blank image with all pixels set to 1 (white)

for i = 1:ballNum

for d = z_min:z_max

for t = x_min:x_max

if t > 0 && t <= x_max && d > 0 && d <= z_max && round(sqrt((t - list(i, 1))^2 + (d - list(i, 2))^2)) <= list(i, 3)

if list(i, 3) == R_small

A1(d, t) = smallColor;

end

continue

end

end

end

end

Answer 1

[Manas]

Hello Wurood,

I understand that you want to write a MATLAB program that can generate an image with balls of varying sizes distributed randomly and you are facing trouble preventing the balls from overlapping.

I infer from the code you provided that you are first generating the ball positions and then checking if there are any overlaps. This approach might be more complex to implement. Instead, a simpler approach could be iteratively generating a new ball and adding it to the list only If there are no overlaps in the configuration of the balls in the image at the current iteration.

Here is a sample implementation of the above logic, I am using the same variables as declared by you in the beginning of the shared code.

% Generate ball positions
  
list = zeros(ballNum, 3);
for i = 1:ballNum
    x_pos = x_min + (x_max - x_min) * rand; % Random x position within the container boundaries
    z_pos = z_min + (z_max - z_min) * rand; % Random z position within the container boundaries
  
    % Check for overlap with balls at the current iteration
    overlap = true;
    while overlap
        overlap = false;
          for j = 1:i-1
            distance = sqrt((x_pos - list(j, 1))^2 + (z_pos - list(j, 2))^2);
              if distance < (R_small + list(j, 3)) * minSeparation
                overlap = true;
                x_pos = x_min + (x_max - x_min) * rand; % Generate new x position
                z_pos = z_min + (z_max - z_min) * rand; % Generate new z position
                break;
            end
        end
    end
  
    % Update the list matrix with the calculated x and z positions.
    list(i, 1) = x_pos;
    list(i, 2) = z_pos;
    list(i, 3) = R_small; % Using only one ball size.
end

Other approaches to consider are the “Packing Circles algorithm”“ and “Disk Packing Algorithm”. You can learn more about circle packing from this Wikipedia Page: https://en.wikipedia.org/wiki/Circle_packing

Hope this helps!