Non overlapping randomly located circles

Question

I need to generate a fixed number of non-overlapping circles located randomly. I can display circles, in this case 20, located randomly with this piece of code,

  for i =1:20
  x=0 + (5+5)*rand(1)
  y=0 + (5+5)*rand(1)
  r=0.5
  circle3(x,y,r)
  hold on 
  end

however circles overlap and I would like to avoid this. This was achieved by previous users with Mathematica https://mathematica.stackexchange.com/questions/69649/generate-nonoverlapping-random-circles , but I am using MATLAB and I would like to stick to it.

For reproducibility, this is the function, circle3, I am using to draw the circles

function h = circle3(x,y,r)
 d = r*2;
 px = x-r;
 py = y-r;
 h = rectangle('Position',[px py d d],'Curvature',[1,1]);
 daspect([1,1,1])

Thank you.

not the same, but reminds me of this: http://stackoverflow.com/q/7833534/97160 — Amro, Mar 23 '16 at 11:52
I think you can cut up your region using Tiles into Squares, and then fill the circle in there — GameOfThrows, Mar 23 '16 at 12:04

score 2 · Accepted Answer · edited Jun 20 '20 at 09:12

you can save a list of all the previously drawn circles. After randomizing a new circle check that it doesn't intersects the previously drawn circles.

code example:

nCircles = 20;
circles = zeros(nCircles ,2);
r = 0.5;

for i=1:nCircles
    %Flag which holds true whenever a new circle was found
    newCircleFound = false;
    
    %loop iteration which runs until finding a circle which doesnt intersect with previous ones
    while ~newCircleFound
        x = 0 + (5+5)*rand(1);
        y = 0 + (5+5)*rand(1);
        
        %calculates distances from previous drawn circles
        prevCirclesY = circles(1:i-1,1);
        prevCirclesX = circles(1:i-1,2);
        distFromPrevCircles = ((prevCirclesX-x).^2+(prevCirclesY-y).^2).^0.5;
        
        %if the distance is not to small - adds the new circle to the list
        if i==1 || sum(distFromPrevCircles<=2*r)==0
            newCircleFound = true;
            circles(i,:) = [y x];
            circle3(x,y,r)
        end
    
    end
    hold on
end

*notice that if the amount of circles is too big relatively to the range in which the x and y coordinates are drawn from, the loop may run infinitely. in order to avoid it - define this range accordingly (it can be defined as a function of nCircles).

score 2 · Answer 2 · answered Mar 23 '16 at 12:08

If you're happy with brute-forcing, consider this solution:

N = 60;                        % number of circles
r = 0.5;                       % radius
newpt = @() rand([1,2]) * 10;  % function to generate a new candidate point

xy = newpt();  % matrix to store XY coordinates
fails = 0;     % to avoid looping forever
while size(xy,1) < N
    % generate new point and test distance
    pt = newpt();
    if all(pdist2(xy, pt) > 2*r)
        xy = [xy; pt];  % add it
        fails = 0;      % reset failure counter
    else
        % increase failure counter,
        fails = fails + 1;
        % give up if exceeded some threshold
        if fails > 1000
            error('this is taking too long...');
        end
    end
end

% plot
plot(xy(:,1), xy(:,2), 'x'), hold on
for i=1:size(xy,1)
    circle3(xy(i,1), xy(i,2), r);
end
hold off

score 0 · Answer 3 · answered Mar 23 '16 at 17:29

Slightly amended code @drorco to make sure exact number of circles I want are drawn

nCircles = 20;
circles = zeros(nCircles ,2);
r = 0.5;
c=0; 

for i=1:nCircles
%Flag which holds true whenever a new circle was found
newCircleFound = false;

%loop iteration which runs until finding a circle which doesnt intersect with     previous ones
while ~newCircleFound & c<=nCircles
    x = 0 + (5+5)*rand(1);
    y = 0 + (5+5)*rand(1);

    %calculates distances from previous drawn circles
    prevCirclesY = circles(1:i-1,1);
    prevCirclesX = circles(1:i-1,2);
    distFromPrevCircles = ((prevCirclesX-x).^2+(prevCirclesY-y).^2).^0.5;

    %if the distance is not to small - adds the new circle to the list
    if i==1 || sum(distFromPrevCircles<=2*r)==0
        newCircleFound = true;
        c=c+1
        circles(i,:) = [y x];
        circle3(x,y,r)
    end

end
hold on

end

score 0 · Answer 4 · answered Jul 02 '18 at 10:56

Although this is an old post, and because I faced the same problem before I would like to share my solution, which uses anonymous functions: https://github.com/davidnsousa/mcsd/blob/master/mcsd/cells.m . This code allows to create 1, 2 or 3-D cell environments from user-defined cell radii distributions. The purpose was to create a complex environment for monte-carlo simulations of diffusion in biological tissues: https://www.mathworks.com/matlabcentral/fileexchange/67903-davidnsousa-mcsd

A simpler but less flexible version of this code would be the simple case of a 2-D environment. The following creates a space distribution of N randomly positioned and non-overlapping circles with radius R and with minimum distance D from other cells. All packed in a square region of length S.

function C = cells(N, R, D, S)
  C = @(x, y, r) 0;
  for n=1:N
    o = randi(S-R,1,2);
    while C(o(1),o(2),2 * R + D) ~= 0
      o = randi(S-R,1,2);
    end
    f = @(x, y) sqrt ((x - o(1)) ^ 2 + (y - o(2)) ^ 2);
    c = @(x, y, r) f(x, y) .* (f(x, y) < r);
    C = @(x, y, r) + C(x, y, r) + c(x, y, r);
  end
  C = @(x, y) + C(x, y, R);
end

where the return C is the combined anonymous functions of all circles. Although it is a brute force solution it is fast and elegant, I believe.

Non overlapping randomly located circles

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