Non overlapping randomly located circles - matlab

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.

Answer 1

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).

Answer 2

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

Answer 3

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

Answer 4

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.