How can I draw many circles without overlapping?

The following code allows overlapping. How can I draw circles without overlapping?

t = linspace(0,2*pi,100);
figure
cx = 100 + (rand(20, 1) .* 1000); %center
cy = 100 + (rand(20, 1) .* 1000); % center
r = 50; % radius
plot(r*sin(t)+cx,r*cos(t)+cy)
y = r*cos(t)+cy
x = r*sin(t)+cx
for i =0:20
  fill(x',y','k')  
  %fill(r*sin(t)+cx,r*cos(t)+cy, 'k')
  r = r+1;    
end
i=i+1;
axis([0,1200,0,1200])
axis square

Answer 1

[michio]

Interesting problem. One way is to keep generating a set of centers until every center is separated by more than the fixed radius from any other centers. Simple logic. Here's an example function that does just that. Inputs are the number of centers required and the radius.

function centers = getCentersWithoutOverlaps(numCenters, radius)
%
% these are parameters you can set
a = 0; 
b = 10;
% 
radius2 = radius^2;
centers = zeros(numCenters,2);
centers(1,:) = a + rand(1,2).*b; % first center 
for ii=2:numCenters
   tmp = a + rand(1,2).*b;
   % keep generating a random number until
   % the new center is separated by "radius" from any other center points.
   while any(sum((centers(1:ii-1,:)-tmp).^2,2) < radius2)
       tmp = a + rand(1,2).*b;
   end 
   % if the condition is met, the new center is added to "centers"
   centers(ii,:) = tmp;
end
%
end

Please save above as a function and the following is the example script that you can try.

t = linspace(0,2*pi,100);
figure
r = 1; % radius
centers = getCentersWithoutOverlaps(10, 2);
cx = centers(:,1);
cy = centers(:,2);
plot(r*sin(t)+cx,r*cos(t)+cy);
y = r*cos(t)+cy;
x = r*sin(t)+cx;
fill(x',y','k')  
axis square

Note that you need to specify reasonable values for numCenters and radius. Otherwise the function will not find the non overlapping set of centers.

Answer 2

[H Y]

Amazing! Thank you for answering my question. On this script, where can I set the definition of the field?

axis([0,1200,0,1200])

[michio]

I think after the fill function would work out just fine?

[Manisha Kumari]

Hi ,

in the below code when i am putting axis([0,100,0,100]) then the above code is not working fine. could you please resolve this issue.

clc

close all

clear all

t = linspace(0,2*pi,100);

r = 1; % radius

centers = getCentersWithoutOverlaps(10,2);

cx = centers(:,1);

cy = centers(:,2);

plot(r*sin(t)+cx,r*cos(t)+cy);

y = r*cos(t)+cy;

x = r*sin(t)+cx;

%axis([0,100,0,100])

fill(x',y','r')

axis([0,100,0,100])

Thank you

Answer 3

[MFB]

@michio

you put different radius in function calling i.e. radius 2 in the function as input argument and in the script you put r = 1. Can you explain why???

[michio]

the r=1 in the script is just for visualization purpose. It can be any value. If you set r to be smaller than 2, you can draw circles without overlapping.