How can I draw many circles without overlapping?
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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
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Accepted Answer
michio
on 12 Jan 2018
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.
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More Answers (2)
H Y
on 13 Jan 2018
2 Comments
Manisha Kumari
on 26 Oct 2021
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
MFB
on 20 Apr 2019
@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???
1 Comment
michio
on 22 Apr 2019
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.
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