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.
