randomly sample as many points as possible where each point has a min set distance from one another

So I solved this problem using a for loop which, starting with a random point, finds the next closest point >= some threshold. then uses that next point to do the same thing. It works as you can test with the below code but I was curious to know if anyone knows of some mathmatic truism or formula that can solve this problem for arbitrarily larger sets of points. To be clear I do not NEED to do this with more points, I could find a workaround for more points (e.g. for each point find the distance between it and all of its partners instead of using matrix operations with say 10000X10000 which would run out of memory)

even if you know a term for this or a better way to define what this is it would be helpful i might post on a math forum too! thank for your help!

numPoints = 1000;
poleDistances = round(rand(numPoints, 2)*100);
removePtsCloserThan = 10;

numPoints = size(poleDistances, 1);

x = poleDistances(:, 1);
y = poleDistances(:, 2);

d = sqrt((x(:) - x(:)').^2 + (y(:) - y(:)').^2);


c = size(d, 1);
dIndex = 1:c+1:numel(d);
d(dIndex) = inf;
k = randsample(numPoints, 1);
keepPoints = k;
d(k, :) = nan;
while true
    %     k = find(isnan(diag(d)), 1, 'first');
    pnt1 = d(:, k);
    farEnough = abs(pnt1)>=removePtsCloserThan & abs(pnt1)<inf;
    
    pnt1(~farEnough) = inf;
    [sdfg, k] = nanmin(abs(pnt1));
%     if isinf(sdfg)
%         keyboard
%     end
    d([k; find(~farEnough)], :) = nan;
    if all(isnan(d(:)))
        break
    end
     keepPoints(end+1) = k;
end


figure; hold on

circSize = repmat(removePtsCloserThan*2, length(keepPoints), 1);
pos = [poleDistances(keepPoints, 1)-removePtsCloserThan, poleDistances(keepPoints, 2)-removePtsCloserThan,circSize,circSize,];
for k = 1:length(keepPoints)
r = rectangle('Position',pos(k, :),'Curvature',[1 1])
r.FaceColor = [0 .5 .5];
end
scatter(poleDistances(:, 1), poleDistances(:, 2), 'bo');
scatter(poleDistances(keepPoints , 1), poleDistances(keepPoints , 2), 'filled', 'MarkerFaceColor','r');

%
x = poleDistances(keepPoints, 1);
y = poleDistances(keepPoints, 2);

d = sqrt((x(:) - x(:)').^2 + (y(:) - y(:)').^2);
d(d==0) = nan
min(d(:))

[Image Analyst]

What is the set distance from each other? I just ran your code and it looks like some of the circles are really very very close to each other, not at some minimum distance.

My own code to place random points with some min spacing is attached.

[Phillip Maire]

you can change

removePtsCloserThan = 70;

I just changed it to 10 in the edit to make it more apparent what im talking about. So I want to sample as many points as possible while also making sure those dots are a min distance away from each other

so

numPoints = 1000;

poleDistances = round(rand(numPoints, 2)*100); % this is simulating real position of objects

removePtsCloserThan = 10; % this is the min distance

[Phillip Maire]

shoot I thought I said this the point are data and you have to select points form the data no make up your own.