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