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I want to genetate two vector X(size=37x1) and Y(size=37x1) of random numbers between

100 to 1900 such that difference between any two numbers of one vector X or Y should be greater than 200.

I have tried generating random number again and again while rejecting if they dont met constraint.

but it make infinte loop.

Actually X and Y are cordinates of turbines. Constraint is no turbine can be in the 200 meter radius of any other turbine. Any idea for doing this very fast? Thanks

Adam Danz
on 26 Sep 2019

Edited: Adam Danz
on 26 Sep 2019

This takes milliseconds.

The main idea is to start off with a set of random coordinates and continually replace coordinates that are too close to another coordinate until either 1) all distances are less than the minimum distance requirement or 2) 100 attempts were made per coordinate.

%Define parameters

nPoints = 37; %number of coordinates

lim = [100,1900]; %bounds of random numbers

minDist = 200; %minimum distance between turbines

% Create random coordinates and continually replace coordinates

% that are too close to another point. Stop when minimum distance

% is satisfied or after making nPoints*100 attempts.

xy = nan(nPoints,2);

c = 0; %Counter

while any(isnan(xy(:))) && c<(nPoints*100)

% Fill NaN values with new random coordinates

xy(isnan(xy)) = rand(1,sum(isnan(xy(:)))) * (lim(2)-lim(1)) + lim(1);

% Identify rows that are too close to another point

[~,isTooClose] = find(triu(squareform(pdist(xy)) < minDist,1));

% Replace too-close coordinates with NaN

xy(isTooClose,:) = NaN;

c = c+1;

end

% Throw error if the loop had to quit and missing values remain

if any(isnan(xy(:)))

error('The while-loop gave up. There are %d coordinates with missing values.',sum(isnan(xy(:,1))))

end

% Display number of attempts

fprintf('%d number of attempts.\n', c)

% Show the minimum distance

distances = squareform(pdist(xy));

fprintf('Min distance = %.2f\n', min(distances(distances~=0)))

% Plot results

figure()

plot(xy(:,1),xy(:,2), 'ks', 'MarkerSize', 10)

grid on

These data in the figure above were produced in <0.08 sec and the minimum distance between coordinates is 205.52.

Siavash Soltanahmadi
on 14 Feb 2021

Is there a way we could generate a second set of random number within the same range specified for the first set of random number, where the numbers in the second set are constrained by a different value to the first constraint?

To clarify, imagine within a same space we aim to obtain 12 coordinates, the minimum separation between 10 random coordinates has to be “2” and the minimum separation between another 2 coordinates (and between these 2 and the first 10 coordinates) has to be “5”.

Thanks,

Sia

Jos (10584)
on 26 Sep 2019

Brute force attempt:

N = 20 ;

xyRange = [100 1900] ;

minimumDistance = 200 ;

attempt_counter = 1 ;

Distances = 0 ;

while any(Distances < minimumDistance) && attempt_counter < 10000

attempt_counter = attempt_counter + 1 ;

Pxy = randi(xyRange, N, 2) ;

Distances = pdist(Pxy) ;

end

if attempt_counter < 1000

plot(Pxy(:,1), Pxy(:,2),'bo') ;

else

disp('No positions found.') ;

end

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