Find n random points with a minimum distance r inside a 2D rectangular box

I would like to generate the (x, y) coordinates of N randomly distributed points within a 2D Square box having 2000 m X 2000m. the points must have a minimum distance of 200m from each other, means a second point should not lies between the area of circle covered by the first point and so on. Any idea for a uniform random distribution?

Answer 1

[John BG]

Hi Jaydeep

just completed a couple functions that may help with your question

1.

download the functions scatter_points7.m and scatter_points_saturate.m

from

http://uk.mathworks.com/matlabcentral/fileexchange/61521-scatter-points-complying-minimal-distance

2.

run this

    [X,Y,Nmax,Dmatrix]=scatter_points7

3.

key in the menu the rectangle size, the amount of points you want and the minimum distance.

4.

scatter_points7 returns:

X Y coordinates of the random points

Nmax the maximum amount of points that would fit in the rectangle if placing them orderly.

Dmatrix the distances between all combinations of points.

5.

Check the minimum distance requirement is met with

    %  test 1
    Ap=20;L=combinator(Ap,2,'c');
    relD2=((X(L(:,2))-X(L(:,1))).^2+(Y(L(:,2))-Y(L(:,1))).^2).^.5
    R0=200;find(relD2<R0)
   =
     Empty matrix: 1-by-0

or

% test 2
Ap=20;L2=combinator(Ap,2);
D2=Dmatrix+NaN*eye(Ap);
 R0=200;D2(D2<R0)
 =
   Empty matrix: 0-by-1

.

'

6.

Now try this

[X,Y,Nmax,Dmatrix]=scatter_points_saturate(2000,2000,200)

.

.

to know the amount of points (below Nmax) actually generated

numel(X)

if you find this answer useful would you please be so kind to mark my answer as Accepted Answer?

To any other reader, please if you find this answer of any help solving your question,

please click on the thumbs-up vote link,

thanks in advance

John BG

<mailto:[e-mail] [e-mail]>

Answer 2

[Doug Hull]

Here is something stupid that just might work.

While NOT_DONE

generate a point
If NOT too close to existing points
  Place point
end

check to see if enough points are placed.
end

Answer 3

[Jan]

See the very similar question https://www.mathworks.com/matlabcentral/answers/322431-randompoints-condition-distance.

function [X, Y, D] = GetPointsRandom(nWant, XWidth, YWidth, MinDist)

X       = zeros(nWant, 1);
Y       = zeros(nWant, 1);
dist_2  = MinDist ^ 2;      % Squared once instead of SQRT each time
iLoop   = 1;                % Security break to yoid infinite loop
nValid  = 0;
while nValid < nWant && iLoop < 1e6
  newX = XWidth * rand;
  newY = YWidth * rand;
  if all(((X(1:nValid) - newX).^2 + (Y(1:nValid) - newY).^2) >= dist_2)
    % Success: The new point does not touch existing points:
    nValid    = nValid + 1;  % Append this point
    X(nValid) = newX;
    Y(nValid) = newY;
  end
  iLoop = iLoop + 1;
end

% Throw an error, if the area is filled too densely:
if nValid < nWant
  error('Cannot find wanted number of points in %d iterations.', iLoop)
end

if nargout > 2
  % D = pdist([X, Y]);   % Faster with statistics toolbox
  D = sqrt(bsxfun(@minus, X, X.') .^ 2 + bsxfun(@minus, Y, Y.') .^ 2);
end
end