Current version, [Last EDITED, 01.02.2017 16:52 UTC]
function [X, Y, D] = GetPointsRandom(nWant, XWidth, YWidth, R)
X = zeros(nWant, 1);
Y = zeros(nWant, 1);
dist_2 = R ^ 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 - 0.5);
newY = YWidth * (rand - 0.5);
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
% An error is safer than a warning:
if nValid < nWant
error('Cannot find wanted number of points in %d iterations.', iLoop)
end
% [Edited start] "figure" inserted, 'Parent' used, 'XGrid' inserted:
FigH = figure;
AxesH = axes('XTick', -100:20:100, 'YTick', -100:20:100, ...
'XLim', [-100, 100], 'YLim', [-100, 100], ...
'XGrid', 'on', 'YGrid', 'on', 'NextPlot', 'add', ...
'Parent', FigH);
plot(X, Y, 'b*', 'Parent', AxesH);
% [EDITED 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
Call this e.g. as:
[X, Y, D] = GetPointsRandom(1000, 1e6, 1e6, 6)
The list of coordinates is expanded, when a new random point does not touch any exitsing points.
If you do not have the Statistics Toolbox for pdist, use e.g. http://www.mathworks.com/matlabcentral/fileexchange/15145-distance-matrix.
The suggested method for the distance matrix computes the full matrix, although it is symmetric. For in the number of points is small (< 10000), this is not tragic.
This rejection method works reliably and fast up to a number of about 700 points for a side length of 200 and a diameter of 6. If it fails due to reaching the iteration limit, check if increasing the limit helps. If not, the area is nearly filled up by circles and there will not be a solution for your problem.
