MATLAB: I want x,y coordinates which are randomly generated between 1 to 300 ,condition is distance between every coordinate is >20. how to proceed further

homeworkrandom point placement

i=5 ;                          %% no. of random coordinates
    xc = round((1 + (60-1)*rand(i,1)),0);   %% random X- coordinates
    yc = round((1 + (40-1)*rand(i,1)),0);    %% random Y- coordinates
    c = [xc,yc] ;                           %% storing random coordinates in a matrix
    d = pdist(c); %% pdist finds distance between each and every coordinate (all possible distances)
    z= squareform(d);%% it gives a 5*5 matrix containing distances
    v = 500; %%
    n = size(z,1);
    z(1:(n+1):end) = v; %% replacing diagonal elements by some scalar because all diag elements wiil be zero
    index = find(z<20) %% find which index  number in matrix which are less than 20

Best Answer

How about the following?

BWremain = true(300);
% Number of random coordinates
N = 5;
% Selected coordinates are stored these variables
row = nan(N,1);
col = nan(N,1);
for kk = 1:N
  BW = false(300);
  p = find(BWremain);
  p = p(randperm(numel(p),1));
  BW(p) = true;
  BW = bwdist(BW) > 20;
  BWremain = BWremain & BW;
  [row(kk),col(kk)] = ind2sub(size(BWremain),p);
end

Selected coordinates and circles (R = 20) around them looks like this.

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MATLAB: I need x,y coordinates which are randomly generated between 1 to 400 for x coordinates and 1 to 100 for y coordinates, condition is minimum distance between coordinates is 10 and maximum distance is 20, distances should vary from 10 to 20? plz help

change

if min(distances > 8)

    mind = min(distances);
    if mind >= 10 && mind <= 20

MATLAB: For the same answer,,suppose, X ranges from 1 to 500, y ranges from 1 to 200 , Is it possible to find how many such coordinates are possible so that distance from each and every coordinate to other coordinate is > 20

The max number varies depending on what points were actually placed. Using numbers from your question, and trying a million coordinates, we can see that we can place from about 150 to 200 points. See code below:

pointsToPlace = 5000000 ;    % # of random coordinates we need to place - some huge number
% Preallocate points
x = zeros(1, pointsToPlace);
y = zeros(1, pointsToPlace);
loopCounter = 1;
maxIterations = 1000000; % Number of tries before giving up.
numberPlaced = 0; % No points placed yet.
while numberPlaced < pointsToPlace && loopCounter <= maxIterations
	% Get new coordinate
	xProposed = 1 + (500-1)*rand();   %% random X- coordinates
	yProposed = 1 + (200-1)*rand();   %% random Y- coordinates
	if loopCounter == 1
		% First one automatically gets added of course.
		numberPlaced = 1;
		x(numberPlaced) = xProposed;
		y(numberPlaced) = yProposed;
	else
		% Compute distance to all prior coordinates.
		distances = sqrt((xProposed - x(1:numberPlaced)) .^ 2 + (yProposed - y(1:numberPlaced)) .^2);
		% If less than 20, add it
		if min(distances > 20)
			numberPlaced = numberPlaced + 1;
			x(numberPlaced) = xProposed;
			y(numberPlaced) = yProposed;
		end
	end
	loopCounter = loopCounter + 1;
end
% Crop to how many we actually got.
x = x(1:numberPlaced);
y = y(1:numberPlaced);
fprintf('Placed %d points after %d iterations\n', numberPlaced, loopCounter-1);
plot(x, y, 'b*', 'LineWidth', 2, 'MarkerSize', 14);
grid on;
axis equal
xlim([0, 500]);
ylim([0, 200]);
xlabel('X', 'FontSize', 20);
ylabel('Y', 'FontSize', 20);

I'm not aware of an analytical statistical answer, so above we solve it numerically.

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Related Solutions

MATLAB: I need x,y coordinates which are randomly generated between 1 to 400 for x coordinates and 1 to 100 for y coordinates, condition is minimum distance between coordinates is 10 and maximum distance is 20, distances should vary from 10 to 20? plz help

MATLAB: For the same answer,,suppose, X ranges from 1 to 500, y ranges from 1 to 200 , Is it possible to find how many such coordinates are possible so that distance from each and every coordinate to other coordinate is > 20

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