align the random number in straight line that will restrict in the box dimension

 N=40;

 phi=0.6;

 % Dimension of the  box

 L=15;

 % Diameter of particles
 d=sqrt(4*phi*L^2/(pi*N));
 a=d/2;
 % Perturbation
 epsilon=[0.0001];
 for run=1:1

    for i=1:N
      % place particle i randomly
      % x position will be randomly from -7.5 to 7.5
       X0in(2*i-1)=L*(rand(1)-1/2);
      % y position will be randomly from -7.5 to 7.5
       X0in(2*i)=L*(rand(1)-1/2);
end 
end

I want to generate 40 different positions in the square box from -7.5 to 7.5 for both x and y direction. Because it has higher area fraction with larger number of position (40), hence it is so hard for Matlab to give me the result without overlapping. I want to generate and put them in a straight line order from -7.5 to 7.5 then move a little bit if they overlap. But I dont know how to put the random number that aligns in the straight line in this box ( dont matter if they overlap or not). Note: I will draw circle for each X-Y position with diameter d.

Any helps would be nice. Thanks

[Walter Roberson]

A straight line along which axis? Are you referring to sort() ?

Question: why are you not using

X0in = L * (rand(2*N) - 1/2);

Answer 1

[Image Analyst]

Phong: Try this code where I compare distances of the point to all other points before I decide whether or not to accept it:

clc;
maxNumberOfParticles = 20;
phi=0.6;
% Dimension of the  box
L=15;
tic;
% Diameter of particles
particleDiameter = sqrt(4*phi*L^2/(pi*maxNumberOfParticles));
particleRadius = particleDiameter / 2;
% Perturbation
epsilon=[0.0001];
numberOfRuns = 1;
p = 1; % Particle counter/index.
for run = 1 : numberOfRuns
  while p <= maxNumberOfParticles % Keep going until we have all the particle.
    % Place particle p randomly
    % x position will be randomly from -7.5 to 7.5
    trialX = L*(rand(1)-1/2);
    % y position will be randomly from -7.5 to 7.5
    trialY = L*(rand(1)-1/2);
    if p > 1
      % Calculate distances from the trial point to all other points.
      distances = sqrt((trialX - x).^2 + (trialY - y).^2);
      % Find the minimum distance to any other particle.
      [minDistance, minIndex] = min(distances);
      % Assign this one if it's not closer to any otehr particle than particleRadius.
      if minDistance > particleRadius
        x(p) = trialX;
        y(p) = trialY;
        % Print out coordinates of the particle that is "Too close"
        % just for fun/informational purposes.
        fprintf('Accepting trial particle #%d located at (%.3f, %.3f)\n',...
          p, trialX, trialY);
        p = p + 1;
      else
        % Print out coordinates of the particle that is "Too close"
        % just for fun/informational purposes.
        fprintf('Skipping trial particle #%d located at (%.3f, %.3f) because it is too close to particle %d at (%.3f, %.3f)\n',...
          p, trialX, trialY, minIndex, x(minIndex), y(minIndex));
      end
    else
      % This is the first particle, so just take it.
      x(p) = trialX;
      y(p) = trialY;
      p = p + 1;
    end
  end
end
toc;

Output in command window:

Accepting trial particle #2 located at (-0.886, 6.843)
Accepting trial particle #3 located at (4.781, 3.424)
Accepting trial particle #4 located at (-4.863, -2.094)
Skipping trial particle #4 located at (-4.668, -7.482) because it is too close to particle 11 at (-4.892, -7.108)
Skipping trial particle #4 located at (-2.754, 2.994) because it is too close to particle 22 at (-3.464, 3.735)
Skipping trial particle #4 located at (1.879, 0.646) because it is too close to particle 31 at (2.195, 0.318)
Accepting trial particle #5 located at (-0.914, -3.189)
Skipping trial particle #5 located at (0.025, 3.923) because it is too close to particle 8 at (-0.074, 3.096)
Accepting trial particle #6 located at (3.936, 1.141)

etc.....

Accepting trial particle #36 located at (-5.493, 2.572)
Skipping trial particle #36 located at (1.065, -4.953) because it is too close to particle 12 at (1.224, -5.758)
Skipping trial particle #36 located at (-5.285, -0.359) because it is too close to particle 6 at (-5.652, 0.066)
Accepting trial particle #37 located at (6.122, 0.783)
Accepting trial particle #38 located at (-7.006, -6.692)
Skipping trial particle #38 located at (4.576, -0.729) because it is too close to particle 20 at (5.196, 0.090)
Accepting trial particle #39 located at (-1.760, 4.345)
Accepting trial particle #40 located at (-2.036, 0.485)
Elapsed time is 0.007953 seconds.

[Phong Pham]

It still has overlapped but I fix it. However. if I want to run numberofparticle=40 then it finishes with x and y coordinate of 39. It missed one particle. Thanks

[Image Analyst]

The line should have said:

while p <= maxNumberOfParticles

I fixed it. I don't know why you say there is still overlap - I don't see how that could be true. Thanks for marking it Accepted.