generating random , non uniform fiber distribution of circle in square

I wanted to generate the square filled with circles of equal radius. Distribution should be random, non uniform and geomtrically periodic(meaning cut out portion of the circles on boundaries of square should be on the opposite side of the square). Though many people posted this question, no answer so far. can someone help me in it.

on esuggestion got to follow the Random sequential expansion(RSE) algorithm.

Answer 1

[Adam Danz]

Using bubblebath() from the file exchange (see another demo here),

figure('Color','w')
ax = axes();
axis off

S.axisHandle = ax;
S.frameSize = [100,100]; % axis size, centered at (0,0)
S.circSize = 2;          % circle radius
S.nSizes = NaN;
S.edgeType = 2;          % Frame should cut off circle edges
S.supressWarning = true;
S.drawFrame = true;      % show the black axis frame

[circData, circHandles] = bubblebath(S);

% View the first 5 rows of circle (x,y) coordinates and radii
circData(1:5,:)
% ans =
%         29.88       -32.97            2
%        13.043      -30.441            2
%        -45.91       1.8186            2
%        33.429       45.709            2
%         35.57      -19.943            2

[Image Analyst]

DIVAKAR, why does your situation require "periodic" where a chopped off circle continues on the opposite side?

Have you checked out "circle packing"? Lots of questions on that.

Your requested distribution is NOT random in the distribution of circle centers unless you allow for overlap.

I never heard of "Random sequential expansion (RSE) algorithm" -- do you have a link with more info. A standard test and accept/reject algorithm is very easy but could be made more efficient and pack more in if you specify certain things, like they're on a rectangular or hex grid with a small random movement of the center allowed.

[DIVAKAR RAJU P V]

I am trying to analyse the composite RVE where we need to maintain periodicity.

the below paper proposed this RSE algorithm. I am having difficulty in following the algorithm.

A new method for generating random fibre distributions for fibre reinforced composites

(10.1016/j.compscitech.2012.12.001)

requirement is circles(r=3.6micro meters) should fall randomly with area fraction of 60% exactly in the square(side=45.12 micro meters)

image is attached for you reference

[DIVAKAR RAJU P V]

Dear Adam Danz,

thanks for the code you posted. is it possible to maintain the periodicity?(chepped circles should fall on other side how it is there in the figure attached above.)

[Adam Danz]

@DIVAKAR RAJU P V download vs 2.3.0 of bubblebath(). This version supports edge wrapping. The section of circles that expand beyond an axis border are wrapped to the other side. If a circle expands beyond two axis borders at a corner, both its x and y components are wrapped. Note that this function relies on random processes and intentionally uses a low-level, unsophisticated algorithm which is different from circle-packing and its wrapping feature may differ from the algorithm in the paper you shared.

Example:

rng('default') % for reproducibility
S = struct(); 
S.frameSize = [30 30];
S.circSize = 4; 
S.nSizes = NaN; 
S.edgeType = 3;  % <-- flag to wrap edges
S.supressWarning = true;

bubblebath(S)

[Adam Danz]

@DIVAKAR RAJU P V Have you tried to new version after I updated it for you and your question?