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Distribute different size circles inside a square

Asked by Kian Babanezhad on 17 May 2018 at 17:45
Latest activity Commented on by Stephen Cobeldick on 18 May 2018 at 15:16

Suppose we have circles with 4 different diameter (A:0.1, B:0.2, C=0.3, D=0.4), We want to arrange them in a square (5*5) to reach the maximum area. How many of each circle put in the square? a.A + b.B + c.C + d.D = 25 , actually we want to detect a, b, c ,d and position of them. How can I do it in MATLAB?


What exactly does "reach the maximum area" mean? What is e.g. "a.A"?

we want to cover maximum area inside the square with 4 different circle (rA=0.1, rB=0.2, rC=0.3 and rD=0.4). How many of each kind of circles we need to reach maximum area by these circles? for example we can cover X=24.404 (<25) by 1400 number of A, 400 number of B, 40 number of C and 15 number of D. we want to reach maximum of X. clear?

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1 Answer

Answer by KSSV
on 18 May 2018 at 3:08

R = 0.1;    % RAdius of circle 
S = 5 ;     % side of square 
% Square coordinates 
xs = [0 5 5 0 0] ; ys = [0 0 5 5 0] ;
% Circle coordinates 
th = linspace(0,2*pi) ;
xc = R*cos(th) ; yc = R*sin(th) ;
% form centers of circle inside the square 
x = R:2*R:S-R ; 
y = R:2*R:S-R ;
[X,Y] = meshgrid(x,y) ;
% plot
hold on
plot(xs,ys,'r') ;
for i = 1:size(X,1)
    for j = 1:size(X,2)
title(sprintf('Number of circles = %d',numel(X)))


this code use just one kind of circles, radius of them is 0.1.

Seems to me that this is a field of ongoing research:

If you find a solution, submit a publication.

Best wishes


You said how many of each took a single circle...

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