## Distribute different size circles inside a square

on 17 May 2018
Latest activity Commented on by Stephen Cobeldick

### Stephen Cobeldick (view profile)

on 18 May 2018
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?

Jan

### Jan (view profile)

on 18 May 2018
What exactly does "reach the maximum area" mean? What is e.g. "a.A"?

on 18 May 2018
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?
Stephen Cobeldick

### Stephen Cobeldick (view profile)

on 18 May 2018
@Kian Babanezhad: there is no general solution to this problem. Just because the task is simple does not mean that there is a tractable solution. Read more here:

### KSSV (view profile)

on 18 May 2018

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
figure
hold on
plot(xs,ys,'r') ;
plot(X,Y,'.b')
%
for i = 1:size(X,1)
for j = 1:size(X,2)
plot(X(i,j)+xc,Y(i,j)+yc,'b')
end
end
title(sprintf('Number of circles = %d',numel(X)))

on 18 May 2018
this code use just one kind of circles, radius of them is 0.1.
Torsten

### Torsten (view profile)

on 18 May 2018
Seems to me that this is a field of ongoing research:
https://en.wikipedia.org/wiki/Circle_packing
If you find a solution, submit a publication.
Best wishes
Torsten.
KSSV

### KSSV (view profile)

on 18 May 2018
You said how many of each circle...so took a single circle...