Distribute different size circles inside a square

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]

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

[Kian Babanezhad]

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?

[Stephen23]

@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:

https://www.mathworks.com/matlabcentral/answers/390517-rectangle-filled-with-equal-circles

https://www.mathworks.com/matlabcentral/answers/389947-how-can-i-packed-equal-circles-with-raduis-r-inside-a-rectangle-l-x-w

Answer 1

[KSSV]

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)))

[Kian Babanezhad]

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

[Torsten]

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]

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