fill the area with random polygons

https://ww2.mathworks.cn/matlabcentral/answers/405186-fill-area-with-random-circles-having-different-diameters

@ Walter Roberson i m trying this way to make polygons packing .generating a random centroid and making a convex polygon and then using scale function i place that polygon at that centroid position .and then generating till the required area percentage condition fullfilled .please guide me for improvement and i want to avoid polyxpoly function i think it make the code slow. 50 percent area is easy but 70 percent takes alot of time ..plus if there is intersection i m reducing the size of the polygon thats again not a good way because i want polygon between two min and max size .

to measure the size of the polygon i m using minboudrect funciton .(attached )

rA=0.5; % 50 percent area

m=1;

N=9;

x=rand; % random centroid x and y

y=rand;

X=rand(N,2);

XX=X(:,1);

XY=X(:,2);

K=convhull(XX,XY);

AB=[XX(K),XY(K)];

polyin = polyshape(AB);

seivesize=[4.75 9.5]; % reuired size of polygon

D=(seivesize(1)+((seivesize(2)-(seivesize(1))).*rand))/100; % random size of polygon

[rx,ry] = minboundrect(AB(:,1),AB(:,2));

side1=sqrt(((rx(1)-rx(2))^2)+(ry(1)-ry(2))^2);

side2=sqrt(((rx(2)-rx(3))^2)+(ry(2)-ry(3))^2);

sizeofpolygons1=min(side1,side2);

FACTOR=D/sizeofpolygons1; % reducing the size of the polygon by factor

poly1 = scale(polyin,FACTOR,[x,y]);

%plot(poly1);

area2=area(poly1);

AC=[poly1.Vertices(:,1),poly1.Vertices(:,2);poly1.Vertices(1,1),poly1.Vertices(1,2)];

A{m}=AC;

rA=rA-area2; Sarea=0;

%m=m+1;

while rA >= area2

chk3=1;

while (chk3)~=0

x=rand;

y=rand;

P=[x,y];

chk2=[];

for i=1:length(A)

AD=A{i};

AD1=polyshape(AD);

chk1=isinterior(AD1,P);

chk2=[chk2,chk1];

end

chk3=any(chk2);

end

N=9;

X=rand(N,2);

XX=X(:,1);

XY=X(:,2);

K=convhull(XX,XY);

AB=[XX(K),XY(K)];

polyin = polyshape(AB);

seivesize=[4.75 9.5];

D=(seivesize(1)+((seivesize(2)-(seivesize(1))).*rand))/100;

[rx,ry] = minboundrect(AB(:,1),AB(:,2));

side1=sqrt(((rx(1)-rx(2))^2)+(ry(1)-ry(2))^2);

side2=sqrt(((rx(2)-rx(3))^2)+(ry(2)-ry(3))^2);

sizeofpolygons1=min(side1,side2);

FACTOR=D/sizeofpolygons1;

poly1 = scale(polyin,FACTOR,[x,y]);

%area1=area(poly1);

AC=[poly1.Vertices(:,1),poly1.Vertices(:,2);poly1.Vertices(1,1),poly1.Vertices(1,2)];

for j=1:length(A)

AF=A{j};

[Cx,Ca] = polyxpoly(AF(:,1), AF(:,2),AC(:,1),AC(:,2));

while ~isempty(Cx)

polyin1 = polyshape(AC);

FACTOR1=.9;

poly1 = scale(polyin1,FACTOR1,[x,y]);

AC=[poly1.Vertices(:,1),poly1.Vertices(:,2);poly1.Vertices(1,1),poly1.Vertices(1,2)];

[Cx,Ca] = polyxpoly(AF(:,1), AF(:,2),AC(:,1),AC(:,2));

end

end

m=m+1;

A{m}=AC;

polyin1 = polyshape(AC);

area2=area( polyin1);

Sarea=Sarea+area2;

rA=rA- area2;

end

axis equal

axis([-0.1 1.1 -0.1 1.1]);

figure(2);

for i =A

plot(i{:}(:,1), i{:}(:,2),'k');

hold on;

end