Draw a circle inside a convex hull with its centre at the origin.

I am trying to draw a circle inside a convex hull with its centre at the origin. I have attached the code generating the points and the convex hull. In what way can i generate the incircle with its centre at the origin.

clc;
clear all;

A=[0 0;0 -5; 5 -5; 5 5;0 5;-2 2;-5 -5;5 8;-5 -8;-8 0;8 0]
x_axis=A(:,1)
y_axis=A(:,2)
k=convhull(x_axis,y_axis);
figure;
plot(x_axis(k),y_axis(k),'r-',x_axis,y_axis,'b*');

Answer 1

[Matt J]

Use vert2lcon (Download) to find the inequality constraint matrices representing the polygon

[Aineq,bineq]=vert2lcon(A);

The bineq are actually distances of each of the sides of the polygon from the origin, so the radius of the largest inscribed circle should be

maxRadius = min(bineq);

Answer 2

[KSSV]

clear all;
A=[0 0;0 -5; 5 -5; 5 5;0 5;-2 2;-5 -5;5 8;-5 -8;-8 0;8 0]
x_axis=A(:,1)
y_axis=A(:,2)
k=convhull(x_axis,y_axis);
figure;
hold on
plot(x_axis(k),y_axis(k),'r-',x_axis,y_axis,'b*');
C = [mean(x_axis(k)) mean(y_axis(k))] ;
plot(C(1),C(2),'*r')
% Get diatnces
d1 = pdist2(C,[x_axis(k) y_axis(k)]) ;
th = linspace(0,2*pi,1000) ;
x = C(1)+min(d1)*cos(th) ;
y = C(2)+min(d1)*sin(th) ;


idx = inpolygon(x', y',x_axis(k), y_axis(k)) ;

count = 0 ;
while nnz(idx)~=1000
    count = count+1 ;   
    R = min(d1)-0.5 ;
   idx = inpolygon(x', y',x_axis(k), y_axis(k)) ;
    x = C(1)+R*cos(th) ;
    y = C(2)+R*sin(th) ;
    
end


plot(x,y)

[Hirak Basumatary]

@kssv Sir, but how to make the circle stay inside the convex hull. ?

[KSSV]

Edited the answer..

[Hirak Basumatary]

@kssv: Sir, i think what you have done is if the circle goes outside the convex hull, you have decreased the minimum distance "min(dl)" by 0.5. But, i was trying to solve with incircle touching the convex hull and without decreasing any min length. I am looking at an answer by John D Errico. Here is the link and trying to get the centre of the inscribed circle at the origin. Here's what i have been successful and still trying.

[Hirak Basumatary]

Trying to get a circle inscribed like this. With its centre at the origin. ( drawing edited in paint, not matlab)