hatch overlap region of two circles

I would like to know how can I hatch overlap region of two circles?

Answer 1

[KSSV]

N1 = 100 ; N2 = 50 ;
th = linspace(0,2*pi,N1)' ;
r1 = 1. ; r2 = 1. ;   % radii of circles 
c1 = [0 0] ;          % center of first cirlce 
c2 = [1.5 0] ;        % center of second circle 
a1 = repmat(c1,[N1 1])+[r1*cos(th)  r1*sin(th)] ;
a2 = repmat(c2,[N1 1])+[r2*cos(th)  r2*sin(th)] ;
%
plot(a1(:,1),a1(:,2),'r') ;
hold on
plot(a2(:,1),a2(:,2),'r') ;
axis equal
%%Get points of first circle lying in second circle
in12 = inpolygon(a1(:,1),a1(:,2),a2(:,1),a2(:,2)) ;
P1 = a1(in12,:) ;
%%Get points of second circle lying in first circle
in21 = inpolygon(a2(:,1),a2(:,2),a1(:,1),a1(:,2)) ;
P2 = a2(in21,:) ;
%%form the oval / intersection boundary 
R = [P1 ;P2] ;
idx = convhull(R(:,1),R(:,2)) ;
patch(R(idx,1),R(idx,2),'r')

[sahar]

thank for the useful answer.BTW, can you describe the approach to hatch the overlap of 3 circles with 3 intersection points?