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')
