%ECE 2290_MATLAB
%cardioid/spiral intersection
%B.Mobasseri, 2/18/98

%generate and plot the cardioid and spiral

t=0:pi/180:2*pi-pi/180;
r1=1+cos(t);
r2=t/(2*pi);
polar(t,r1,'r');
hold
polar(t,r2,'b')

%to find out where they meet, find where r1=r2

equal=[r1==r2];

%since we are in discrete space, r1 is never equal to r2

diff=[r1'-r2'];

%diff will never be exactly zero but it has a minimum
%i.e. where r1 comes closests to r2( disregard the sign of
%r1-r2)

[diff_min,position]=min(abs(diff))

%position is the location in the angle array t
%where diff is minimum

%convert to angle

angle=t(position)*180/pi