% Examples of a 2d curves in polar coordinates:
% USAGE: CUT and PASTE into MATLAB command line. 
figure(1);
clf;
subplot(2,2,1);
q = [0:pi/100:2*pi];
%%%% cardioid r = 6-6sin(q) %%%%% 
r = 6-6.*sin(q);
plot(r.*cos(q),r.*sin(q),'b-');
subplot(2,2,2);
polar(q,6-6.*sin(q),'b-');
%%%% lemnicate r=sqrt(9cos(2q)) %%%%
q = [-pi/2:pi/100:pi/2];
r=sqrt(9.*cos(2.*q));
subplot(2,2,3);
plot(r.*cos(q),r.*sin(q),'r-');
hold;
plot(-r.*cos(q),-r.*sin(q),'r-');
subplot(2,2,4);
polar(q,sqrt(9.*cos(2.*q)),'r-');
hold;
polar(q,-sqrt(9.*cos(2.*q)),'r-');