% ### EXclassicCurves.m ###       11.25.14  (C.Bergevin)
% Motivated by DeVries (1994), this code plots a handful of 'classic' curves
% (simply turn on/off below)

clear
% +++
% three-leaved rose
if 1==0
    a= 1;   N= 200; 
    theta= linspace(0,2*pi,N);  % polar coord.
    r= a*sin(3*theta);
    x= r.*cos(theta); y= r.*sin(theta);  % convert to Cartesian
end
% +++
% spiral of Galileo
if 1==0
    a= 1;   N= 2000; 
    theta= linspace(0,10*pi,N);  % polar coord.
    r= a*theta.^2;
    x= r.*cos(theta); y= r.*sin(theta);  % convert to Cartesian
end
% +++
% Witch of Agnesi
if 1==0
    a= 1;   N= 2000; 
    x= linspace(-20,20,N);  % polar coord.
    y= (8*a^3)./(x.^2+4*a^2);
end
% +++
% Involute of a circle
if 1==0
    a= 1;   N= 200; 
    theta= linspace(0,4*pi,N);  % polar coord.
    x= a*cos(theta)+a*theta.*sin(theta); y= a*sin(theta)-a*theta.*cos(theta);
end
% +++
% Cissoid of Diocles
if 1==0
    a= 1;   N= 100; 
    theta= linspace(0,2*pi,N);  % polar coord.
    r= a*sin(theta).*tan(theta);
    x= r.*cos(theta); y= r.*sin(theta);  % convert to Cartesian
end
% +++
% Cochleoid
if 1==0
    a= 1;   N= 2000; 
    theta= linspace(pi,16*pi,N);  % polar coord.
    r= a*sin(theta)./theta;
    x= r.*cos(theta); y= r.*sin(theta);  % convert to Cartesian
end
% +++
% Folium of Descartes
if 1==0
    a= 1;   N= 2000; 
    theta= linspace(0.8*pi,1.7*pi,N);  % polar coord.
    r= (3*a*sin(theta).*cos(theta))./((cos(theta)).^3 + (sin(theta)).^3);
    x= r.*cos(theta); y= r.*sin(theta);  % convert to Cartesian
end
% +++
% Lemniscate of Bernoulli
if 1==0
    a= 1;   N= 1000; 
    theta= linspace(0,2*pi,N);  % polar coord.
    r= sqrt(a^2*cos(2*theta));
    x= r.*cos(theta); y= r.*sin(theta);  % convert to Cartesian
end
% +++
% Logairthmic spiral
if 1==0
    a= 0.25;   N= 1000; 
    theta= linspace(0,6*pi,N);  % polar coord.
    r= exp(a*theta);
    x= r.*cos(theta); y= r.*sin(theta);  % convert to Cartesian
end
% +++
% Fey's butterfly
if 1==1
    N= 5000; 
    theta= linspace(0,24*pi,N);  % polar coord.
    r= exp(cos(theta))-2*cos(4*theta)+ (sin(theta/12)).^5;
    x= r.*cos(theta+pi/2); y= r.*sin(theta+pi/2);  % convert to Cartesian
end
% +++
figure(1); clf; plot(x,y,'k.','LineWidth',1); xlabel('x'); ylabel('y');