Homepage: http://www.math.sc.edu/~meade/ 

>

>

restart;

>	with( plots );

Warning, the name changecoords has been redefined

>

>	AnimatePolarCurve := proc( R, Domain )

>	local FOpt, Frames, Opts, Plist, PP, r, Tlist, X, Xlo, Xhi;

>	(X,Xlo,Xhi) := lhs(Domain),op(1..2,rhs(Domain));

>	r := unapply( R, X );

>	if nargs>2 then Opts := [args[3..-1]] else Opts := [] end if;

>	if has( Opts, frames ) then

>	(FOpt,Opts) := selectremove( has, Opts, frames );

>	Frames := rhs(FOpt[]);

>

else

>	Frames := 10

>

end if;

>	Tlist := Xlo + (Xhi-Xlo)/Frames * i $ i=1..Frames;

>	PP := (r,T,Xlo) -> display( [ polarplot( r(theta), theta=Xlo..T ),

>	plot( [[0,0],[r(T),T]], coords=polar, color=cyan ) ],

>	title=sprintf("theta = %a = %8.4f", T, T) );

>	Plist := [seq( PP(r,T,Xlo), T=Tlist )];

>	display( Plist, insequence=true, Opts[] );

>

end proc:

>

>	R1 := 2+3*sin(theta);

>	R2 := 0+2*cos(theta);

>

>	AnimatePolarCurve( R1, theta=0..2*Pi, frames=20, scaling=constrained );

>

>	AnimatePolarCurve( R2, theta=0..2*Pi, frames=20, scaling=constrained );

>

>

>	A := [ (3-i/10) $ i=0..60 ]:

>	Limacon := (a,b) -> a+b*sin(theta);

>

>	display( [seq( polarplot( Limacon(a,2), theta=0..2*Pi,

>	title=sprintf("r=%a+3sin(theta)", a, b) ), a=A )],

>	insequence=true );

>

>	polarplot( [seq( Limacon(a,2), a=A )], theta=0..2*Pi );

>

>	polarplot( theta*cos(theta), theta=-4*Pi..4*Pi );

>

>	AnimatePolarCurve( theta*cos(theta), theta=-4*Pi..4*Pi, frames=50 );

>

>	polarplot( sqrt(1-sin(theta)^2/2), theta=0..2*Pi );

>

>	polarplot( cos(13*theta/5), theta=0..80*Pi/13 );

>

>	AnimatePolarCurve( cos(13*theta/5), theta=0..5*Pi, frames=20 );

>

>	polarplot( [ sqrt(3)*sin(theta), 1+cos(theta) ], theta=0..2*Pi );

>

>	AnimatePolarCurve( 4*cos(3*theta), theta=0..Pi, scaling=constrained );

>

>	polarplot( 4*cos(3*theta), theta=-Pi/6..Pi/6, scaling=constrained );

>

>