> # cross section examples
> # sfb jan 30, 2003
> with(plots);
> # we are going to use the animate command which is not very powerful. Later we will show how to animate by hand.
> f:=x^2-y^2;#f:=x*y; 
> L:=3;
> title1:=cat("3D plot of ",convert(f,string));
> plot3d(f,x=-L..L,y=-L..L,title=title1,style=wireframe,axes=boxed,shading=zhue);
> titlex:=cat("animation of x = c cross sections ",convert(f,string));
> animate(f,y=-L..L,x=-L..L,title=titlex);# plots of f(c,y)
> titley:=cat("animation of y = c cross sections ",convert(f,string));
> animate(f,x=-L..L,y=-L..L,title=titlex);# plots of f(x, c)
> g:=eval(f,{x=r*cos(t),y=r*sin(t)});#convert to polar coordinates
> titlepolar:=cat("polar view of ",convert(f,string));
> #cylinderplot(g,r=0..L,t=0..2*Pi);
> #cylinderplot(g,t=0..2*Pi,r=0..L);
> plot3d([r*cos(t),r*sin(t),g],r=0..L,t=0..2*Pi,title=titlepolar);
> titletheta:=cat("animation of theta = c cross sections ",convert(f,string));
> animate(g,r=-L..L,t=0..2*Pi,title=titletheta);
> #
> # Now with more advanced techniques
> #
> background:=plot3d(f,x=-L..L,y=-L..L,style=wireframe,shading=z,axes=boxed):
> background;
> for i from 1 to 21 do thisx:=-L+(i-1)*L/10: P[i]:=display(background,
> spacecurve([thisx,y,eval(f,{x=thisx})],y=-L..L,thickness=3,color=black)):od:
> display(seq(P[i],i=1..21),insequence=true);
> #
> polarbackground :=plot3d([r*cos(t),r*sin(t),g],r=0..L,t=0..2*Pi,style=wireframe,shading=z,axes=boxed):
> polarbackground;
> for i from 1 to 21 do thist:=(i-1)*2*Pi/20: P[i]:=display(polarbackground,
> spacecurve([r*cos(thist),r*sin(thist),eval(g,{t=thist})],r=0..L,thickness=3,color=black)):od:
> display(seq(P[i],i=1..21),insequence=true);
>