week1.sagews

var('u v w');
f(u,v) = (u^2+v,u*v);
steps=10; hor_init = Graphics(); vert_init = Graphics(); hor_out = Graphics(); vert_out = Graphics();
for t in [0..steps]: 
    hor_init += parametric_plot((u,t/steps),(u,0,1),rgbcolor=hue(t/(2*steps)));
    vert_init += parametric_plot((t/steps,v),(v,0,1),rgbcolor=hue(1/2+t/(2*steps)));
    hor_out += parametric_plot(f(u,t/steps),(u,0,1),rgbcolor=hue(t/(2*steps)));
    vert_out += parametric_plot(f(t/steps,v),(v,0,1),rgbcolor=hue(1/2+t/(2*steps)));

(u, v, w)

#frames=20; hor=Graphics(); vert=Graphics();
#H(u,v,w)=(u^(1+w)+w*v,u^w*v);
#def fimage(w):
#    hor=Graphics();vert=Graphics();
#    for t in [0..steps]:
#        hor += parametric_plot(H(u,t/steps,w),(u,0,1),rgbcolor=hue(t/(2*steps)));
#        vert += parametric_plot(H(t/steps,v,w),(v,0,1),rgbcolor=hue(1/2+t/(2*steps)));
#    return(hor+vert);

#Hmovie = [fimage(w) for w in srange(0,1+1/frames,1/frames)];
#a = animate(Hmovie);

(hor_init+vert_init).show(figsize=[2,2]);
(hor_out+vert_out).show(figsize=[4,4]);

Df(u,v)=(1/2*u+v,3/4*u+1/4*v);
Dhor = Graphics(); Dvert = Graphics();
for t in [0..steps]: 
    Dhor += parametric_plot(Df(u,t/steps),(u,0,1),rgbcolor=hue(t/(2*steps)));
    Dvert += parametric_plot(Df(t/steps,v),(v,0,1),rgbcolor=hue(1/2+t/(2*steps)));

(hor_init+vert_init).show(axes=false,figsize=[2,2]);
(Dhor+Dvert).show(axes=false,figsize=[4,4]);

Dhor = Graphics(); Dvert = Graphics(); hor_init = Graphics(); vert_init = Graphics(); hor_out = Graphics(); vert_out = Graphics();
zoom = 1/32;
for t in [0..steps]:
    hor_init += parametric_plot((u,3/4-zoom+2*zoom*t/steps),(u,1/4-zoom,1/4+zoom),rgbcolor=hue(t/(2*steps)));
    vert_init += parametric_plot((1/4-zoom+2*zoom*t/steps,v),(v,3/4-zoom,3/4+zoom),rgbcolor=hue(1/2+t/(2*steps)));
    hor_out += parametric_plot(f(u,3/4-zoom+2*zoom*t/steps),(u,1/4-zoom,1/4+zoom),rgbcolor=hue(t/(2*steps)));
    vert_out += parametric_plot(f(1/4-zoom+2*zoom*t/steps,v),(v,3/4-zoom,3/4+zoom),rgbcolor=hue(1/2+t/(2*steps)));
    Dhor += parametric_plot(Df(u,3/4-zoom+2*zoom*t/steps),(u,1/4-zoom,1/4+zoom),rgbcolor=hue(t/(2*steps)));
    Dvert += parametric_plot(Df(1/4-zoom+2*zoom*t/steps,v),(v,3/4-zoom,3/4+zoom),rgbcolor=hue(1/2+t/(2*steps)));

(hor_init+vert_init).show(axes=false,figsize=[2,2]);
(hor_out+vert_out).show(axes=false,figsize=[4,4]);
(Dhor+Dvert).show(axes=false,figsize=[4,4]);

g = parametric_plot3d([v*cos(u),v*sin(u),v^2],(u,pi-1,pi+1),(v,0,2),opacity=0.2);
Tg = parametric_plot3d([-v,pi-u,2*v-1],(u,pi-1,pi+1),(v,0,2),color="red",opacity=0.2);
g+Tg

3D rendering not yet implemented

h = plot3d(u^2+v^2,(u,0,2),(v,0,2),opacity=0.2);
Th = plot3d(2*u+2*v-2,(u,0,2),(v,0,2),color="red",opacity=0.2);
h+Th

3D rendering not yet implemented

T = parametric_plot3d([(2+cos(v))*cos(u),(2+cos(v))*sin(u),sin(v)],(u,-2*pi,2*pi),(v,-2*pi,2*pi),opacity=0.2);
TT = parametric_plot3d([3,3*u,v],(u,-2*pi,2*pi),(v,-2*pi,2*pi),color="red",opacity=0.2);
T+TT

3D rendering not yet implemented