實驗十

restart;

a:=2;

b:=5;

c:=sqrt(a^2+b^2);

z:=a*sin(t);

r:=c+a*cos(t);

x:=r*cos(s);

y:=r*sin(s);

with(plots):

t:=2.5*s;

tubeplot([x,y,z],s=0..4*Pi,scaling=constrained,radius=1,grid=[201,11]);

restart;

a:=2;

b:=5;

c:=sqrt(a^2+b^2);

z:=a*sin(t);

r:=c+a*cos(t);

x:=r*cos(s);

y:=r*sin(s);

with(plots):

s:=1.5*t;

tubeplot([x,y,z],t=0..4*Pi,scaling=constrained,radius=1,grid=[201,11]);

restart;

with(plots):

tubeplot([cos(3*t),sin(4*t),sin(5*t)],t=0..2*Pi,scaling=constrained,radius=0.1,grid=[201,11]);

restart;

with(plots):

tubeplot([cos(13*t),sin(4*t),sin(17*t)],t=0..2*Pi,scaling=constrained,radius=0.1,grid=[201,11]);

restart;

with(plots):

a:=2;

b:=5;

c:=sqrt(a^2+b^2);

q:=tubeplot([b*cos(t),a+c*sin(t),a*cos(t)],t=0..2*Pi,radius=0.5,scaling=constrained):

with(plottools):

for n to 5 do p[n]:=rotate(q,0,0,2*Pi*n/5): od:

display(p[k]$k=1..5,scaling=constrained);

restart;

with(plots):

with(plottools):

a:=coordplot(cartesian,[-10..10,-10..10],scaling=constrained):

f:=transform((x,y)->[2*x/(x^2+y^2+1),2*y/(x^2+y^2+1),(x^2+y^2-1)/(x^2+y^2+1)]):

b:=display(f(a),scaling=constrained):

c:=sphere([0,0,0],0.99,style=patchnogrid,color=yellow):

display(b,c);

restart;

z:=sin(t);

r:=3+cos(t);

x:=7+r*cos(s);

y:=r*sin(s);

q:=expand([x,y,z]/(x^2+y^2+z^2)):

plot3d(q,s=0..2*Pi,t=0..2*Pi,scaling=constrained,grid=[101,101],style=patchnogrid);

　

restart;

with(plots):

with(plottools):

f:=transform((x,y,z)->expand([x,y,z]/(x^2+y^2+z^2))):

p1:=sphere([5,-1,-1],sqrt(2)):

p2:=sphere([7,1,-1],sqrt(2)):

p3:=sphere([7,-1,1],sqrt(2)):

p4:=sphere([5,1,1],sqrt(2)):

display(f(p1),f(p2),f(p3),f(p4),scaling=constrained,style=patchnogrid);

restart;

with(plots):

tubeplot([t*cos(t),t*sin(t),2*t],t=0..4*Pi,radius=t/2,scaling=constrained,style=patchnogrid);

restart;

x:=cos(u)^3*cos(v)^3;

y:=sin(u)^3*cos(v)^3;

z:=sin(v)^3;

plot3d([x,y,z],u=0..2*Pi,v=0..2*Pi,scaling=constrained,grid=[51,51],style=patchnogrid);