restart;

x:=r*cos(t);

y:=r*sin(t);

r:=cos(t);

p1:=plot3d([x,y,z],t=-Pi/2..Pi/2,z=-sqrt(1-r^2)..sqrt(1-r^2),scaling=constrained,style=patchnogrid,color=blue):

p2:=plot3d([s*x,s*y,sqrt(1-s*s*r*r)],t=-Pi/2..Pi/2,s=0..1,scaling=constrained,style=patchnogrid,color=red):

p3:=plot3d([s*x,s*y,-sqrt(1-s*s*r*r)],t=-Pi/2..Pi/2,s=0..1,scaling=constrained,style=patchnogrid,color=red):

with(plots):

restart;

x:=r*cos(t);

y:=r*sin(t);

r:=cos(t);

restart;

with(plots):

with(plottools):

p:=Pi/2;

x1:=cos(t);

y1:=sin(t);

x2:=cos(t+p);

y2:=sin(t+p);

z:=Pi/2-t;

q:=expand((1-u)*[z*x1,z*y1,z]+u*[z*x2,z*y2,z],scaling=constrained):

p1:=plot3d(q,u=0..1,t=0..Pi/2):

p2:=display(rotate(p1,0,0,p),color=green,style=patchnogrid):

p3:=display(rotate(p1,0,0,2*p),color=blue,style=patchnogrid):

p4:=display(rotate(p1,0,0,3*p),color=yellow,style=patchnogrid):

p5:=plot3d(q,u=0..1,t=0..Pi/2,scaling=constrained,color=red,style=patchnogrid):

restart;

x1:=1;

y1:=(1-u)*1+u*(-1);

x2:=cos(t)*x1-sin(t)*y1;

y2:=sin(t)*x1+cos(t)*y1;

z:=t;

p1:=plot3d([(Pi-t)*x2,(Pi-t)*y2,z],u=0..1,t=0..Pi,scaling=constrained,style=patchnogrid):

with(plottools):

p2:=display(rotate(p1,0,0,Pi/2),color=green):

p3:=display(rotate(p1,0,0,Pi),color=blue):

p4:=display(rotate(p1,0,0,3*Pi/2),color=yellow):

p5:=plot3d([(Pi-t)*x2,(Pi-t)*y2,z],u=0..1,t=0..Pi,scaling=constrained,color=red,style=patchnogrid):

with(plots):

restart;

with(plots):

 with(plottools):

p:=2*Pi/3;

x1:=cos(t);

y1:=sin(t);

x2:=cos(t+p);

y2:=sin(t+p);

z:=Pi-t;

q:=expand((1-u)*[z*x1,z*y1,z]+u*[z*x2,z*y2,z],scaling=constrained):

p1:=plot3d(q,u=0..1,t=0..Pi):

p2:=display(rotate(p1,0,0,p),color=green,style=patchnogrid):

p3:=display(rotate(p1,0,0,2*p),color=blue,style=patchnogrid):

p4:=plot3d(q,u=0..1,t=0..Pi,scaling=constrained,color=red,style=patchnogrid):

restart;

with(plots):

x:=r*cos(t);

y:=r*sin(t);

p1:=plot3d([x,y,-x^2+1/2],r=0..1,t=0..2*Pi,scaling=constrained,grid=[11,51],color=yellow):

p2:=plot3d([x,y,y^2-1/2],r=0..1,t=0..2*Pi,scaling=constrained,grid=[11,51],color=blue):

restart;

with(plots):

x:=cos(t);

y:=sin(t);

p1:=tubeplot([x,y,0],t=0..2*Pi,radius=0.2,scaling=constrained,color=red,style=patchnogrid):

p2:=tubeplot([0+0.6,x+0.6,y+0.6],t=0..2*Pi,radius=0.2,scaling=constrained,color=green,style=patchnogrid):

p3:=tubeplot([y+0.6,0+0.6,x-0.6],t=0..2*Pi,radius=0.2,scaling=constrained,color=blue,style=patchnogrid):

restart;

with(plots):

x:=5*cos(t);

y:=3*sin(t);

p1:=tubeplot([x,y,0],t=0..2*Pi,radius=0.5,scaling=constrained,color=red,style=patchnogrid):

p2:=tubeplot([0,x,y],t=0..2*Pi,radius=0.5,scaling=constrained,color=green,style=patchnogrid):

p3:=tubeplot([y,0,x],t=0..2*Pi,radius=0.5,scaling=constrained,color=blue,style=patchnogrid):