Construct a VRML file illustrating the intersection of two cylinders having the same radius, with axes meet and perpendicular to each other.

> restart;

> x:=cos(t):

> y:=sin(t):

> z1:=x:

> z2:=-x:

> z:=(1-s)*z1+s*z2:

> a:=plot3d([x,y,z],s=0..1,t=0..2*Pi,scaling=constrained,color=green):

> b:=plot3d([z,y,x],s=0..1,t=0..2*Pi,scaling=constrained,color=blue):

> with(plots):

Warning, the name changecoords has been redefined

> c:=display(a,b):

> vrml(c,"d:/9/10-1.wrl",background_color=white);

> c;

Construct the portion of the cylinder x2 + z2 = 0.81 lying outside x2 + y2 =1.

> restart;

> x:=0.9*cos(t):z:=0.9*sin(t):

> y1:=sqrt(1-x^2):

> y2:=2:

> y:=(1-s)*y1+s*y2:

> a:=plot3d([x,y,z],t=0..2*Pi,s=0..1,scaling=constrained,color=red):

> b:=plot3d([x,-y,z],t=0..2*Pi,s=0..1,scaling=constrained,color=red):

> x:=cos(t):y:=sin(t):

> z1:=x:z2:=-x:

> z:=(1-s)*z1+s*z2:

> c:=plot3d([y,x,z],t=0..2*Pi,s=0..1,scaling=constrained,color=blue):

> d:=plot3d([y,x,z],t=0..2*Pi,s=0..1,scaling=constrained,color=blue):

> with(plots):

Warning, the name changecoords has been redefined

> with(plottools):

> vrml(e,"d:/9/10-2.wrl",background_color=white);

> e;

Construct the solid bounded by the parabolic cylinder
z = 4 - y2
and the elliptic paraboloid
z = x2 + 3y2.

>

> restart;

> x:=2*r*cos(t):

> y:=r*sin(t):

> z:=4-y^2:

> a:=plot3d([x,y,z],t=0..2*Pi,r=0..1,scaling=constrained,color=yellow):

> z:=x^2+3*y^2:

> b:=plot3d([x,y,z],t=0..2*Pi,r=0..1,scaling=constrained,color=green):

> with(plots):

Warning, the name changecoords has been redefined

> with(plottools):

> vrml(c,"d:/9/10-3.wrl",background_color=white):

> c;

Construct the Astroidal Ellipsoid given by
x = (cos(u)cos(v))3,
y = (sin(u)cos(v))3
z = sin3(v)

> restart;

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

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

> z:=sin(v)^3:

> a:=plot3d([x,y,z],u=0..2*Pi,v=0..2*Pi,scaling=constrained,color=green):

> with(plottools):

> vrml(a,"d:/9/10-4.wrl",background_color=white);

> a;

Construct this surface:

> restart;

> x:=r*cos(t):

> y:=r*sin(t):

> r:=0.05*t:

> c:=plot3d([s*x,s*y,(1-s)],s=0..1,t=0..30,scaling=constrained,grid=[5,200],color=COLOR(RGB,1,0.7,0.3)):

> with(plottools):

> vrml(c,"d:/9/10-5.wrl",background_color=white);

> c;

Construct this surface:

> restart;

> r:=exp(-t):

> z:=r*cos(s/2):x:=r*sin(s/2):y:=t+0.1*s:

> c:=plot3d([x,y,z],s=0..12*Pi,t=1..6,grid=[200,20],color=green):

> with(plottools):

> vrml(c,"d:/9/10-6.wrl",background_color=white):

> c;

>