Moebius Strip

Example from the PscFunctions   package

With the help of routines of the PscFunctions package it is possible to obtain parametric equations of regions with boundaries .
For creation the equation of the Moebius strip we need to know how to create the equation of a segment. At the segment displacement and rotation around of a closed curve we can obtain a strip surface. For produce the equation of the segment we use PR(x , a , w )  function of the PSCFunctions  package.

>    with(PscFunctions):
R:=3: # radius of directing circle
N:=1: # number of turns (for mobius band it should be odd)
H:=2: # width of the band
x0:=t->R*cos(t): y0:=t->R*sin(t): z0:=t->0:
lx:=u->cos(u/(2/N))*cos(u): ly:=u->cos(u/(2/N))*sin(u): lz:=u->sin(u/(2/N)):
x:=(u,v)->x0(u)+lx(u)*(H*PR(v,0,H)-H/2):
y:=(u,v)->y0(u)+ly(u)*(H*PR(v,0,H)-H/2):
z:=(u,v)->z0(u)+lz(u)*(H*PR(v,0,H)-H/2):
ps:=plot3d([x(u,v),y(u,v),z(u,v)],u=0..2*Pi,v=0..H, grid=[51,8],scaling=CONSTRAINED,orientation=[-45,30]):
plots[display](ps);
'X'=x(u,v);
'Y'=y(u,v);
'Z'=z(u,v);

[Maple Plot]

X = 3*cos(u)+cos(1/2*u)*cos(u)*(1/2*abs(v)-1/2*abs(v-2))
Y = 3*sin(u)+cos(1/2*u)*sin(u)*(1/2*abs(v)-1/2*abs(v-2))
Z = sin(1/2*u)*(1/2*abs(v)-1/2*abs(v-2))

>    N:=3: # number of turns
ps:=plot3d([x(u,v),y(u,v),z(u,v)],u=0..2*Pi,v=0..H, grid=[51,8],scaling=CONSTRAINED,orientation=[-45,60],axes=BOXED):
plots[display](ps);

[Maple Plot]