Re: puzzling revolution surface

• To: mathgroup at smc.vnet.net
• Subject: [mg67436] Re: puzzling revolution surface
• From: "Narasimham" <mathma18 at hotmail.com>
• Date: Sat, 24 Jun 2006 05:27:59 -0400 (EDT)
• References: <e757vn\$l2t\$1@smc.vnet.net><e7844t\$fmh\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```dh wrote:

> Hi Narasimham,
> if you plot a surface of revolution, the curve in the x-z plane is
> independent of the rotation angle. However, your curve does depend on
> this angle and therefore, your surface is no more a surface of
> revolution. That this works at all is an undocumented feature of
> SurfaceOfRevolution.
>
> Daniel
>
> Narasimham wrote:
> > Am not able to comprehend how this is a surface of revolution.(When 2D
> > plots on two parameters are also possible).
> >
> > << Graphics`SurfaceOfRevolution`
> > <<RealTime3D`
> > SurfaceOfRevolution[{Sin[u] ,0.8 Cos[ v] +1 },{u,0, Pi},{v,0,2
> > Pi},RevolutionAxis->{0,0,1}]
> >

Yes indeed Daniel, the following are certainly not surfaces of
revolution:

<<  Graphics`SurfaceOfRevolution`
<<  RealTime3D`
SurfaceOfRevolution[{ u ,v },{u,0, 1},{v,0,6},RevolutionAxis->{1,2,1},
PlotPoints->{7,60}  ]  ;
SurfaceOfRevolution[{ u ,v },{u,0, 3},{v,0, 3},
RevolutionAxis->{0,1,0},   PlotPoints->  {7,10}  ]  ;
SurfaceOfRevolution[{ u ,v },{u,0,3},{v,0,6},RevolutionAxis->{0,0,1},
PlotPoints->{7,55}   ]  ;
SurfaceOfRevolution[{ u ,v },{u,0, 1},{v,0,6},RevolutionAxis->{1,1,0},
PlotPoints->{7,125} ]  ;
SurfaceOfRevolution[{ u ,v },{u,0, 8},{v,0,12},
RevolutionAxis->{0,1,1},   PlotPoints->{7,75}]  ;
SurfaceOfRevolution[{ u ,v },{u,0, 3},{v,-10,10},
RevolutionAxis->{1,0,1}, PlotPoints->{7,175}]  ;
SurfaceOfRevolution[{ u ,v },{u,0, 8},{v,0,12},
RevolutionAxis->{1,1,1},    PlotPoints->{7,60}]  ;
SurfaceOfRevolution[{ u+v ,u*v/5 },{u,-1
,1},{v,-1,1},RevolutionAxis->{-1,+1,-1},    PlotPoints->{7,20}]  ;
SurfaceOfRevolution[{ 1-Cos[u] ,1+  Cos[ v]  },{u,0.1, Pi/2},{v,0,2
Pi},RevolutionAxis->{1,0,0},PlotPoints->{8,30}]  ;
SurfaceOfRevolution[{ 1-Cos[u] ,1+  Cos[ v]  },{u,0.1, Pi/2},{v,0,2
Pi},RevolutionAxis->{0,1,0},PlotPoints->{8,30}]  ;
SurfaceOfRevolution[{ 1-Cos[u] ,1+  Cos[ v]  },{u,0.1, Pi/2},{v,0,2
Pi},RevolutionAxis->{0,0,1},PlotPoints->{8,30}]  ;
<<  Default3D`

The command name (SurfaceOfRevolution) in  case of rotation dependence
is  a misnomer.May be some alternative names  like:
ParametricSurface3D[{ u+v ,  u*v/5 },{u,-1 ,1},{v,-1,1}, Generatrix->
{1,1,0}]  could be  considered.

The command appears quite versatile  by incorporation of surface
variation with rotations and  has  a promise to generate  many types of
surfaces  by the triple choice viz., f[u,v], g[u,v]  and RevolutionAxis
or Direction-Cosines -> {l,m,n} ). I mean not  just the surfaces of
revolution or extrutions but a larger section of surface
parameterizations can be in some way be included.

I am wondering what could have  held  back its declaration  in versions
so far..swept out surface is not hitherto known? so not useful? ..But
such symbolic variable generalizations have already been elsewhere used