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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
to advantage in Mathematica.
Best Regards,
Narasimham
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