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MathGroup Archive 2004

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Re: Solid plot

  • To: mathgroup at smc.vnet.net
  • Subject: [mg49344] Re: Solid plot
  • From: mathma18 at hotmail.com (Narasimham G.L.)
  • Date: Thu, 15 Jul 2004 07:00:07 -0400 (EDT)
  • References: <ccb6e8$eqd$1@smc.vnet.net> <ccdlkv$sch$1@smc.vnet.net> <ccg4ba$oqk$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Dear Roger,

You sure would agree that 3D is a necessary bridge when jumping from
2D visualization to 4D. This is because you can work on any of the
three dimensions, to find out which parameter in 4D is behaving in a
particular way.

Expectedly, non-orientable surfaces (Steiner Roman) would not be
amenable for good definition even for a smooth surface.I was trying
out the Moebius Band before posting this  and found that Mathematica
in old versions is not good enough  even for surfaces of revolution 
repeatedly sweeping over itself,e.g. a cone in :

ParametricPlot3D[{r Cos[th],r Sin[th],-r},{r,1,3},{th,0,2 Pi}]
ParametricPlot3D[{r Cos[th],r Sin[th],-r},{r,1,3},{th,0,8 Pi}]
visually deforms it towards  Origami, so non-orientable surfaces
depiction especially if intersections are involved, may take some more
time for implementation.I had earlier posted on this topic too.

In software like IDEAS, defined geometry can be inputted for futher
Finite Element analysis, such interfaces may perhaps be possible here
also.

"Roger L. Bagula" <rlbtftn at netscape.net> wrote in message news:<ccg4ba$oqk$1 at smc.vnet.net>...
> Dear G.L.Narasimham,

> It works pretty good.
> I tried it with several other  surfaces as well. It doesn't work will with
> a Steiner Roman surface but a hyperboloid of one sheet works fine.
> 
> Roger L. Bagula wrote:
> > Dear G.L.Narasimham.
> > As usual you are trying to make Mathematica
> > more useful to people interested in geometry
> > research.
> > I'll try it!
> > 
> > G.L.Narasimham wrote:
> > 
> >>I suggest that a single "Solid" command for 3D be made available
> >>to users in Mathemtica, if not already in existence.
> >>
> >>Generally, constants still appearing in 3D parameterizations can be
> >>varied to obtain a thickness dimension of a solid.This should be  
> >>equivalent to depicting the following 6 individual external surface
> >>plots using ParametricPlot3D.
> >>
> >>The command could be useful in solid modelling in
> >>Architecure, Finite Element Method of structural
> >>analysis and in faster 3D visualizations of sections of 
> >>four dimensional manifolds.The example here shows a radially
> >>thickened spherical segment bounded by 6 parameter values.
> >>A more real 3D feel object would be obtained by click/drag
> >>of mouse, Spinshow etc.  
> >>
> >>"Solid[XYZ,{u,umin,umax},{v,vmin,vmax},{w,wmin,wmax}]"
> >>
> >>Clear[u,v,w,umin,umax,vmin,vmax,wmin,wmax];
> >>umin=0;umax=1;vmin=0;vmax=1;wmin=.8;wmax=1;
> >>XYZ={w Cos[u]Cos[v],w Cos[u]Sin[v],w Sin[u]}; 
> >>w=wmin;
> >>uvlo=ParametricPlot3D[XYZ,{u,umin,umax},{v,vmin,vmax}];
> >>w=wmax;
> >>uvhi=ParametricPlot3D[XYZ,{u,umin,umax},{v,vmin,vmax}];
> >>u=umin;
> >>vwlo=ParametricPlot3D[XYZ,{v,vmin,vmax},{w,wmin,wmax}];
> >>u=umax;
> >>vwhi=ParametricPlot3D[XYZ,{v,vmin,vmax},{w,wmin,wmax}];
> >>v=vmin;
> >>wulo=ParametricPlot3D[XYZ,{w,wmin,wmax},{u,umin,umax}];
> >>v=vmax;
> >>wuhi=ParametricPlot3D[XYZ,{w,wmin,wmax},{u,umin,umax}];
> >>Show[{uvlo,uvhi,vwlo,vwhi,wulo,wuhi},
> >>ViewPoint->{-1,2,-3},Boxed->False,Axes->None];
> >>
> >>Best Regards,
> >>Narasimham
> >>
> > 
> >


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