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MathGroup Archive 2004

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Re: Solid plot

  • To: mathgroup at smc.vnet.net
  • Subject: [mg49198] Re: Solid plot
  • From: "Roger L. Bagula" <rlbtftn at netscape.net>
  • Date: Wed, 7 Jul 2004 01:42:35 -0400 (EDT)
  • References: <ccb6e8$eqd$1@smc.vnet.net> <ccdlkv$sch$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

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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