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MathGroup Archive 2004

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Re: Solid plot

  • To: mathgroup at
  • Subject: [mg49176] Re: Solid plot
  • From: "Roger L. Bagula" <rlbtftn at>
  • Date: Tue, 6 Jul 2004 03:33:52 -0400 (EDT)
  • References: <ccb6e8$eqd$>
  • Sender: owner-wri-mathgroup at

Dear G.L.Narasimham.
As usual you are trying to make Mathematica
more useful to people interested in geometry
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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