       Solid plot

• To: mathgroup at smc.vnet.net
• Subject: [mg49159] Solid plot
• From: mathma18 at hotmail.com ("G.L.Narasimham")
• Date: Mon, 5 Jul 2004 04:54:55 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```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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