Variable section and hollow Tubes for economic 3D printing

• To: mathgroup at smc.vnet.net
• Subject: [mg132564] Variable section and hollow Tubes for economic 3D printing
• From: Narasimham <mathma18 at gmail.com>
• Date: Sat, 12 Apr 2014 05:15:19 -0400 (EDT)
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```Although the tube is not fully filled, a constant thickness prescribed on a variable cross section works. This meets a good number of solid modeling requirements.

TubeRadius = 0.2 ; TR[u_] = 0.2 + 0.15 Cos[u] ; a = 1; Plot[TR[t], {t, 0, 2 Pi}]

tor = ParametricPlot3D[ {(a + TR[t] Cos[ph]) Cos[t], (a + TR[t] Cos[ph]) Sin[t], .5 t + TR[t] Sin[ph]}, {ph, -Pi,Pi}, {t, 0,  Pi}];

torTHK = ParametricPlot3D[ {(a + TR[t] Cos[ph]) Cos[t], (a + TR[t] Cos[ph]) Sin[t], .5 t + TR[t] Sin[ph]}, {ph, -Pi,Pi}, {t, 0,  Pi}, PlotStyle -> Thickness[.07], Axes -> None, Boxed -> False]

HelTHK = ParametricPlot3D[ {(a + TR[2 ph] Cos[ph])
Cos[ t], (a + TR[2 ph] Cos[ph]) Sin[t], .8 t + TR[2 ph] Sin[ph]}, {ph, -Pi, Pi}, {t, 0, Pi}, PlotStyle -> Thickness[.04], Axes -> None, Boxed -> False]

Narasimham

```

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