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From: Narasimham <mathma18@gmail.com>
Newsgroups: comp.soft-sys.math.mathematica
Subject: Variable section and hollow Tubes for economic 3D printing
Date: Sat, 12 Apr 2014 09:15:52 +0000 (UTC)
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Xref: csiph.com comp.soft-sys.math.mathematica:16784

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