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Re: Tube plot function in Mathematica???

• To: mathgroup at smc.vnet.net
• Subject: [mg108579] Re: Tube plot function in Mathematica???
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Wed, 24 Mar 2010 04:42:01 -0500 (EST)

The code to which you linked works if you take out the outdated option LightSources. You can use Lighting instead (I didn't bother).

TubePlotFrenet[curve_List, {var_, min_, max_},
  radius_, opts___] :=
 Module[
  {tangent, unitTangent, normal, unitNormal, biNormal},
  tangent = D[curve, t];
  unitTangent = tangent/Sqrt[tangent.tangent];
  normal = D[unitTangent, t];
  unitNormal = normal/Sqrt[normal.normal];
  biNormal = Cross[unitTangent, unitNormal];
  ParametricPlot3D[curve + radius Cos[s] unitNormal +
     radius Sin[s] biNormal // Evaluate,
   {var, min, max}, {s, 0, 2 Pi}, opts]]

trefoil = {Sin[3 t], Sin[t] + 2 Sin[2 t], Cos[t] - 2 Cos[2 t]};

TubePlotFrenet[trefoil, {t, 0, 2*Pi}, 0.3,
 Axes -> None,
 Boxed -> False,
 ViewPoint -> {10, 0, 0},
 PlotPoints -> {64, 16},
 PlotLabel -> "The Trefoil Knot"]

TubePlot[curve_List, {var_, min_, max_}, radius_,
  crossVector_List: {1, 1, 1}, opts___] :=
 Module[
  {tangent, unitTangent, normal, unitNormal, biNormal},
  tangent = D[curve, t];
  unitTangent = tangent/Sqrt[tangent.tangent];
  normal = Cross[tangent, crossVector];
  unitNormal = normal/Sqrt[normal.normal];
  biNormal = Cross[unitTangent, unitNormal];
  ParametricPlot3D[curve + radius Cos[s] unitNormal +
     radius Sin[s] biNormal // Evaluate,
   {var, min, max}, {s, 0, 2 Pi}, opts]]

TorusKnotPlot[p_, q_, opts___] :=
 TubePlot[{Cos[t] (1 + .5 Cos[(q/p) t]),
   Sin[t] (1 + .5 Cos[(q/p) t]), .5 Sin[(q/p) t]},
  {t, 0, 2 Pi p}, .1, {0, 0, 1},
  ViewPoint -> {0, 0, 1}, Boxed -> False, Axes -> False, opts]

TorusKnotPlot[3, 5,
 PlotPoints -> {128, 16},
 PlotLabel -> "The (3,5) Torus Knot"]

Alternatively, in a 3D plot replace Line with Tube. Example from Doc Center 
http://reference.wolfram.com/mathematica/ref/Tube.html

ParametricPlot3D[
  {Cos[2 t], Sin[2 t], Cos[t]}, {t, 0, 2 Pi},
  PlotStyle -> Directive[Opacity[0.7], CapForm[None],
    JoinForm["Miter"], Red],
  PlotRange -> All,
  ColorFunction -> Hue,
  Boxed -> False,
  MaxRecursion -> 0,
  PlotPoints -> 100,
  Axes -> None,
  Method -> {"TubePoints" -> 30}] /.
 Line[pts_, rest___] :> Tube[pts, 0.2, rest]


Bob Hanlon

---- NeuroPulse <cosmicvoyager at gmail.com> wrote: 

=============
Greetings,

New to Mathematica.  Can't seem to find a way to plot a line as a tube
like this:

http://facstaff.unca.edu/mcmcclur/java/LiveMathematica/trefoil.html

Seems such an obvious function to have built in.  Is there one?

If not, can someone point me to one I can use in Mathematica?

Thanks