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Re: tubes program not working in version 9

  • To: mathgroup at smc.vnet.net
  • Subject: [mg129029] Re: tubes program not working in version 9
  • From: Mark McClure <mcmcclur at unca.edu>
  • Date: Sun, 9 Dec 2012 10:59:55 -0500 (EST)
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  • References: <20121207063953.888006934@smc.vnet.net>

On Fri, Dec 7, 2012 at 1:39 AM, Roger Bagula <roger.bagula at gmail.com> wrote:

> The tubes program was written for an earlier version
> ( works in version 5 I think) by Mark McClure
> and has worked fine for literally years.
> I haven't got a clue what has gone wrong.

I originally developed that code for version 2.  Of course, since V7,
there's a Tube primitive.  Thus, perhaps the easiest way to generate a
tube is as follows.

trefoil[t_] = {Sin[3 t], Sin[t] + 2 Sin[2 t], Cos[t] - 2 Cos[2 t]};
ParametricPlot3D[trefoil[t], {t, 0, 2 Pi},
  PlotRangePadding -> 2, ViewPoint -> {8, 0, 0},
  Boxed -> False, Axes -> False, PlotPoints -> 100,
  PlotStyle -> Directive[Lighter[Blue], Specularity[White, 40]]] /.
   Line[pts_] -> Tube[BSplineCurve[pts], 0.5]

Here's a working version of TubePlotFrenet, if you prefer.  As Bob
points out, simplification is really necessary in V9.

trefoil[t_] = {Sin[3 t], Sin[t] + 2 Sin[2 t], Cos[t] - 2 Cos[2 t]};
TubePlotFrenet[curve_List, {var_, min_, max_}, radius_, opts___] := Module[
   {tangent, unitTangent, normal, unitNormal, biNormal},
   tangent = D[curve, var];
   unitTangent = Simplify[tangent/Sqrt[tangent . tangent]];
   normal = D[unitTangent, var];
   unitNormal = Simplify[normal/Sqrt[normal . normal]];
   biNormal = Simplify[Cross[unitTangent, unitNormal]];
   ParametricPlot3D[Evaluate[curve + radius*Cos[s]*unitNormal +
      radius*Sin[s]*biNormal],
    {var, min, max}, {s, 0, 2*Pi}, opts]
   ];
TubePlotFrenet[trefoil[t], {t, 0, 2 Pi}, 0.5,
 Axes -> None, Boxed -> False, ViewPoint -> {10, 0, 0},
 PlotPoints -> {64, 16}]

An alternative approach is to take the cross product of the unit
tangent with an arbitrary vector.

trefoil[t_] = {Sin[3 t], Sin[t] + 2 Sin[2 t], Cos[t] - 2 Cos[2 t]};
TubePlot[curve_List, {var_, min_, max_}, radius_,
   crossVector_List: {1, 1, 1}, opts___] := Module[
   {tangent, unitTangent, normal, unitNormal, biNormal},
   tangent = D[curve, var];
   unitTangent = Simplify[tangent/Sqrt[tangent . tangent]];
   normal = Cross[tangent, crossVector];
   unitNormal = Simplify[normal/Sqrt[normal . normal]];
   biNormal = Simplify[Cross[unitTangent, unitNormal]];
   ParametricPlot3D[Evaluate[curve + radius*Cos[s]*unitNormal +
      radius*Sin[s]*biNormal],
    {var, min, max}, {s, 0, 2*Pi}, opts]];
TubePlot[trefoil[t], {t, 0, 2 Pi}, 0.5, {1, 0, 0},
 Axes -> None, Boxed -> False, ViewPoint -> {10, 0, 0},
 PlotPoints -> {64, 16}]

Hope that helps,
MM



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