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)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*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

**References**:**tubes program not working in version 9***From:*Roger Bagula <roger.bagula@gmail.com>