Tube plot function in Mathematica???

NeuroPulse

unread,

Mar 23, 2010, 6:52:47 AM3/23/10

to

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

dr DanW

unread,

Mar 24, 2010, 5:30:57 AM3/24/10

to

Umm...its called Tube[]. It's a 3D graphics primitive, so you do
Graphics3D[{Tube[...],...}]. It's a new function in version 7.

Daniel

Hans Michel

unread,

Mar 24, 2010, 5:32:15 AM3/24/10

to

NeuroPulse:

See

http://reference.wolfram.com/mathematica/ref/Tube.html

New in version 7.

Hans
"NeuroPulse" <cosmic...@gmail.com> wrote in message
news:hoa6hv$hr0$1...@smc.vnet.net...

Peltio

unread,

Mar 24, 2010, 5:32:04 AM3/24/10

to

NeuroPulse wrote :

>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?

How about that very function?
http://facstaff.unca.edu/mcmcclur/java/LiveMathematica/tubes.html

(first result in google)

cheers,
Peltio

Mark McClure

unread,

Mar 24, 2010, 5:32:59 AM3/24/10

to

On Tue, Mar 23, 2010 at 6:52 AM, NeuroPulse <cosmic...@gmail.com> wrote:

> 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

The TubePlotFrenet command and the TubePlot command are defined on this webpage:
http://facstaff.unca.edu/mcmcclur/java/LiveMathematica/tubes.html

I did all that quite some time ago and quite a lot of things have
changed since then. There is now a Tube primitive that can generate
nice tubes like so:

trefoil[t_] == {Sin[3 t], Sin[t] + 2 Sin[2 t], Cos[t] - 2 Cos[2 t]};
Graphics3D[{Tube[BezierCurve[Table[trefoil[t],
{t, 0., 2 Pi, Pi/200}]], 0.4]}]

If you still want to try my old TubePlot functions, there are a couple
of things that should be changed. First, a few Simplify commands will
speed things up again. Second, the Lighting specificiations on my
webpage are obsolete. Putting it all together, you can generate a
nice image like so:

TubePlotFrenet[curve_List, {var_, min_, max_}, radius_, opts___] :==
Module[{tangent, unitTangent, normal, unitNormal, biNormal},
tangent == D[curve, t];
unitTangent == Simplify[tangent/Sqrt[tangent.tangent]];
normal == D[unitTangent, t];
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]];

trefoil[t_] == {Sin[3 t], Sin[t] + 2 Sin[2 t], Cos[t] - 2 Cos[2 t]};
TubePlotFrenet[trefoil[t], {t, 0, 2*Pi}, 0.3,
Axes -> None, Mesh -> Full, Boxed -> False,
ViewPoint -> {10, 0, 0}, PlotPoints -> {64, 16}]

Hope that helps,
Mark McClure

Bob Hanlon

unread,

Mar 24, 2010, 5:33:10 AM3/24/10

to

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 <cosmic...@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

Jaebum Jung

unread,

Mar 24, 2010, 5:34:50 AM3/24/10

to

On 3/23/10 5:52 AM, NeuroPulse 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
>
>

Check graphics primitive Tube:

http://reference.wolfram.com/mathematica/ref/Tube.html

Here's example,

ParametricPlot3D[{Sin[3t],Sin[t]+2Sin[2t],Cos[t]-2Cos[2t]},{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]

- Jaebum

M.Roellig

unread,

Mar 24, 2010, 5:34:17 AM3/24/10

to

Hi,

actually, if you search for Tube in the Mathematica-Help you will
find all you need. Concerning your example:

ParametricPlot3D[trefoil, {t, 0, 2*Pi}, Axes -> None, Boxed -> False,
PlotRange -> All, ViewPoint -> {10, 0, 0}, PlotPoints -> {64, 16},
PlotLabel -> "The Trefoil Knot"] /.

Line[pts_, rest___] :> Tube[pts, 0.2, rest]

Cheers,

Markus

dh

unread,

Mar 24, 2010, 5:35:01 AM3/24/10

to

Hi,
there is e.g.: Tube. here is an example:
myLine[d_] := Tube[ d, 0.2];
Graphics3D@myLine@Table[{Sin[x], Cos[x], 0.1 x}, {x, 0, 4 Pi, Pi/8}]

Daniel

--

Daniel Huber
Metrohm Ltd.
Oberdorfstr. 68
CH-9100 Herisau
Tel. +41 71 353 8585, Fax +41 71 353 8907
E-Mail:<mailto:d...@metrohm.com>
Internet:<http://www.metrohm.com>

Sjoerd C. de Vries

unread,

Mar 24, 2010, 6:03:05 AM3/24/10

to

Well you probably have not been looking in the documentation for long
as typing the word 'tube' already provides you with the answer.
Something like

Graphics3D[
Tube[Table[{Sin[3 t], Sin[t] + 2 Sin[2 t], Cos[t] - 2 Cos[2 t]}, {t,
0, 2 \[Pi], \[Pi]/40}], 0.1]]

should work for you (at least, if you have version 7). Otherwise you
have to resort to ParametricPlot3D and have a parametric description
of the surface of your object available.

Cheers -- Sjoerd