Drawing with TubePlot

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(For In[1] see Setup)

In[1]:= ?TubePlot

TubePlot[gamma, {t, t0, t1}, r, opts] plots the space curve gamma with the variable t running from t0 to t1, as a tube of radius r. The available options are TubeSubdivision, TubeFraming and TubePlotPrelude. All other options are passed on to Graphics3D. TubePlot[TorusKnot[m, n], opts] produces a tube plot of the (m,n) torus knot.

Thus here's a thin unknot:

In[2]:=
Show[TubePlot[{Cos[t], Sin[t], 0}, {t, 0, 2Pi}, 0.1]]
Drawing with TubePlot Out 2.gif
Out[2]= -Graphics-
In[3]:= ?TubeSubdivision

TubeSubdivision is an option for TubePlot. TubePlot[__, TubeSubdivision -> {l, m} draws the tube subdivided to l pieces lengthwise and m pieces around. The default is TubeSubdivision -> {50, 12}.

In[4]:= ?TubeFraming

TubeFraming is an option for TubePlot. TubePlot[gamma, {t, __}, _, TubeFraming -> n] sets the framing of the tube (visible when TubeSubdivision -> {l, m} with small m) to be the vector n, which in itself may be a function of t. Thus TubeFraming -> {0,0,1} is "blackboard framing". TubeFraming -> Normal (default) uses the normal vector of the curve gamma.

In[5]:= ?TubePlotPrelude

TubePlotPrelude is an option for TubePlot. Its value is passed to Graphics3D before the main part of the plot, allowing to set various graphics options. For example, TubePlotPrelude -> EdgeForm[{}] will suppress the drawing of edges between the polygons making up the tube. The default is TubePlotPrelude -> {}.

Here's the same unknot, made thicker and not as smooth:

In[6]:=
Show[TubePlot[
  {Cos[t], Sin[t], 0}, {t, 0, 2Pi}, 0.3, TubeSubdivision -> {6, 3}
]]
Drawing with TubePlot Out 6.gif
Out[6]= -Graphics-

Let's play with the framing now:

In[7]:=
Show[TubePlot[
  {Cos[t], Sin[t], 0}, {t, 0, 2Pi}, 0.2,
  TubeSubdivision -> {50, 2},
  TubeFraming -> {Cos[2t]Cos[t], Cos[2t]Sin[t], Sin[3t]}
]]
Drawing with TubePlot Out 7.gif
Out[7]= -Graphics-

Here's an example that uses a prelude and passes options on to Graphics3D:

In[8]:=
Show[TubePlot[
  {Cos[2t], Sin[2t], 0} +
    0.5{Cos[3t]Cos[2t], Cos[3t]Sin[2t], -Sin[3t]},
  {t, 0, 2Pi}, 1/3,
  TubeSubdivision -> {280, 12}, TubeFraming -> {0,0,1},
  TubePlotPrelude -> EdgeForm[{}],
  Boxed -> False, ViewPoint -> {0,0,1}
]]
Drawing with TubePlot Out 8.gif
Out[8]= -Graphics-

The last example serves as the basis for the definition of TubePlot[TorusKnot[m, n]]. Here's a final example:

In[9]:=
Show[TubePlot[TorusKnot[3, 5]]]
Drawing with TubePlot Out 9.gif
Out[9]= -Graphics-

Standalone TubePlot

There may be some independent interest in the routine TubePlot, and hence it is available also as an independent package. Here it is: TubePlot.m.