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(For In[1] see Setup)
| In[1]:=
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?TubePlot
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| 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.
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Thus here's a thin unknot:
In[3]:=
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Show[TubePlot[{Cos[t], Sin[t], 0}, {t, 0, 2Pi}, 0.1]]
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Out[3]=
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-Graphics3D-
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| In[4]:=
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?TubeSubdivision
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| 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}.
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| In[5]:=
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?TubeFraming
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| 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.
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| In[6]:=
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?TubePlotPrelude
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| 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 -> {}.
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Here's the same unknot, made thicker and not as smooth:
In[8]:=
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Show[TubePlot[
{Cos[t], Sin[t], 0}, {t, 0, 2Pi}, 0.3, TubeSubdivision -> {6, 3}
]]
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Out[8]=
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-Graphics3D-
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Let's play with the framing now:
In[10]:=
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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]}
]]
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Out[10]=
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-Graphics3D-
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Here's an example that uses a prelude and passes options on to Graphics3D:
In[12]:=
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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}
]]
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Out[12]=
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-Graphics3D-
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The last example serves as the basis for the definition of TubePlot[TorusKnot[m, n]]. Here's a final example:
In[14]:=
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Show[TubePlot[TorusKnot[3, 5]]]
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Out[14]=
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-Graphics3D-
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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 (File:TubePlot.m).
