Notice. The Knot Atlas is now recovering from a major crash. Hopefully all functionality will return slowly over the next few days. --Drorbn (talk) 21:23, 4 July 2013 (EDT)

Drawing with TubePlot

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(For In[1] see Setup)

In[2]:= ?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[3]:= Show[TubePlot[{Cos[t], Sin[t], 0}, {t, 0, 2Pi}, 0.1]]
Drawing with TubePlot Out 3.gif
Out[3]= -Graphics3D-
In[4]:= ?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[5]:= ?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[6]:= ?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[7]:= Show[TubePlot[ {Cos[t], Sin[t], 0}, {t, 0, 2Pi}, 0.3, TubeSubdivision -> {6, 3} ]]
Drawing with TubePlot Out 7.gif
Out[7]= -Graphics3D-

Let's play with the framing now:

In[8]:= 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 8.gif
Out[8]= -Graphics3D-

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

In[9]:= 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 9.gif
Out[9]= -Graphics3D-

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

In[10]:= Show[TubePlot[TorusKnot[3, 5]]]
Drawing with TubePlot Out 10.gif
Out[10]= -Graphics3D-

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).