Knot Atlas - User contributions [en]

Drawing with TubePlot

2009-05-27T08:57:01Z

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{{Manual TOC Sidebar}}

{{Startup Note}}



{{HelpLine|
n = 1 |
in = <nowiki>TubePlot</nowiki> |
out= <nowiki>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.</nowiki>}}


Thus here's a thin unknot:



{{Graphics|
n = 3 |
in = <nowiki>Show[TubePlot[{Cos[t], Sin[t], 0}, {t, 0, 2Pi}, 0.1]]</nowiki> |
img= Drawing_with_TubePlot_Out_2.gif |
out= <nowiki>-Graphics3D-</nowiki>}}




{{HelpLine|
n = 4 |
in = <nowiki>TubeSubdivision</nowiki> |
out= <nowiki>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}.</nowiki>}}




{{HelpLine|
n = 5 |
in = <nowiki>TubeFraming</nowiki> |
out= <nowiki>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.</nowiki>}}




{{HelpLine|
n = 6 |
in = <nowiki>TubePlotPrelude</nowiki> |
out= <nowiki>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 -> {}.</nowiki>}}


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



{{Graphics|
n = 8 |
in = <nowiki>Show[TubePlot[
{Cos[t], Sin[t], 0}, {t, 0, 2Pi}, 0.3, TubeSubdivision -> {6, 3}
]]</nowiki> |
img= Drawing_with_TubePlot_Out_7.gif |
out= <nowiki>-Graphics3D-</nowiki>}}


Let's play with the framing now:



{{Graphics|
n = 10 |
in = <nowiki>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]}
]]</nowiki> |
img= Drawing_with_TubePlot_Out_9.gif |
out= <nowiki>-Graphics3D-</nowiki>}}


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



{{Graphics|
n = 12 |
in = <nowiki>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}
]]</nowiki> |
img= Drawing_with_TubePlot_Out_11.gif |
out= <nowiki>-Graphics3D-</nowiki>}}


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



{{Graphics|
n = 14 |
in = <nowiki>Show[TubePlot[TorusKnot[3, 5]]]</nowiki> |
img= Drawing_with_TubePlot_Out_13.gif |
out= <nowiki>-Graphics3D-</nowiki>}}



==== Standalone <code>TubePlot</code> ====


There may be some independent interest in the routine <code>TubePlot</code>, and hence it is available also as an independent package. Here it is: [[Media:TubePlot.m|TubePlot.m]] ([[Image:TubePlot.m|file description]]).

Drawing with TubePlot

2009-05-26T12:04:24Z

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{{Manual TOC Sidebar}}

{{Startup Note}}



{{HelpLine|
n = 1 |
in = <nowiki>TubePlot</nowiki> |
out= <nowiki>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.</nowiki>}}


Thus here's a thin unknot:



{{Graphics|
n = 3 |
in = <nowiki>Show[TubePlot[{Cos[t], Sin[t], 0}, {t, 0, 2Pi}, 0.1]]</nowiki> |
img= Drawing_with_TubePlot_Out_2.gif |
out= <nowiki>-Graphics3D-</nowiki>}}




{{HelpLine|
n = 4 |
in = <nowiki>TubeSubdivision</nowiki> |
out= <nowiki>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}.</nowiki>}}




{{HelpLine|
n = 5 |
in = <nowiki>TubeFraming</nowiki> |
out= <nowiki>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.</nowiki>}}




{{HelpLine|
n = 6 |
in = <nowiki>TubePlotPrelude</nowiki> |
out= <nowiki>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 -> {}.</nowiki>}}


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



{{Graphics|
n = 8 |
in = <nowiki>Show[TubePlot[
{Cos[t], Sin[t], 0}, {t, 0, 2Pi}, 0.3, TubeSubdivision -> {6, 3}
]]</nowiki> |
img= Drawing_with_TubePlot_Out_7.gif |
out= <nowiki>-Graphics3D-</nowiki>}}


Let's play with the framing now:



{{Graphics|
n = 10 |
in = <nowiki>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]}
]]</nowiki> |
img= Drawing_with_TubePlot_Out_9.gif |
out= <nowiki>-Graphics3D-</nowiki>}}


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



{{Graphics|
n = 12 |
in = <nowiki>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}
]]</nowiki> |
img= Drawing_with_TubePlot_Out_11.gif |
out= <nowiki>-Graphics3D-</nowiki>}}


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



{{Graphics|
n = 14 |
in = <nowiki>Show[TubePlot[TorusKnot[3, 5]]]</nowiki> |
img= Drawing_with_TubePlot_Out_13.gif |
out= <nowiki>-Graphics3D-</nowiki>}}



==== Standalone <code>TubePlot</code> ====


There may be some independent interest in the routine <code>TubePlot</code>, and hence it is available also as an independent package. Here it is: [[Media:TubePlot.m|TubePlot.m]] ([[Image:TubePlot.m|file description]]).

Drawing with TubePlot

2009-05-22T15:28:47Z

DeldaRcoal:

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{{Manual TOC Sidebar}}

{{Startup Note}}



{{HelpLine|
n = 1 |
in = <nowiki>TubePlot</nowiki> |
out= <nowiki>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.</nowiki>}}


Thus here's a thin unknot:



{{Graphics|
n = 3 |
in = <nowiki>Show[TubePlot[{Cos[t], Sin[t], 0}, {t, 0, 2Pi}, 0.1]]</nowiki> |
img= Drawing_with_TubePlot_Out_2.gif |
out= <nowiki>-Graphics3D-</nowiki>}}




{{HelpLine|
n = 4 |
in = <nowiki>TubeSubdivision</nowiki> |
out= <nowiki>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}.</nowiki>}}




{{HelpLine|
n = 5 |
in = <nowiki>TubeFraming</nowiki> |
out= <nowiki>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.</nowiki>}}




{{HelpLine|
n = 6 |
in = <nowiki>TubePlotPrelude</nowiki> |
out= <nowiki>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 -> {}.</nowiki>}}


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



{{Graphics|
n = 8 |
in = <nowiki>Show[TubePlot[
{Cos[t], Sin[t], 0}, {t, 0, 2Pi}, 0.3, TubeSubdivision -> {6, 3}
]]</nowiki> |
img= Drawing_with_TubePlot_Out_7.gif |
out= <nowiki>-Graphics3D-</nowiki>}}


Let's play with the framing now:



{{Graphics|
n = 10 |
in = <nowiki>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]}
]]</nowiki> |
img= Drawing_with_TubePlot_Out_9.gif |
out= <nowiki>-Graphics3D-</nowiki>}}


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



{{Graphics|
n = 12 |
in = <nowiki>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}
]]</nowiki> |
img= Drawing_with_TubePlot_Out_11.gif |
out= <nowiki>-Graphics3D-</nowiki>}}


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



{{Graphics|
n = 14 |
in = <nowiki>Show[TubePlot[TorusKnot[3, 5]]]</nowiki> |
img= Drawing_with_TubePlot_Out_13.gif |
out= <nowiki>-Graphics3D-</nowiki>}}



==== Standalone <code>TubePlot</code> ====


There may be some independent interest in the routine <code>TubePlot</code>, and hence it is available also as an independent package. Here it is: [[Media:TubePlot.m|TubePlot.m]] ([[Image:TubePlot.m|file description]]).