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Graphics and Visualization Wolfram Language

How to get a nice trefoil knot other than using KnotData

Vincent Jonker

Posted 6 months ago

I wonder how to get the trefoil knot enclosed. Of course I can use KnotData["Trefoil"] but then I like to have a more colorful and thicker knot. Who can/will help? Thanks, Vincent Jonker (from the Freudenthal Institute, Utrecht University).

POSTED BY: Vincent Jonker

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Michael Rogers

Michael Rogers, Emory University

Posted 27 days ago

Or use the built-in parametrization in `KnotData`: param = KnotData["Trefoil", "SpaceCurve"]; ParametricPlot3D[ (* reflect/rotate around to get like the picture *) {1, -1, 1} RotationMatrix[{{0, 1, 0}, {0, 0, 1}}] . param[t], {t, 0, 2 Pi}, PlotStyle -> {Tube[0.5]}, ColorFunction -> (Hue[0.92 - #3/1.4] &), PlotPoints -> 100, Axes -> False, Boxed -> False, PlotRangePadding -> 0.55, ViewPoint -> {0., -4, -0.5}, ViewVertical -> {-0.05 , 0, 1}, Lighting -> { DirectionalLight[GrayLevel[0.9], {0, 2, 3}], DirectionalLight[GrayLevel[0.9], {2, -1, 3}], AmbientLight[GrayLevel[0.4]]}]

Or use the built-in parametrization in KnotData:

param = KnotData["Trefoil", "SpaceCurve"];
ParametricPlot3D[
 (* reflect/rotate around to get like the picture *)
 {1, -1, 1} RotationMatrix[{{0, 1, 0}, {0, 0, 1}}] . param[t],
 {t, 0, 2 Pi},
 PlotStyle -> {Tube[0.5]}, ColorFunction -> (Hue[0.92 - #3/1.4] &),
 PlotPoints -> 100, Axes -> False, Boxed -> False, 
 PlotRangePadding -> 0.55,
 ViewPoint -> {0., -4, -0.5}, ViewVertical -> {-0.05 , 0, 1},
 Lighting -> {
   DirectionalLight[GrayLevel[0.9], {0, 2, 3}],
   DirectionalLight[GrayLevel[0.9], {2, -1, 3}],
   AmbientLight[GrayLevel[0.4]]}]

enter image description here

POSTED BY: Michael Rogers

Hans Milton

Posted 27 days ago

Maybe: trefoil[t_] := {Sin[t] - 2 Sin[2 t], Cos[t] + 2 Cos[2 t], -Sin[3 t]} ParametricPlot3D[trefoil[t],{t,0,2 Pi},Boxed->False,Axes->False, ViewPoint->{0,0,50},ViewVertical->{0,-1,0},PlotRange->4, ColorFunction->Function[{x,y,z,u},Hue@u],PlotPoints->300 ]/.Line[pts_,rest___]:>Tube[pts,0.8,rest]

Maybe:

trefoil[t_] := {Sin[t] - 2 Sin[2 t], Cos[t] + 2 Cos[2 t], -Sin[3 t]}

ParametricPlot3D[trefoil[t],{t,0,2 Pi},Boxed->False,Axes->False,
  ViewPoint->{0,0,50},ViewVertical->{0,-1,0},PlotRange->4,
  ColorFunction->Function[{x,y,z,u},Hue@u],PlotPoints->300
]/.Line[pts_,rest___]:>Tube[pts,0.8,rest]

POSTED BY: Hans Milton

Vincent Jonker

Posted 27 days ago

is there anybody who likes to help me, please! vincent

POSTED BY: Vincent Jonker

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