Message Boards

WOLFRAM COMMUNITY

9386 Views

2 Replies

2 Total Likes

View groups...

Follow this post

Share this post:

GROUPS:

Plot a torus knot with ParametricPlot3D?

Luis Ledesma

Posted 8 years ago

Hello everyone, I hope you can explain why I am getting an empty graphic, I happen to be taking the code that Paul Nylander shares on his web page, and when I run it in mathematica I do not get any graphics, here I share a screenshot so that understand my problem better, I think the problem is in how it uses ParametricPlot3D, but I hope someone who knows the reason, please explain, thanks in advance. Image and code from Paul`s page Code used for me, this is normalize[x_] := x/Sqrt[x.x]; p[t_] := {(1 + 0.3 Cos[11 t/3]) Cos[t], (1 + 0.3 Cos[11 t/3]) Sin[t], 0.3 Sin[11 t/3]}; f[t_, theta_] := Module[{dp = p'[t], ddp = p''[t], tangent, normal1, normal2}, tangent = normalize[dp]; normal1 = normalize[ddp (dp.dp) - dp (dp.ddp)]; normal2 = Cross[tangent, normal1]; p[t] + 0.1 (normal1 Cos[theta] + normal2 Sin[theta])]; ParametricPlot3D[ Append[f[t, theta], {EdgeForm[], SurfaceColor[Hue[t/(2 Pi)]]}], {t, 0, 6 Pi}, {theta, 0, 2 Pi}, PlotPoints -> {360, 15}, Compiled -> False]

Hello everyone, I hope you can explain why I am getting an empty graphic, I happen to be taking the code that Paul Nylander shares on his web page, and when I run it in mathematica I do not get any graphics, here I share a screenshot so that understand my problem better,

graphic obtained

I think the problem is in how it uses ParametricPlot3D, but I hope someone who knows the reason, please explain, thanks in advance.

Image and code from Paul`s page

how make it

Code used for me, this is

normalize[x_] := x/Sqrt[x.x]; 
p[t_] := {(1 + 0.3 Cos[11 t/3]) Cos[t], (1 + 0.3 Cos[11 t/3]) Sin[t], 
  0.3 Sin[11 t/3]};
f[t_, theta_] := 
  Module[{dp = p'[t], ddp = p''[t], tangent, normal1, normal2}, 
   tangent = normalize[dp]; 
   normal1 = normalize[ddp (dp.dp) - dp (dp.ddp)]; 
   normal2 = Cross[tangent, normal1]; 
   p[t] + 0.1 (normal1 Cos[theta] + normal2 Sin[theta])];

ParametricPlot3D[
 Append[f[t, theta], {EdgeForm[], SurfaceColor[Hue[t/(2 Pi)]]}], {t, 
  0, 6 Pi}, {theta, 0, 2 Pi}, PlotPoints -> {360, 15}, 
 Compiled -> False]

POSTED BY: Luis Ledesma

2 Replies

Sort By:

Luis Ledesma

Posted 8 years ago

Thank you very much for your great help Sander now if you get the graph that I thought, I kept browsing Paul's page and I'm interested in the following image, But now it turns out that you get another error message related to Raster Array, I share the image so you have an idea of what I am talking about, when switching from RasterArray to Raster I get an empty graph again. To conclude I would like to tell you that Paul used version 4 of Mathematica that is why it changes the commands considerably. Saludos y gracias amigo. V1[{x_, y_}] := {Sin[x], Sin[y]}; F1[p_] := Module[{p2 = {{0.81, -0.33}, {0.08, 0.89}}.p + {0.24, -0.07}}, 0.88p2 + 0.12V1[p2]]; F2[p_] := Module[{p2 = {{0.3, 0.52}, {-0.56, 0.37}}.p + {-0.09, -0.42}}, 0.88p2 + 0.12V1[p2]]; F3[p_] := V1[{{-0.43, 0.38}, {-0.2, -0.44}}.p + {1.74, 1.21}]; F4[p_] := V1[{{-0.49, -0.27}, {0.28, -0.53}}.p + {0.51, 0.62}]; w1 = 0.65; w2 = 0.29; w3 = 0.03; w4 = 0.03; n = 275; image = Table[{0, 0, 0}, {n}, {n}]; p = {0, 0}; Do[x = Random[]; k = Which[x < w1, 1, x < w1 + w2, 2, x < w1 + w2 + w3, 3, True, 4]; p = {F1, F2, F3, F4}[[k]][p]; {j,i} = Round[n{p[[1]] + 1.1, p[[2]] + 1.8}/3]; image[[i, j]] += List @@ ToColor[Hue[k/4.0], RGBColor], {100000}]; Show[Graphics[RasterArray[Map[RGBColor @@ Map[(1 - Exp[-0.2#]) &, #] &, image, {2}]], AspectRatio -> 1]]

Thank you very much for your great help Sander now if you get the graph that I thought, I kept browsing Paul's page and I'm interested in the following image, But now it turns out that you get another error message related to Raster Array, I share the image so you have an idea of what I am talking about, when switching from RasterArray to Raster I get an empty graph again. To conclude I would like to tell you that Paul used version 4 of Mathematica that is why it changes the commands considerably. Saludos y gracias amigo.

RasterArray

V1[{x_, y_}] := {Sin[x], Sin[y]};
F1[p_] := Module[{p2 = {{0.81, -0.33}, {0.08, 0.89}}.p + {0.24, -0.07}}, 0.88p2 + 0.12V1[p2]];
F2[p_] := Module[{p2 = {{0.3, 0.52}, {-0.56, 0.37}}.p + {-0.09, -0.42}}, 0.88p2 + 0.12V1[p2]];
F3[p_] := V1[{{-0.43, 0.38}, {-0.2, -0.44}}.p + {1.74, 1.21}];
F4[p_] := V1[{{-0.49, -0.27}, {0.28, -0.53}}.p + {0.51, 0.62}];
w1 = 0.65; w2 = 0.29; w3 = 0.03; w4 = 0.03;
n = 275; image = Table[{0, 0, 0}, {n}, {n}]; p = {0, 0};
Do[x = Random[]; k = Which[x < w1, 1, x < w1 + w2, 2, x < w1 + w2 + w3, 3, True, 4]; p = {F1, F2, F3, F4}[[k]][p]; {j,i} = Round[n{p[[1]] + 1.1, p[[2]] + 1.8}/3]; image[[i, j]] += List @@ ToColor[Hue[k/4.0], RGBColor], {100000}];
Show[Graphics[RasterArray[Map[RGBColor @@ Map[(1 - Exp[-0.2#]) &, #] &, image, {2}]], AspectRatio -> 1]]

POSTED BY: Luis Ledesma

Sander Huisman

Sander Huisman, University of Twente

Posted 8 years ago

Here is the correct one: p[t_]:={(1+0.3 Cos[11 t/3]) Cos[t],(1+0.3 Cos[11 t/3]) Sin[t],0.3 Sin[11 t/3]}; f[t_,theta_]:=Module[{dp=p'[t],ddp=p''[t],tangent,normal1,normal2}, tangent=Normalize[dp]; normal1=Normalize[ddp (dp.dp)-dp (dp.ddp)]; normal2=Cross[tangent,normal1]; p[t]+0.1 (normal1 Cos[theta]+normal2 Sin[theta]) ]; ParametricPlot3D[f[t,theta],{t,0,6 Pi},{theta,0,2 Pi},ColorFunction->Function[{x,y,z,u,v},Hue[u]],PlotPoints->{160, 20},MaxRecursion->0] You can't specify the surface color like the website does, perhaps in a VERY old version it was possible. I can't remember that though... You have to use ColorFunction. Note that Normalize is available in the Wolfram Language. Speed can be improved by not repeating the differentiation each time...

Here is the correct one:

p[t_]:={(1+0.3 Cos[11 t/3]) Cos[t],(1+0.3 Cos[11 t/3]) Sin[t],0.3 Sin[11 t/3]};
f[t_,theta_]:=Module[{dp=p'[t],ddp=p''[t],tangent,normal1,normal2},
    tangent=Normalize[dp];
    normal1=Normalize[ddp (dp.dp)-dp (dp.ddp)];
    normal2=Cross[tangent,normal1];
    p[t]+0.1 (normal1 Cos[theta]+normal2 Sin[theta])
];

ParametricPlot3D[f[t,theta],{t,0,6 Pi},{theta,0,2 Pi},ColorFunction->Function[{x,y,z,u,v},Hue[u]],PlotPoints->{160, 20},MaxRecursion->0]

You can't specify the surface color like the website does, perhaps in a VERY old version it was possible. I can't remember that though... You have to use ColorFunction. Note that Normalize is available in the Wolfram Language. Speed can be improved by not repeating the differentiation each time...

POSTED BY: Sander Huisman

Reply to this discussion

Reply Preview

Attachments

Remove Add a file to this post

Follow this discussion

or Discard

Group Abstract

Feedback