Newbie to Mathematica ... Help to create a Deltoid Torus

Questions
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1

I want to create a Deltoid Torus where I can vary the parameters…the code I have is:

Manipulate[
 ParametricPlot3D[
  {Sin[u] (7 + Cos[u/3 - 2 v] + 2 Cos[u/3 + v]),
   Cos[u] (7 + Cos[u/3 - 2 v] + 2 Cos[u/3 + v]),
   Sin[u/3 - 2 v] + 2 Sin[u/3 + v]},
  {u, -Pi, Pi}, {v, -Pi, Pi}]
 ]

I need Manipulate I think.
Is ParametricPlot3D the right function?
I want to vary u and v with sliders.

Help! Thanks!

2

If you use Google to search for
Mathematica Umbilic torus
then hopefully one of the results you should see is a couple of pages from “Mathematica by Example” and on page 84 that shows one method of plotting what you are looking for.

If you have access to a library with a copy of the book or you can find a new or used copy to buy that might be even better.

3

The parameters “u” and “v” are local to the parametric plot, so it does not make sense to try and vary those. But you can vary just about everything else in this plot, for example:

Manipulate[
 ParametricPlot3D[{
   Sin[u] (rx + Cos[u/3 - 2 v] + 2 Cos[u/3 + v]),
   Cos[u] (ry + Cos[u/3 - 2 v] + 2 Cos[u/3 + v]),
   Sin[u/3 - 2 v] + 2 Sin[u/3 + v]},
  {u, umin, umax}, {v, vmin, vmax}],
 {{rx, 7}, 1, 10, 1},
 {{ry, 7}, 1, 10, 1},
 {{umin, -Pi}, -2 Pi, 2 Pi},
 {{umax, Pi}, -2 Pi, 2 Pi},
 {{vmin, -Pi}, -2 Pi, 2 Pi},
 {{vmax, Pi}, -2 Pi, 2 Pi}
 ]

2692Capture.PNG
2692Capture.PNG434×550 25.9 KB

4

Thank you very much Arnoud..