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Making a Torus seems simple enough, but how do I project it along the x-axis?

For example, I want to rotate this:

flat torus

And make it look like this:

x-axis torus

Thanks for who can help!

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    $\begingroup$ related q/a: How to set viewpoint Graphics3D to a different default orientation? $\endgroup$
    – kglr
    Apr 6 '15 at 0:34
  • $\begingroup$ maybe ParametricPlot3D[ RotateLeft@{Cos[t] (3 + Cos[u]), Sin[t] (3 + Cos[u]), Sin[u]}, {u, 0, 2 Pi}, {t, 0, 2 Pi}, ViewPoint -> {-2., -1.5, 2.5}]? $\endgroup$
    – kglr
    Apr 6 '15 at 0:51
  • $\begingroup$ RotateLeft seems to have done the trick. Did you want to write that up in an answer? I can then edit it with the final code. Thank you $\endgroup$ Apr 6 '15 at 1:10
  • $\begingroup$ crockpotveggies, just posted the comment as an answer. $\endgroup$
    – kglr
    Apr 6 '15 at 1:13
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ParametricPlot3D[ RotateLeft@{Cos[t] (3 + Cos[u]), Sin[t] (3 + Cos[u]), Sin[u]}, 
  {u, 0, 2 Pi}, {t, 0, 2 Pi}, ViewPoint -> {-2., -1.5, 2.5}]

enter image description here

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Direct swap among orthogonal vector components:

ParametricPlot3D[{Sin[t] (3 + Cos[u]), Cos[t] (3 + Cos[u]), 
  Sin[u]}, {u, 0, 2 Pi}, {t, 0, 2 Pi}]
ParametricPlot3D[{Sin[u], Cos[t] (3 + Cos[u]), 
  Sin[t] (3 + Cos[u])}, {u, 0, 2 Pi}, {t, 0, 2 Pi}]
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