Drawing a ring around a torus (doughnut) using TikZ

Question

I was trying to draw a 2-torus (a doughnut) using TikZ, based on the answer to my previous question Moebius Strip using Tikz, and got the following

The result is impressive! However, the vertical circle does not look as surrounding the torus.

Q:

How could I give the right perspective of 3D?

MWE

WARNING: main tex-memory of my computer has been enhanced to compite this code

\documentclass{report}
\usepackage{amsmath,units}
\usepackage{pgfplots}

\begin{document}
\begin{tikzpicture}
  \begin{axis}[
      hide axis,
      view={60}{60}
    ]
    \addplot3 [
      surf, shader=interp,
      point meta=x,
      colormap/greenyellow,
      samples=40,
      samples y=40,
      z buffer=sort,
      domain=0:360,
      y domain=0:360
    ] (
              {(3.5 + 0.5*cos(y))*cos(x)},
              {(3.5 + 0.5*cos(y))*sin(x)},
              {0.5*sin(y)});
    \addplot3 [
     samples=40,
     domain=0:360,
     thick
    ] (
              {(3.5 + 0.5*cos(80))*cos(x)},
              {(3.5 + 0.5*cos(80))*sin(x)},
              {0.5*sin(80)});
    \addplot3 [
      samples=40,
      domain=0:360,
      thick
    ] (
              {3.5 + 0.5*cos(x)},
              {0},
              {0.5*sin(x)});

  \end{axis}
\end{tikzpicture}

\end{document}

Answer 1

You'll have to manually adjust the domain over which the circle is evaluated, so that it's only drawn on the visible side:

\documentclass{report}
\usepackage{amsmath,units}
\usepackage{pgfplots}

\begin{document}
\begin{tikzpicture}
  \begin{axis}[
      hide axis,
      view={60}{30},
      axis equal image,
    ]
    \addplot3 [
      surf, shader=interp,
      point meta=x,
      colormap/greenyellow,
      samples=40,
      samples y=20,
      z buffer=sort,
      domain=0:360,
      y domain=0:360
    ] (
              {(3.5 + 0.5*cos(y))*cos(x)},
              {(3.5 + 0.5*cos(y))*sin(x)},
              {0.5*sin(y)});
    \addplot3 [
     samples=40,
     samples y=1,
     domain=0:360,
     thick
    ] (
              {(3.5 + 0.5*cos(80))*cos(x)},
              {(3.5 + 0.5*cos(80))*sin(x)},
              {0.5*sin(80)});
    \addplot3 [
      samples=10,
      samples y=1,
      domain=-65:130,
      thick
    ] (
              {3.5 + 0.5*cos(x)},
              {0},
              {0.5*sin(x)});

  \end{axis}
\end{tikzpicture}

\end{document}