Drawing a 3D plot of a lower half of a torus

Question

As the title suggests, I would like a 3D plot of a lower half of a hollow torus with small radius 1 and large radius 2. I found an image online that resembles what I am looking for.

Could anyone find a simple way to recreate the above image, including the downward pointing blue arrow and labelled axes drawn on?

Answer 1

I present an asymptote example because this yields the arguably nicer output. However, the parametrization of the half-torus can be used for other packages as well.

 \documentclass{article}
 \usepackage[inline]{asymptote}
 \begin{document}
 \thispagestyle{empty}
 \begin{asy}
  size(200);
  import graph3;

  currentprojection=perspective(5,6,3);
  real R=4;
  real a=1;

  triple fs(pair t) {
    return ((R+a*Cos(t.y))*Cos(t.x),(R+a*Cos(t.y))*Sin(t.x),a*Sin(t.y));
  };

  surface s=surface(fs,(0,180),(360,360),8,8,Spline);
  draw(s,surfacepen=material(green+opacity(0.6), emissivepen=0.2*white),render(compression=Low,merge=true));

  xaxis3(Label("$x$",1),xmin=0,xmax=7,Arrow3);
  yaxis3(Label("$y$",1),ymin=0,ymax=7,Arrow3);
  zaxis3(Label("$z$",1),zmin=0,zmax=4,Arrow3);

  draw((4/sqrt(2),4/sqrt(2),-1)--(4/sqrt(2),4/sqrt(2),-4),blue,Arrow3);
 \end{asy}
 \end{document}

Of course, one needs to run asy between two compilations.

It is possible to draw similar picture with pgfplots.

\documentclass[svgnames]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.13}

\begin{document}
\begin{tikzpicture}
    \begin{axis}[
        axis lines=center,
        axis equal,
        domain=0:360,
        y domain=180:360,
         ticks=none,
        view={130}{-35}
    ]

        \addplot3 [surf, color=green, opacity=0.1,faceted
        color=green!50!black,fill opacity=0.5%,faceted color=blue,z buffer=sort
        ]({(4+cos(y))*cos(x)},{(4+cos(y))*sin(x)},{sin(y)-0.01});
    \end{axis}
\end{tikzpicture}
\end{document}

However, the outcome is, arguably, less appealing. Of course, with additional effort one may improve this. On the other hand, the nice thing about asymptote is that there this additional effort is not necessary.