Arcs on a plane in 3-D drawing

Question

I'd like to do the following figure using TikZ:

I would know how to to this using \clip, \draw, arc and \draw[->] in 2D. But how can I draw this on a plane that lies in the x-z plane?

Answer 1

The tikz-3dplot package totally rocks. I just drew my picture in the x-y-plane and rotated it then. The only caveat is that rectangle does not work any more, one has to supply all four corners by hand.

\begin{tikzpicture}[scale=2]
    \tdplotsetmaincoords{45}{200}

    \begin{scope}[tdplot_main_coords]
        \draw (0, 0) -- (5, 0) -- (5, 5) -- (0, 5) -- cycle;
        \node[below right] at (0, 5) {$\R^3$};

        \begin{scope}
            \clip (0, 0) -- (5, 0) -- (5, 5) -- (0, 5) -- cycle;
            \fill[opacity=20, color=black!20] ($(1, 1)+(45:3)+(0.5, 0)$) arc (0:360:0.5);
            \begin{scope}[->, thick]
                \draw (1, 1) -- ++(60:3) node[midway, below] {$t$};
                \draw (1, 1) -- ++(100:2.5) node[midway, right] {$t_0$};
                \draw (1, 1) -- ++(30:3.5) node[midway, below] {$t_1$};
                \draw (1, 1) -- ++(0:1.5) node[midway, above] {$t$};
            \end{scope}
            \draw (4, 1) arc (0:360:3);
            \draw (3.5, 1) arc (0:360:2.5);
            \draw (4.5, 1) arc (0:360:3.5);
            \draw (2.5, 1) arc (0:360:1.5);
        \end{scope}

        \draw[thick, ->] (5, 5, 0) -- ++(0, 0, 2) node[sloped, midway, above] {Zeitachse};  
    \end{scope}
\end{tikzpicture}