How to draw a ring-like diagram with some labels on its arcs?

Question

I would like to draw a figure that looks like the following scenario:

Consider a circle of radius $r$, described parametrically by $x = cos(t) and y = sin(t)$. I'd like to draw a figure where the 90 to 180 degrees arc and the 270 to 360 arc are stretched by adding 1 to the previous point, while keeping the figure connected. Here is a sketch of the figure below: (x and y axis should not be included in the final figure).

The respective labels are $\Omega_1$, $\partial \varphi(1)$, $\partial \varphi (1)$, $t=0$, $t=1$, $t=0$, $t=1$, $\phi^2$, $\Omega_2$

Any help would be greatly appreciated.

Here is part of the picture that I have drawn:

\begin{pspicture}(-.5,-.5)(3.5,3.5)
\psaxes[labels=none,ticks=none]{->}(0,0)(-.5,-.5)(3,3)[$x$,0][$y$,90]
\pscustom[fillstyle=solid,fillcolor=lightgray]
{
 \psarc(0,0){2.5}{0}{90}
 \psarcn(0,0){1.5}{90}{0}
 \closepath
   }
   \rput(2;45){$\Delta \mathfrak{M}$}
    \end{pspicture}

I'd also like to have an additional label $\Delta \mathfrak{M}$ in each annulus as well as for them to be shaded.

Answer 1

\documentclass[tikz,margin=10pt]{standalone}
\usepackage{mathtools,amssymb}
\begin{document}
\begin{tikzpicture}[scale=2,transform shape]
\draw (1,0) arc (0:90:1);
\draw (-1,0) arc (180:270:1);
\draw[fill=gray!30] (-1,0) -- (-2,0) arc (180:90:2) -- (0,1) arc (90:180:1);
\draw[fill=gray!30] (1,0) -- (2,0) arc (0:-90:2) -- (0,-1) arc (-90:0:1);
\node at (0.2,0.75) {\tiny $\phi^2$};
\node[rotate=50] at (-0.7,0.5) {\tiny $t=0$};
\node[rotate=50] at (0.7,-0.5) {\tiny $t=0$};
\node[rotate=50] at (-1.45,1.2) {\tiny $t=1$};
\node[rotate=50] at (1.45,-1.2) {\tiny $t=1$};
\node[rotate=50] at (-1.6,1.4) {\tiny $\partial \varphi (1)$};
\node[rotate=50] at (1.6,-1.4) {\tiny $\partial \varphi (1)$};
\node at (-2,2) {\tiny $\Omega_1$};
\node at (2,-2) {\tiny $\Omega_2$};
\node at (-1,1) {\tiny $\Delta \mathfrak{M}^2$};
\node at (1,-1) {\tiny $\Delta \mathfrak{M}^2$};
\end{tikzpicture}

\end{document}

Answer 2

With the next version of TikZ it is finally possible to place nodes along arcs. This is used here with the CVS version of TikZ. (Although, it is relatively easy to calculate the positions and rotations here manually.)

For more information, refer to

• How can I update TikZ/PGF?
• How to place a node in the middle of an arc? (and many more)
• Draw arc in tikz when center of circle is specified
• TikZ: using the ellipse command with a start and end angle instead of an arc

Code

\documentclass[tikz]{standalone}
\usepackage{amssymb}
\begin{document}
\begin{tikzpicture}[>=latex, declare function={smallR=2; bigR=2*smallR;}, delta angle=90,
  my ring sectors/.style={fill=gray, nodes={midway, sloped}}]
\filldraw[my ring sectors]
  (left:smallR) arc[radius=smallR, start angle=180, delta angle=-90] node[below] {$t=0$}
   -- (up:bigR) arc[radius=bigR, start angle=90]                     node[below] {$t=1$}
                  node[above] {$\partial\varphi(1)$} -- cycle
  (right:smallR) arc[radius=smallR, start angle=0, delta angle=-90]  node[above] {$t=0$}
  -- (down:bigR) arc[radius=bigR, start angle=-90]                   node[above] {$t=1$}
                   node[below] {$\partial\varphi(1)$} -- cycle;

\draw[radius=smallR] (right:smallR) arc[start angle=0]
                      (left:smallR) arc[start angle=180];
\node[below] at (up:smallR) {$\phi^2$};
\path (-bigR,bigR) -- 
  node[at start]   {$\Omega_1$}
  node[near start] {$\Delta \mathfrak{M}^2$}% or at (135:.5*bigR+.5*smallR)
  node[near end]   {$\Delta \mathfrak{M}^2$}% or at (-45:.5*bigR+.5*smallR)
  node[at end]     {$\Omega_2$} (bigR,-bigR);
\end{tikzpicture}
\end{document}

Output

Answer 3

Exploiting the symmetrical properties of the diagram in question with PSTricks. It only consumes 583 characters.

\documentclass[pstricks,border=12pt]{standalone}
\usepackage{amssymb}
\SpecialCoor
\degrees[8]

\def\Atom#1%
{%
    \pscustom[fillstyle=solid,fillcolor=lightgray]
    {
        \psarc(0,0){4}{2}{4}
        \psarcn(0,0){2}{4}{2}
        \closepath
    }
    \foreach \A/\B/\C in 
    {   
        1.7/0/t=0, 
        3.0/1/\Delta \mathfrak{M}^2, 
        3.7/0/t=1, 
        4.3/0/\partial \varphi (1)
    }
    {
        \rput{\ifnum\B=1 *0\else *1\fi}(\A;3){$\C$}
        \rput{*0}(-4,4){$\Omega_#1$}
    }%
}

\begin{document}
\begin{pspicture}(-4,-4)(4,4)
    \Atom1
    \rput{4}{\Atom2}
    \pscircle[dimen=m]{2}
    \rput(1.7;2){$\phi^2$}
\end{pspicture}
\end{document}

Answer 4

An alternative to the answers already given:

\documentclass{standalone}
\usepackage{tikz}
\usepackage{amssymb}
\begin{document}
\tikz{\foreach\i in{0,180}
 \path[rotate=\i,fill=gray,draw=black](0:0)--(0:3)arc(0:-90:3)--cycle;
\fill[draw=black,fill=white]circle[radius=1.5];
\foreach\i in{1,2}
 \foreach\r/\s[count=\c]in{5/t=0,8/\Delta\mathfrak M^2,11/t=1,20/\Omega_\i,13/\partial\varphi(1)}
  \node[rotate={mod(\c,2)*45}]at(\i*180-45:\r/4){$\s$};
\node at(90:1.25){$\Phi^2$};}
\end{document}

Answer 5

Countdown=457 characters (Asymptote,Linux). ring.asy:

size(220);
usepackage("amssymb");
draw(unitcircle);
string[] s={"$\partial\varphi(1)$","$t=0$","$t=1$","$\Omega_","$\Delta\mathfrak{M}^2$"};
real[] d={2,1,2,-2,-1,-2};
pair[] p={NW,SE,SE,SE,NW,NW};
guide r=arc(N-N,2,90,180)--arc(N-N,1,180,90,CW)--cycle;
filldraw(rotate(180)*r^^r,gray);
for(int i=0;i<6;++i){
  label(rotate(45)*s[i%3],d[i]*NW,p[i]);
}
label("$\phi^2$",N,S);
label(s[3]+"1$",3NW);
label(s[3]+"2$",3SE);
label(s[4],1.5NW);
label(s[4],1.5SE);

To get a standalone ring.pdf, run asy -f pdf ring.asy.

Answer 6

Here is my crack at it. I personally find the notation draw(x1,y1) to[in=A,out=B](x2,y2); much easier to work with, as opposed to the crypto mind-bending arc and friends which makes me want to go and drink something strong.

@Jake made a great suggestion to replace with bend right=45 or bend left=45 instead which is even easier to understand.

\documentclass[tikz]{standalone}
\usepackage{amssymb,mathpazo}
\begin{document}
    \begin{tikzpicture}
        \tikzset{e/.style={rotate=45},
                 n/.style={e,anchor=north},
                 s/.style={e,anchor=south},
                 f/.style={fill=lightgray},
                 bl/.style={bend left=45},
                 br/.style={bend right=45},}
        \draw   (2, 0) to[br] (0, 2) 
                (-2,0) to[br] (0,-2);
        \draw[f](0, 2) to[br] (-2,0) -- (-4,0) to[bl] (0, 4) -- (0, 2) 
                (0,-2) to[br] (2, 0) -- (4, 0) to[bl] (0,-4) -- (0,-2);
        \node[anchor=north]at (0,2){$\phi^2$};
        \node at (-4,4){$\Omega_1$};
        \node at (4,-4){$\Omega_2$};
        \node[n] at (-1.4,1.4){$t=0$};
        \node[s] at (1.4,-1.4){$t=0$};
        \node[n] at (-2.8,2.8){$t=1$};
        \node[s] at (2.8,-2.8){$t=1$};
        \node[s] at (-2.8,2.8){$\partial \varphi(1)$};
        \node[n] at (2.8,-2.8){$\partial \varphi(1)$};
        \node at (-2.1,2.1) {$\Delta \mathfrak{M}^2$};
        \node at (2.1,-2.1) {$\Delta \mathfrak{M}^2$};
    \end{tikzpicture}
\end{document}