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.