I am trying to reconstruct this image here
I am not very happy with the code, as it uses hacking and adding white boxes and alike. My problem is now how do I draw the somewhat arbitary function in the figure? I tried to do a polynomial fit, but that did not work. I got dimensions to large, would a spline solution work better?
\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{patterns}
\usepackage{pgfplots}
\pgfplotsset{compat=1.6}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
xmin=-0.1,xmax=5,
xlabel={z},
ymin=0,ymax=4.5,
xtick={2.5,4},
xticklabels={$v_1$,$v_2$},
ytick={2.5,3.5},
yticklabels={$u_1$,$u_2$},
xlabel={$u$},
ylabel={$v$},
axis lines=middle]
\draw [fill=gray!40!white,thick,dashed] (axis cs:0,0) rectangle (axis cs:4,3.5);
\draw [color=black,fill=white,thick,dashed] (axis cs:0,0) rectangle (axis cs:2.5,2);
\draw [fill=black] (axis cs:0,0) rectangle (axis cs:0.01,4.45);
\addplot+[black,thick,domain=0:5,no marks] {0};
%
\node at (axis cs:2.5,0) [anchor=south west] {$A$};
\node at (axis cs:4,0) [anchor=south west] {$A'$};
\node at (axis cs:2.8,2.2) [anchor=north] {$B$};
\node at (axis cs:4.2,4) [anchor=north] {$B'$};
\node at (axis cs:0.25,2.5) [anchor=north] {$C$};
\node at (axis cs:0.25,4) [anchor=north] {$C'$};
\node at (axis cs:0,0) [anchor=south west] {$O$};
%
\end{axis}
\end{tikzpicture}
\end{document}