doc/klein-model.tkz.tex

\begin{figure}[thb]
  \centering
  \begin{tikzpicture}[scale=4.4]
    \coordinate [] (O) at (0, 0) {};

    \coordinate [label=above right:$X$] (X) at (60:1) {};
    \coordinate [label=below left:$Y$] (Y) at (200:1) {};

    \coordinate [label=above left:$A$] (A) at ($ (Y)!.3!(X)$) {};
    \coordinate [label=above left:$B$] (B) at ($ (X)!.2!(Y)$) {};

    \coordinate [label=below:$M$] (M) at (280:1) {};
    \coordinate [label=below right:$N$] (N) at (330:1) {};
    
    \coordinate [label=above left:$P$] (P) at (intersection of X--M and Y--N) {};
    
    % disk model
    \node [draw,thick,circle through=(X)] (circle) at (O) {};

    % chords
    \draw (X) --node[auto]{$l$} (Y);
    \draw (X) -- (M);
    \draw (Y) -- (N);

    % a bundle of parallel lines
    \begin{scope}
      \clip (O) circle(1);
      \foreach \a in {0,...,6} \draw[very thin]
                                ($ (P)+(180+\a*12:2) $) -- 
                                ($ (P)+(\a*12:2) $);
    \end{scope}

    %dot marks
    \foreach \p in {X, Y, A, B, P, M, N} \draw node[dot] at (\p) {};
  \end{tikzpicture}
  \caption{Модель Клейна в круге}
  \label{fig:klein-model}
\end{figure}