term-paper-hypergeom
view doc/klein-to-poincare.tkz.tex @ 91:c0059cb09e04
providecommand → newcommand
| author | Dmitry Dzhus <dima@sphinx.net.ru> |
|---|---|
| date | Thu Dec 18 20:21:03 2008 +0300 (14 months ago) |
| parents | 7622fa588b4f |
| children |
line source
1 \begin{figure}[!hbt]
2 \centering
3 \begin{tikzpicture}[scale=1.85]
4 \coordinate (O) at (0, 0) {};
6 % Klein model points
7 \coordinate (P) at (-1.42, .04) {};
8 \coordinate (Q) at (-0.933,-0.48) {};
10 % Projections onto sphere
11 \coordinate (Ps) at (-1.42,-.85) {};
12 \coordinate (Qs) at (-0.93,-1.3) {};
14 % Sphere poles
15 \coordinate [label=above:$N$] (N) at (0, 2) {};
16 \coordinate (S) at (0, -2) {};
18 % Disk control points
19 \coordinate [] (L) at ($ (O)-(2,0) $) {};
20 \coordinate [] (R) at ($ (O)+(2,0) $) {};
22 % Projection lines
23 \draw (P)--(Ps);
24 \coordinate (Pp)
25 at (intersection of Ps--N and O--P);
26 \draw (Ps)--(Pp);
27 \draw (Q)--(Qs);
28 \coordinate (Qp)
29 at (intersection of Qs--N and O--Q);
30 \draw (Qs)--(Qp);
33 % Fade lower hemisphere
34 \path [fill=white, opacity=.5]
35 (L) to[out=270,in=180] (S)
36 to[out=0,in=270] (R)
37 (O) ellipse(2 and 1);
39 % Klein disk
40 \draw [opacity=.3, pattern=north east lines]
41 (O) ellipse(2 and 1);
42 \draw [thick] (O) ellipse(2 and 1);
44 % Chord
45 \coordinate [dot] (X) at (-1.8,0.4358) {};
46 \coordinate [dot] (Y) at (-0.464,-0.97) {};
47 \draw[] (X)--(Y);
48 \draw[] (X) to[out=-15,in=135,looseness=.9] (Pp)
49 to [out=315,in=120,looseness=.7] (Qp)
50 to[out=300,in=65,looseness=.8] (Y);
52 % Visible projection lines
53 \draw (Pp)--(N);
54 \draw (P)--(O);
55 \draw (Qp)--(N);
56 \draw (Q)--(O);
58 % Sphere
59 \draw[thick] (O) circle(2);
61 % labels placed last
62 \begin{scope}[inner sep=2pt]
63 \node [label=below:$X$] at (X){};
64 \node [label=below:$Y$] at (Y){};
65 \node [label=right:$O$] at (O){};
66 \node [label=left:$P$] at (P){};
67 \node [label=left:$Q$] at (Q){};
68 \node [label=above:$P^\prime$] at (Pp){};
69 \node [inner sep=4pt,label=right:$Q^\prime$] at (Qp){};
70 \node [label=below:$P_s$] at (Ps){};
71 \node [label=below:$Q_s$] at (Qs){};
72 \end{scope}
74 % dot marks
75 \foreach \p in {O,P,Pp,Q,Qp,N} \draw node[dot] at (\p) {};
76 \node[dot,color=gray] at (Ps) {};
77 \node[dot,color=gray] at (Qs) {};
78 \end{tikzpicture}
79 \caption[Связь моделей Клейна и Пуанкаре]{Связь моделей Клейна и
80 Пуанкаре: $\xi(P) = P^\prime,\: \xi(Q)=Q^\prime$}
81 \label{fig:klein-to-poincare}
82 \end{figure}