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-rw-r--r--buch/papers/punktgruppen/tikz/stereographic-projections.tex34
1 files changed, 26 insertions, 8 deletions
diff --git a/buch/papers/punktgruppen/tikz/stereographic-projections.tex b/buch/papers/punktgruppen/tikz/stereographic-projections.tex
index 4091ad9..7d612fb 100644
--- a/buch/papers/punktgruppen/tikz/stereographic-projections.tex
+++ b/buch/papers/punktgruppen/tikz/stereographic-projections.tex
@@ -50,9 +50,9 @@
% \draw[->] (O) -- ++(0,0,1.5*\l);
% gray unit circle
- \tdplotdrawarc[gray, dashed]{(O)}{\l}{0}{360}{}{};
- \draw[gray, dashed] (-\l, 0, 0) to (\l, 0, 0);
- \draw[gray, dashed] (0, -\l, 0) to (0, \l, 0);
+ \tdplotdrawarc[gray, thick]{(O)}{\l}{0}{360}{}{};
+ \draw[gray, dotted] (-\l, 0, 0) to (\l, 0, 0);
+ \draw[gray, dotted] (0, -\l, 0) to (0, \l, 0);
% meridians
\foreach \phi in {0, 30, 60, ..., 150}{
@@ -71,19 +71,37 @@
\coordinate (A) at (\px,\py,\pz);
\coordinate (Aproj) at ({\px * \l / (\l + \pz)}, {\py * \l / (\l + \pz)}, 0);
- % projection line
- \draw[] (A) to (SP);
+ % dot below and its projection
+ \pgfmathsetmacro{\phi}{-60}
+ \pgfmathsetmacro{\theta}{120}
+
+ \pgfmathsetmacro{\px}{cos(\phi)*sin(\theta)*\l}
+ \pgfmathsetmacro{\py}{sin(\phi)*sin(\theta)*\l}
+ \pgfmathsetmacro{\pz}{cos(\theta)*\l})
+
+ \coordinate (B) at (\px,\py,\pz);
+ \coordinate (Bproj) at ({\px * \l / (\l - \pz)}, {\py * \l / (\l - \pz)}, 0);
+
+ % projection lines
+ \draw[gray] (A) to (SP);
\draw[gray] (SP) to (O) to (Aproj);
- % dot
+ \draw[gray] (B) to (NP);
+ \draw[gray] (NP) to (O) to (Bproj);
+
+ % dots
\draw (O) node[dot] {};
\draw (SP) node[dot] {};
- \draw (A) node[dot, fill=magenta] {};
+ \draw (NP) node[dot] {};
+ \draw (A) node[dot, fill = magenta, minimum size = 1.5mm] {};
+ \draw (B) node[dot, fill = orange, minimum size = 1.5mm] {};
+
+ % projection markers
\draw[very thick, magenta]
(Aproj) ++(.15,0) to ($(Aproj)+(-.15, 0)$)
(Aproj) ++(0,.15) to ($(Aproj) +(0, -.15)$);
- % \draw (O) to ({cos(\phi)*\l}, {sin(\phi)*\l}, 0);
+ \tdplotdrawarc[orange, very thick]{(Bproj)}{.1}{0}{360}{}{};
\end{tikzpicture}
\end{document}