From f5dc85609d5db143cbdefcbb1430b4dfec7a8d3f Mon Sep 17 00:00:00 2001
From: Nao Pross <np@0hm.ch>
Date: Thu, 22 Jul 2021 09:38:24 +0200
Subject: Create figure for stereographic projection

---
 .../tikz/stereographic-projections.tex             | 90 ++++++++++++++++++++++
 1 file changed, 90 insertions(+)
 create mode 100644 buch/papers/punktgruppen/tikz/stereographic-projections.tex

(limited to 'buch/papers/punktgruppen/tikz/stereographic-projections.tex')

diff --git a/buch/papers/punktgruppen/tikz/stereographic-projections.tex b/buch/papers/punktgruppen/tikz/stereographic-projections.tex
new file mode 100644
index 0000000..4091ad9
--- /dev/null
+++ b/buch/papers/punktgruppen/tikz/stereographic-projections.tex
@@ -0,0 +1,90 @@
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{times}
+\usepackage{txfonts}
+\usepackage{tikz-3dplot}
+
+\usetikzlibrary{arrows}
+\usetikzlibrary{intersections}
+\usetikzlibrary{math}
+\usetikzlibrary{positioning}
+\usetikzlibrary{arrows.meta}
+\usetikzlibrary{shapes.misc}
+\usetikzlibrary{calc}
+
+\begin{document}
+
+\tdplotsetmaincoords{60}{130}
+\pgfmathsetmacro{\l}{2}
+
+\begin{tikzpicture}[
+    >=latex,
+    tdplot_main_coords,
+    dot/.style = {
+      black, fill = black, circle,
+      outer sep = 0, inner sep = 0,
+      minimum size = 1mm 
+    },
+    round/.style = {
+      draw = orange, thick, circle,
+      minimum size = 1mm,
+      inner sep = 0pt, outer sep = 0pt,
+    },
+    cross/.style = {
+      cross out, draw = magenta, thick,
+      minimum size = 1mm, 
+      inner sep = 0pt, outer sep = 0pt
+    },
+  ]
+
+  % origin
+  \coordinate (O) at (0,0,0);
+
+  % poles
+  \coordinate (NP) at (0,0,\l);
+  \coordinate (SP) at (0,0,-\l);
+
+  % axis
+  % \draw[->] (O) -- ++(1.5*\l,0,0);
+  % \draw[->] (O) -- ++(0,1.5*\l,0);
+  % \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);
+
+  % meridians
+  \foreach \phi in {0, 30, 60, ..., 150}{
+    \tdplotsetrotatedcoords{\phi}{90}{0};
+    \tdplotdrawarc[lightgray, dashed, tdplot_rotated_coords]{(O)}{\l}{0}{360}{}{};
+  }
+
+  % dot above and its projection
+  \pgfmathsetmacro{\phi}{120}
+  \pgfmathsetmacro{\theta}{60}
+
+  \pgfmathsetmacro{\px}{cos(\phi)*sin(\theta)*\l}
+  \pgfmathsetmacro{\py}{sin(\phi)*sin(\theta)*\l}
+  \pgfmathsetmacro{\pz}{cos(\theta)*\l})
+
+  \coordinate (A) at (\px,\py,\pz);
+  \coordinate (Aproj) at ({\px * \l / (\l + \pz)}, {\py * \l / (\l + \pz)}, 0);
+
+  % projection line
+  \draw[] (A) to (SP);
+  \draw[gray] (SP) to (O) to (Aproj);
+
+  % dot
+  \draw (O) node[dot] {};
+  \draw (SP) node[dot] {};
+  \draw (A) node[dot, fill=magenta] {};
+  \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);
+
+\end{tikzpicture}
+\end{document}
+% vim:ts=2 sw=2 et:
-- 
cgit v1.2.1


From 472b3d0a253879552d139cc4f41a2e00e5f6e4f5 Mon Sep 17 00:00:00 2001
From: Nao Pross <np@0hm.ch>
Date: Fri, 23 Jul 2021 09:08:08 +0200
Subject: Change stereographic projection to Ci

---
 .../tikz/stereographic-projections.tex             | 34 +++++++++++++++++-----
 1 file changed, 26 insertions(+), 8 deletions(-)

(limited to 'buch/papers/punktgruppen/tikz/stereographic-projections.tex')

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}
-- 
cgit v1.2.1