12 files changed, 337 insertions, 14 deletions
diff --git a/buch/papers/punktgruppen/tikz/atoms-grid-force.tex b/buch/papers/punktgruppen/tikz/atoms-grid-force.tex
new file mode 100644
index 0000000..05742cf
--- /dev/null
+++ b/buch/papers/punktgruppen/tikz/atoms-grid-force.tex
@@ -0,0 +1,42 @@
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{times}
+\usepackage{txfonts}
+
+\usetikzlibrary{arrows}
+\usetikzlibrary{intersections}
+\usetikzlibrary{math}
+\usetikzlibrary{positioning}
+\usetikzlibrary{arrows.meta}
+\usetikzlibrary{shapes.misc}
+\usetikzlibrary{calc}
+
+\begin{document}
+  \begin{tikzpicture}[
+      >=latex, 
+      node distance = 2mm,
+      charge/.style = {
+        circle, draw = black, thick,
+        minimum size = 5mm
+      },
+      positive/.style = { fill = red!50 },
+      negative/.style = { fill = blue!50 },
+    ]
+
+    \matrix[nodes = { charge }, row sep = 5mm, column sep = 1cm] {
+      \node[positive] (NW) {}; & \node[negative] (N) {}; & \node [positive] (NE) {}; \\
+      \node[negative] (W) {}; & \node[positive] {}; & \node [negative] (E) {}; \\
+      \node[positive] (SW) {}; & \node[negative] (S) {}; & \node [positive] (SE) {}; \\
+    };
+
+    \foreach \d in {NW, N, NE} {
+      \draw[orange, very thick, <-] (\d) to ++(0,.7);
+    }
+
+    \foreach \d in {SW, S, SE} {
+      \draw[orange, very thick, <-] (\d) to ++(0,-.7);
+    }
+
+    \draw[gray, dashed] (W) to (N) to (E) to (S) to (W);
+  \end{tikzpicture}
+\end{document}
diff --git a/buch/papers/punktgruppen/tikz/atoms-grid-still.tex b/buch/papers/punktgruppen/tikz/atoms-grid-still.tex
new file mode 100644
index 0000000..4e43856
--- /dev/null
+++ b/buch/papers/punktgruppen/tikz/atoms-grid-still.tex
@@ -0,0 +1,33 @@
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{times}
+\usepackage{txfonts}
+
+\usetikzlibrary{arrows}
+\usetikzlibrary{intersections}
+\usetikzlibrary{math}
+\usetikzlibrary{positioning}
+\usetikzlibrary{arrows.meta}
+\usetikzlibrary{shapes.misc}
+\usetikzlibrary{calc}
+
+\begin{document}
+  \begin{tikzpicture}[
+      >=latex, 
+      node distance = 2mm,
+      charge/.style = {
+        circle, draw = black, thick,
+        minimum size = 5mm
+      },
+      positive/.style = { fill = red!50 },
+      negative/.style = { fill = blue!50 },
+    ]
+
+    \matrix[nodes = { charge }, row sep = 8mm, column sep = 8mm] {
+      \node[positive] {}; & \node[negative] (N) {}; & \node [positive] {}; \\
+      \node[negative] (W) {}; & \node[positive] {}; & \node [negative] (E) {}; \\
+      \node[positive] {}; & \node[negative] (S) {}; & \node [positive] {}; \\
+    };
+    \draw[gray, dashed] (W) to (N) to (E) to (S) to (W);
+  \end{tikzpicture}
+\end{document}
diff --git a/buch/papers/punktgruppen/tikz/atoms-piezo-force-horizontal.tex b/buch/papers/punktgruppen/tikz/atoms-piezo-force-horizontal.tex
new file mode 100644
index 0000000..e4c3f93
--- /dev/null
+++ b/buch/papers/punktgruppen/tikz/atoms-piezo-force-horizontal.tex
@@ -0,0 +1,47 @@
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{times}
+\usepackage{txfonts}
+
+\usetikzlibrary{arrows}
+\usetikzlibrary{intersections}
+\usetikzlibrary{math}
+\usetikzlibrary{positioning}
+\usetikzlibrary{arrows.meta}
+\usetikzlibrary{shapes.misc}
+\usetikzlibrary{calc}
+
+\begin{document}
+  \begin{tikzpicture}[
+      >=latex, 
+      node distance = 2mm,
+      charge/.style = {
+        circle, draw = black, thick,
+        minimum size = 5mm
+      },
+      positive/.style = { fill = red!50 },
+      negative/.style = { fill = blue!50 },
+    ]
+
+    \node[charge, positive, yshift= 2.5mm] (C1) at ( 60:1.5cm) {};
+    \node[charge, negative, yshift= 2.5mm] (C2) at (120:1.5cm) {};
+    \node[charge, positive, xshift= 2.5mm] (C3) at (180:1.5cm) {};
+    \node[charge, negative, yshift=-2.5mm] (C4) at (240:1.5cm) {};
+    \node[charge, positive, yshift=-2.5mm] (C5) at (300:1.5cm) {};
+    \node[charge, negative, xshift=-2.5mm] (C6) at (360:1.5cm) {};
+
+    \draw[black] (C1) to (C2) to (C3) to (C4) to (C5) to (C6) to (C1);
+    % \draw[gray, dashed] (C2) to (C4) to (C6) to (C2);
+
+    \draw[orange, very thick, <-] (C6) to ++(.7,0);
+    \draw[orange, very thick, <-] (C3) to ++(-.7,0);
+
+    \node[black] (E) {\(\vec{E}_p\)};
+    \begin{scope}[node distance = .5mm]
+      \node[blue!50, right = of E] {\(-\)};
+      \node[red!50, left = of E] {\(+\)};
+    \end{scope}
+    % \draw[gray, thick, dotted] (E) to ++(0,2);
+    % \draw[gray, thick, dotted] (E) to ++(0,-2);
+  \end{tikzpicture}
+\end{document}
diff --git a/buch/papers/punktgruppen/tikz/atoms-piezo-force-vertical.tex b/buch/papers/punktgruppen/tikz/atoms-piezo-force-vertical.tex
new file mode 100644
index 0000000..892ab42
--- /dev/null
+++ b/buch/papers/punktgruppen/tikz/atoms-piezo-force-vertical.tex
@@ -0,0 +1,52 @@
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{times}
+\usepackage{txfonts}
+
+\usetikzlibrary{arrows}
+\usetikzlibrary{intersections}
+\usetikzlibrary{math}
+\usetikzlibrary{positioning}
+\usetikzlibrary{arrows.meta}
+\usetikzlibrary{shapes.misc}
+\usetikzlibrary{calc}
+
+\begin{document}
+  \begin{tikzpicture}[
+      >=latex, 
+      node distance = 2mm,
+      charge/.style = {
+        circle, draw = black, thick,
+        minimum size = 5mm
+      },
+      positive/.style = { fill = red!50 },
+      negative/.style = { fill = blue!50 },
+    ]
+
+    \node[charge, positive, yshift=-2.5mm] (C1) at ( 60:1.5cm) {};
+    \node[charge, negative, yshift=-2.5mm] (C2) at (120:1.5cm) {};
+    \node[charge, positive, xshift=-2.5mm] (C3) at (180:1.5cm) {};
+    \node[charge, negative, yshift= 2.5mm] (C4) at (240:1.5cm) {};
+    \node[charge, positive, yshift= 2.5mm] (C5) at (300:1.5cm) {};
+    \node[charge, negative, xshift= 2.5mm] (C6) at (360:1.5cm) {};
+
+    \draw[black] (C1) to (C2) to (C3) to (C4) to (C5) to (C6) to (C1);
+    % \draw[gray, dashed] (C2) to (C4) to (C6) to (C2);
+
+    \foreach \d in {C1, C2} {
+      \draw[orange, very thick, <-] (\d) to ++(0,.7);
+    }
+
+    \foreach \d in {C4, C5} {
+      \draw[orange, very thick, <-] (\d) to ++(0,-.7);
+    }
+
+    \node[black] (E) {\(\vec{E}_p\)};
+    \begin{scope}[node distance = .5mm]
+      \node[red!50, right = of E] {\(+\)};
+      \node[blue!50, left = of E] {\(-\)};
+    \end{scope}
+    % \draw[gray, thick, dotted] (E) to ++(0,2);
+    % \draw[gray, thick, dotted] (E) to ++(0,-2);
+  \end{tikzpicture}
+\end{document}
diff --git a/buch/papers/punktgruppen/tikz/atoms-piezo-still.tex b/buch/papers/punktgruppen/tikz/atoms-piezo-still.tex
new file mode 100644
index 0000000..2eb78ba
--- /dev/null
+++ b/buch/papers/punktgruppen/tikz/atoms-piezo-still.tex
@@ -0,0 +1,34 @@
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{times}
+\usepackage{txfonts}
+
+\usetikzlibrary{arrows}
+\usetikzlibrary{intersections}
+\usetikzlibrary{math}
+\usetikzlibrary{positioning}
+\usetikzlibrary{arrows.meta}
+\usetikzlibrary{shapes.misc}
+\usetikzlibrary{calc}
+
+\begin{document}
+  \begin{tikzpicture}[
+      >=latex, 
+      node distance = 2mm,
+      charge/.style = {
+        circle, draw = black, thick,
+        minimum size = 5mm
+      },
+      positive/.style = { fill = red!50 },
+      negative/.style = { fill = blue!50 },
+    ]
+
+    \foreach \x/\t [count=\i] in {60/positive, 120/negative, 180/positive, 240/negative, 300/positive, 360/negative} {
+      \node[charge, \t] (C\i) at (\x:1.5cm) {};
+    }
+
+    \draw[black] (C1) to (C2) to (C3) to (C4) to (C5) to (C6) to (C1);
+    \node[circle, draw=gray, fill=gray, outer sep = 0, inner sep = 0, minimum size = 3mm] {};
+    % \draw[gray, dashed] (C2) to (C4) to (C6) to (C2);
+  \end{tikzpicture}
+\end{document}
diff --git a/buch/papers/punktgruppen/tikz/combine-symmetries.tex b/buch/papers/punktgruppen/tikz/combine-symmetries.tex
index 84e0a76..fa669ae 100644
--- a/buch/papers/punktgruppen/tikz/combine-symmetries.tex
+++ b/buch/papers/punktgruppen/tikz/combine-symmetries.tex
@@ -13,6 +13,7 @@
 
 \begin{document}
 \begin{tikzpicture}[
+    >=latex, 
     dot/.style = {
       draw, circle, thick, black, fill = gray!40!white,
       minimum size = 2mm,
@@ -45,7 +46,7 @@
     (A2) ++(-.5,0) arc (180:60:.5);
   \draw[red!80!black, dashed, thick, ->] (A2) to (B2);
 
-  \draw[yellow!50!orange, thick, ->]
+  \draw[cyan!40!blue, thick, ->]
     (B1) to node[above, midway] {\(\vec{Q}'\)} (B2);
 
   \draw[gray, dashed, thick] (A1) to (A1 |- B1) node (Xl) {};
diff --git a/buch/papers/punktgruppen/tikz/lattice.tex b/buch/papers/punktgruppen/tikz/lattice.tex
index 9c05af3..a6b1876 100644
--- a/buch/papers/punktgruppen/tikz/lattice.tex
+++ b/buch/papers/punktgruppen/tikz/lattice.tex
@@ -13,23 +13,24 @@
 
 \begin{document}
 \begin{tikzpicture}[
-	dot/.style = {
-	  draw, circle, thick, black, fill = gray!40!white,
-	  minimum size = 2mm,
-	  inner sep = 0pt,
-	  outer sep = 1mm,
-	},
+    >=latex, 
+    dot/.style = {
+      draw, circle, thick, black, fill = gray!40!white,
+      minimum size = 2mm,
+      inner sep = 0pt,
+      outer sep = 1mm,
+    },
   ]
 
   \begin{scope}
-	\clip (-2,-2) rectangle (3,4);
+	\clip (-2,-2) rectangle (7,2);
 	\foreach \y in {-7,-6,...,7} {
 	  \foreach \x in {-7,-6,...,7} {
 		\node[dot, xshift=3mm*\y] (N\x\y) at (\x, \y) {};
 	  }
 	}
   \end{scope}
-  \draw[black, thick] (-2, -2) rectangle (3,4);
+  \draw[black, thick] (-2, -2) rectangle (7,2);
 
   \draw[red!80!black, thick, ->] 
 	(N00) to node[midway, below] {\(\vec{a}_1\)} (N10);
diff --git a/buch/papers/punktgruppen/tikz/piezo-atoms.tex b/buch/papers/punktgruppen/tikz/piezo-atoms.tex
index 82a2710..1811392 100644
--- a/buch/papers/punktgruppen/tikz/piezo-atoms.tex
+++ b/buch/papers/punktgruppen/tikz/piezo-atoms.tex
@@ -13,6 +13,7 @@
 
 \begin{document}
   \begin{tikzpicture}[
+      >=latex, 
       node distance = 2mm,
       charge/.style = {
         circle, draw = black, thick,
diff --git a/buch/papers/punktgruppen/tikz/piezo.tex b/buch/papers/punktgruppen/tikz/piezo.tex
index 1d16ab7..6542f26 100644
--- a/buch/papers/punktgruppen/tikz/piezo.tex
+++ b/buch/papers/punktgruppen/tikz/piezo.tex
@@ -12,12 +12,14 @@
 \usetikzlibrary{calc}
 
 \begin{document}
-\begin{tikzpicture}
+\begin{tikzpicture}[
+    >=latex, 
+  ]
   \begin{scope}[
         node distance = 0cm
     ]
     \node[
-        rectangle, fill = gray!60!white,
+        rectangle, fill = gray!20!white,
         minimum width = 3cm, minimum height = 2cm,
     ] (body) {\(\vec{E}_p = \vec{0}\)};
 
@@ -43,9 +45,9 @@
         xshift = 7cm
     ]
     \node[
-        rectangle, fill = gray!40!white,
+        rectangle, fill = gray!20!white,
         minimum width = 3cm, minimum height = 1.5cm,
-    ] (body) {\(\vec{E}_p = \vec{0}\)};
+    ] (body) {\(\vec{E}_p \neq \vec{0}\)};
 
     \node[
         draw, rectangle, thick, black, fill = red!50,
diff --git a/buch/papers/punktgruppen/tikz/projections.tex b/buch/papers/punktgruppen/tikz/projections.tex
index a763e77..e8a4a2e 100644
--- a/buch/papers/punktgruppen/tikz/projections.tex
+++ b/buch/papers/punktgruppen/tikz/projections.tex
@@ -13,6 +13,7 @@
 
 \begin{document}
 \begin{tikzpicture}[
+    >=latex, 
     classcirc/.style = {
       draw = gray, thick, circle,
       minimum size = 12mm,
@@ -43,7 +44,7 @@
     \node[classcirc] (C2h) {} node[classlabel] {\(C_{2h}\)}; &
     \node[classcirc] (D2)  {} node[classlabel] {\(D_{2}\)};  \\
 
-    \node[classcirc] (D3d) {} node[classlabel] {\(D_{3d}\)}; &
+    \node[classcirc] (D3d) {} node[classlabel] {\(C_{3v}\)}; &
     \node[classcirc] (C2v) {} node[classlabel] {\(C_{2v}\)}; & 
     \node[classcirc] (D2h) {} node[classlabel] {\(D_{2h}\)}; & 
     \node[classcirc] (D3)  {} node[classlabel] {\(D_{3}\)};  &
diff --git a/buch/papers/punktgruppen/tikz/stereographic-projections.tex b/buch/papers/punktgruppen/tikz/stereographic-projections.tex
new file mode 100644
index 0000000..7d612fb
--- /dev/null
+++ b/buch/papers/punktgruppen/tikz/stereographic-projections.tex
@@ -0,0 +1,108 @@
+\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, 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}{
+    \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);
+
+  % 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);
+
+  \draw[gray] (B) to (NP);
+  \draw[gray] (NP) to (O) to (Bproj);
+
+  % dots
+  \draw (O) node[dot] {};
+  \draw (SP) node[dot] {};
+  \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 ($(Aproj) +(0, -.15)$);
+
+  \tdplotdrawarc[orange, very thick]{(Bproj)}{.1}{0}{360}{}{};
+
+\end{tikzpicture}
+\end{document}
+% vim:ts=2 sw=2 et:
diff --git a/buch/papers/punktgruppen/tikz/symmetric-shapes.tex b/buch/papers/punktgruppen/tikz/symmetric-shapes.tex
index b2c051f..688fb61 100644
--- a/buch/papers/punktgruppen/tikz/symmetric-shapes.tex
+++ b/buch/papers/punktgruppen/tikz/symmetric-shapes.tex
@@ -14,6 +14,7 @@
 
 \begin{document}
 	\begin{tikzpicture}[
+      >=latex, 
 			node distance = 2cm,
 			shapetheme/.style = {
 				very thick, draw = black, fill = magenta!20!white,