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authorAndreas Müller <andreas.mueller@ost.ch>2021-07-26 07:58:40 +0200
committerGitHub <noreply@github.com>2021-07-26 07:58:40 +0200
commit56443dfc2486e08b0ed3bf8ecc61c9ad8a83e213 (patch)
treef3cf93ea263d777c2396ee5e21369ec99868d53b /buch/papers/punktgruppen/tikz
parentadd munkres files (diff)
parentFix typo (diff)
downloadSeminarMatrizen-56443dfc2486e08b0ed3bf8ecc61c9ad8a83e213.tar.gz
SeminarMatrizen-56443dfc2486e08b0ed3bf8ecc61c9ad8a83e213.zip
Merge pull request #45 from NaoPross/master
Almost complete
Diffstat (limited to '')
-rw-r--r--buch/papers/punktgruppen/tikz/atoms-grid-force.tex42
-rw-r--r--buch/papers/punktgruppen/tikz/atoms-grid-still.tex33
-rw-r--r--buch/papers/punktgruppen/tikz/atoms-piezo-force-horizontal.tex47
-rw-r--r--buch/papers/punktgruppen/tikz/atoms-piezo-force-vertical.tex52
-rw-r--r--buch/papers/punktgruppen/tikz/atoms-piezo-still.tex34
-rw-r--r--buch/papers/punktgruppen/tikz/combine-symmetries.tex3
-rw-r--r--buch/papers/punktgruppen/tikz/lattice.tex17
-rw-r--r--buch/papers/punktgruppen/tikz/piezo-atoms.tex1
-rw-r--r--buch/papers/punktgruppen/tikz/piezo.tex10
-rw-r--r--buch/papers/punktgruppen/tikz/projections.tex1
-rw-r--r--buch/papers/punktgruppen/tikz/stereographic-projections.tex108
-rw-r--r--buch/papers/punktgruppen/tikz/symmetric-shapes.tex1
12 files changed, 336 insertions, 13 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..64ab468 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,
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,