Add images for mu_i

ausarbeitung.tex

@@ -7,14 +7,19 @@
 %\usepackage{libertine}
 
 \usepackage{tikz}
+\usetikzlibrary{calc}
+
 \usepackage{amsmath}
 \usepackage{amssymb}
 \usepackage{amsthm}
+\usepackage{subcaption}
 \usepackage[style=alphabetic]{biblatex}
 \addbibresource{bibtex.bib}
 
 \usepackage[ngerman]{todonotes}
 
+\include{figures}
+
 \newtheorem{lemma}{Lemma}
 
 \newcommand{\teilnehmername}{Philipp Adolf}
@@ -173,9 +178,36 @@ Betrachten wir zunächst die Hilfsmengen
 
 $$\mu_i = (3ir, 3ir, \dots, 3ir) + [r, 3(d+1)r - r - 1]^d \qquad 0 \leq i \leq d$$
 
-Diese Mengen sind Hyperwürfel, die mit wachsendem $i$ gleichmäßig in allen Dimensionen verschoben werden.
-
-\missingfigure{Diagramm mit Beispielen zu $\mu_i$}
+Diese Mengen sind Hyperwürfel, die mit wachsendem $i$ gleichmäßig in allen Dimensionen verschoben werden. Ein Beispiel für diese Mengen ist in Abbildung~\ref{fig:hilfsmengen} gegeben.
+
+\begin{figure*}
+  \centering
+  \begin{subfigure}[b]{0.475\textwidth}
+    \centering
+    \begin{tikzpicture}[scale=0.3]
+      \drawmuzero
+    \end{tikzpicture}
+    \caption{\small $\mu_0$}
+  \end{subfigure}
+  \hfill
+  \begin{subfigure}[b]{0.475\textwidth}
+    \centering
+    \begin{tikzpicture}[scale=0.3]
+      \drawmuone
+    \end{tikzpicture}
+    \caption{\small $\mu_1$}
+  \end{subfigure}
+  \vskip\baselineskip
+  \begin{subfigure}[b]{0.475\textwidth}
+    \centering
+    \begin{tikzpicture}[scale=0.3]
+      \drawmutwo
+    \end{tikzpicture}
+    \caption{\small $\mu_2$}
+  \end{subfigure}
+  \caption{Die Hilfsmengen für $d = 2$ und $r = 1$. Es sind jeweils vier Blöcke gezeichnet, die Blockgrenzen sind blau markiert.}
+  \label{fig:hilfsmengen}
+\end{figure*}
 
 Mit diesen Mengen können wir nun für $0 \leq \lambda \leq d$ folgende Mengen bilden:
 

figures.tex

+\newcommand{\drawgrid}[1]{
+  \foreach \x in {0,...,#1}
+  {
+    \foreach \y in {0,...,#1}
+    {
+      \draw (\x,\y) rectangle +(1,1);
+    }
+  }
+}
+
+\newcommand{\muzero}{1,2,3,4,5,6,7}
+\newcommand{\muone}{0,1,4,5,6,7,8}
+\newcommand{\mutwo}{0,1,2,3,4,7,8}
+
+\newcommand{\drawempty}[2]{
+  \foreach \x in #1
+  {
+    \foreach \y in #1
+    {
+      \draw [color=black] ($(\x, \y)+#2$) +(0.1, 0.1) rectangle +(0.9, 0.9);
+    }
+  }
+}
+
+\newcommand{\drawfull}[2]{
+  \foreach \x in #1
+  {
+    \foreach \y in #1
+    {
+      \fill [color=black] ($(\x, \y)+#2$) +(0.1, 0.1) rectangle +(0.9, 0.9);
+    }
+  }
+}
+
+\newcommand{\drawprevious}[2]{
+  \foreach \x in #1
+  {
+    \foreach \y in #1
+    {
+      \fill [color=white!30!blue] ($(\x, \y)+#2$) +(0.1, 0.1) -- +(0.8,0.1) -- +(0.1,0.8);
+    }
+  }
+}
+
+\newcommand{\drawnext}[2]{
+  \foreach \x in #1
+  {
+    \foreach \y in #1
+    {
+      \fill [color=purple] ($(\x, \y)+#2$) +(0.9, 0.9) -- +(0.9,0.2) -- +(0.2,0.9);
+    }
+  }
+}
+
+\newcommand{\drawmuzero}{
+  \drawgrid{17}
+
+  \draw [line width=0.5mm,color=blue!75!white] (0,9) -- (18,9);
+  \draw [line width=0.5mm,color=blue!75!white] (9,0) -- (9,18);
+
+  \drawfull{\muzero}{(0,0)}
+  \drawfull{\muzero}{(0,9)}
+  \drawfull{\muzero}{(9,0)}
+  \drawfull{\muzero}{(9,9)}
+}
+
+\newcommand{\drawmuone}{
+  \drawgrid{17}
+
+  \draw [line width=0.5mm,color=blue!75!white] (0,9) -- (18,9);
+  \draw [line width=0.5mm,color=blue!75!white] (9,0) -- (9,18);
+
+  \drawfull{\muone}{(0,0)}
+  \drawfull{\muone}{(0,9)}
+  \drawfull{\muone}{(9,0)}
+  \drawfull{\muone}{(9,9)}
+}
+
+\newcommand{\drawmutwo}{
+  \drawgrid{17}
+
+  \draw [line width=0.5mm,color=blue!75!white] (0,9) -- (18,9);
+  \draw [line width=0.5mm,color=blue!75!white] (9,0) -- (9,18);
+
+  \drawfull{\mutwo}{(0,0)}
+  \drawfull{\mutwo}{(0,9)}
+  \drawfull{\mutwo}{(9,0)}
+  \drawfull{\mutwo}{(9,9)}
+}
+
+\newcommand{\drawepzero}{
+  \drawgrid{17}
+
+  \draw [line width=0.5mm,color=blue!75!white] (0,9) -- (18,9);
+  \draw [line width=0.5mm,color=blue!75!white] (9,0) -- (9,18);
+
+  \drawfull{\muzero}{(0,0)}
+  \drawfull{\muzero}{(0,9)}
+  \drawfull{\muzero}{(9,0)}
+  \drawfull{\muzero}{(9,9)}
+
+  \drawfull{\muone}{(0,0)}
+  \drawfull{\muone}{(0,9)}
+  \drawfull{\muone}{(9,0)}
+  \drawfull{\muone}{(9,9)}
+
+  \drawfull{\mutwo}{(0,0)}
+  \drawfull{\mutwo}{(0,9)}
+  \drawfull{\mutwo}{(9,0)}
+  \drawfull{\mutwo}{(9,9)}
+}
+
+\newcommand{\drawepone}{
+  \drawgrid{17}
+
+  \draw [line width=0.5mm,color=blue!75!white] (0,12) -- (18,12);
+  \draw [line width=0.5mm,color=blue!75!white] (12,0) -- (12,18);
+  \draw [line width=0.5mm,color=blue!75!white] (0,3) -- (18,3);
+  \draw [line width=0.5mm,color=blue!75!white] (3,0) -- (3,18);
+
+  \drawfull{\muone}{(0,0)}
+  \drawfull{\muone}{(0,9)}
+  \drawfull{\muone}{(9,0)}
+  \drawfull{\muone}{(9,9)}
+
+  \drawfull{\mutwo}{(0,0)}
+  \drawfull{\mutwo}{(0,9)}
+  \drawfull{\mutwo}{(9,0)}
+  \drawfull{\mutwo}{(9,9)}
+}
+
+\newcommand{\draweptwo}{
+  \drawgrid{17}
+
+  \draw [line width=0.5mm,color=blue!75!white] (0,15) -- (18,15);
+  \draw [line width=0.5mm,color=blue!75!white] (15,0) -- (15,18);
+  \draw [line width=0.5mm,color=blue!75!white] (0,6) -- (18,6);
+  \draw [line width=0.5mm,color=blue!75!white] (6,0) -- (6,18);
+
+  \drawfull{\mutwo}{(0,0)}
+  \drawfull{\mutwo}{(0,9)}
+  \drawfull{\mutwo}{(9,0)}
+  \drawfull{\mutwo}{(9,9)}
+}
+
+\newcommand{\drawepthree}{
+  \drawgrid{17}
+
+  \draw [line width=0.5mm,color=blue!75!white] (0,9) -- (18,9);
+  \draw [line width=0.5mm,color=blue!75!white] (9,0) -- (9,18);
+}
+
+\newcommand{\drawenzero}{
+  \drawgrid{17}
+
+  \draw [line width=0.5mm,color=blue!75!white] (0,9) -- (18,9);
+  \draw [line width=0.5mm,color=blue!75!white] (9,0) -- (9,18);
+}
+
+\newcommand{\drawenone}{
+  \drawgrid{17}
+
+  \draw [line width=0.5mm,color=blue!75!white] (0,12) -- (18,12);
+  \draw [line width=0.5mm,color=blue!75!white] (12,0) -- (12,18);
+  \draw [line width=0.5mm,color=blue!75!white] (0,3) -- (18,3);
+  \draw [line width=0.5mm,color=blue!75!white] (3,0) -- (3,18);
+
+  \drawfull{\muzero}{(0,0)}
+  \drawfull{\muzero}{(0,9)}
+  \drawfull{\muzero}{(9,0)}
+  \drawfull{\muzero}{(9,9)}
+}
+
+\newcommand{\drawentwo}{
+  \drawgrid{17}
+
+  \draw [line width=0.5mm,color=blue!75!white] (0,15) -- (18,15);
+  \draw [line width=0.5mm,color=blue!75!white] (15,0) -- (15,18);
+  \draw [line width=0.5mm,color=blue!75!white] (0,6) -- (18,6);
+  \draw [line width=0.5mm,color=blue!75!white] (6,0) -- (6,18);
+
+  \drawfull{\muzero}{(0,0)}
+  \drawfull{\muzero}{(0,9)}
+  \drawfull{\muzero}{(9,0)}
+  \drawfull{\muzero}{(9,9)}
+
+  \drawfull{\muone}{(0,0)}
+  \drawfull{\muone}{(0,9)}
+  \drawfull{\muone}{(9,0)}
+  \drawfull{\muone}{(9,9)}
+}
+
+\newcommand{\drawenthree}{
+  \drawgrid{17}
+
+  \draw [line width=0.5mm,color=blue!75!white] (0,9) -- (18,9);
+  \draw [line width=0.5mm,color=blue!75!white] (9,0) -- (9,18);
+
+  \drawfull{\muzero}{(0,0)}
+  \drawfull{\muzero}{(0,9)}
+  \drawfull{\muzero}{(9,0)}
+  \drawfull{\muzero}{(9,9)}
+
+  \drawfull{\muone}{(0,0)}
+  \drawfull{\muone}{(0,9)}
+  \drawfull{\muone}{(9,0)}
+  \drawfull{\muone}{(9,9)}
+
+  \drawfull{\mutwo}{(0,0)}
+  \drawfull{\mutwo}{(0,9)}
+  \drawfull{\mutwo}{(9,0)}
+  \drawfull{\mutwo}{(9,9)}
+}
+