diff --git a/mr/ub7/mr7.pdf b/mr/ub7/mr7.pdf new file mode 100644 index 0000000..28cf21e --- /dev/null +++ b/mr/ub7/mr7.pdf Binary files differ diff --git a/mr/ub7/mr7.tex b/mr/ub7/mr7.tex new file mode 100644 index 0000000..cae81b4 --- /dev/null +++ b/mr/ub7/mr7.tex @@ -0,0 +1,133 @@ +\documentclass[a4paper,12pt]{scrartcl} +\usepackage[ngerman]{babel} +\usepackage{graphicx} %BIlder einbinden +\usepackage{amsmath} %erweiterte Mathe-Zeichen +\usepackage{amsfonts} %weitere fonts +\usepackage[utf8]{inputenc} %Umlaute & Co +\usepackage{hyperref} %Links +\usepackage{ifthen} %ifthenelse +\usepackage{enumerate} +\usepackage{pdfpages} +\usepackage{algpseudocode} %Pseudocode +\usepackage{dsfont} % schöne Zahlenräumezeichen +\usepackage{amssymb, amsthm} %noch stärker erweiterte Mathe-Zeichen +\usepackage{tikz} %TikZ ist kein Zeichenprogramm +\usetikzlibrary{trees,automata,arrows,shapes} + +\pagestyle{empty} + + +\topmargin-50pt + +\newcounter{aufgabe} +\def\tand{&} + +\newcommand{\makeTableLine}[2][0]{% + \setcounter{aufgabe}{1}% + \whiledo{\value{aufgabe} < #1}% + {% + #2\tand\stepcounter{aufgabe}% + } +} + +\newcommand{\aufgTable}[1]{ + \def\spalten{\numexpr #1 + 1 \relax} + \begin{tabular}{|*{\spalten}{p{1cm}|}} + \makeTableLine[\spalten]{A\theaufgabe}$\Sigma$~~\\ \hline + \rule{0pt}{15pt}\makeTableLine[\spalten]{}\\ + \end{tabular} +} + +\def\header#1#2#3#4#5#6#7{\pagestyle{empty} +\begin{minipage}[t]{0.47\textwidth} +\begin{flushleft} +{\bf #4}\\ +#5 +\end{flushleft} +\end{minipage} +\begin{minipage}[t]{0.5\textwidth} +\begin{flushright} +#6 \vspace{0.5cm}\\ +% Number of Columns Definition of Columns second empty line +% \begin{tabular}{|*{5}{C{1cm}|}}\hline A1&A2&A3&A4&$\Sigma$\\\hline&&&&\\\hline\end{tabular}\\\vspace*{0.1cm} +\aufgTable{#7} +\end{flushright} +\end{minipage} +\vspace{1cm} +\begin{center} +{\Large\bf Assignment #1} + +{(Hand-in date #3)} +\end{center} +} + + + +%counts the exercisenumber +\newcounter{n} + +%Kommando für Aufgaben +%\Aufgabe{AufgTitel}{Punktezahl} +\newcommand{\Aufgabe}[2]{\stepcounter{n} +\textbf{Exercise \arabic{n}: #1} (#2 Punkte)\\} + + + + +\begin{document} + %\header{BlattNr}{Tutor}{Abgabedatum}{Vorlesungsname}{Namen}{Semester}{Anzahl Aufgaben} + \header{7}{}{2015-06-16}{Mobile Robots}{ + \textit{Jan-Peter Hohloch}\\ \textit{Maximus Mutschler} + }{SS 15}{3} + \vspace{1cm} + + \Aufgabe{Occupancy Gridmap}{9} + \begin{enumerate}[(a)] + \item $\frac{p(m_i|z_{1,\dots,t})}{1-p(m_i|z_{1,\dots,t})}=\frac{p(m_i|z_t)}{1-p(m_i|z_t)}\frac{p(m_i|z_{1,\dots,t-1})}{1-p(m_i|z_{1,\dots,t-1})}\frac{1-p(m_i)}{p(m_i)}$\\ + $\Leftrightarrow\frac{A}{1-A}=\underbrace{\frac{B}{1-B}\frac{C}{1-C}\frac{1-D}{D}}_F$\\ + $\Leftrightarrow A=(1-A)F$\\ + $\Leftrightarrow A=\left(1+\frac{1}{F}\right)^{-1}=\left(1+\frac{1-B}{B}\frac{1-C}{C}\frac{D}{1-D}\right)^{-1}=\left(1+\frac{1-p(m_i|z_t)}{p(m_i|z_t)}\frac{1-p(m_i|z_{1,\dots,t-1})}{p(m_i|z_{1,\dots,t-1})}\frac{p(m_i)}{1-p(m_i)}\right)^{-1}$ + \item 4 Add/Sub, 6 Div/Mult + \item 1 Add/Sub, 3 Div/Mult + \item TODO %TODO, ... + \end{enumerate} + \Aufgabe{Quadtree}{6} + \begin{enumerate}[(a)] + \item TODO %TODO + \item TODO %TODO wtf? + \item $256^2=\left(2^8\right)^2=4^8$\\ + $\Rightarrow$ maxdepth: 9\\ + $\Rightarrow$ maxnodes: $\sum\limits_{i=0}^9\frac{4^9-1}{4-1}=87381$ + \end{enumerate} + \Aufgabe{Topological Maps}{5} + \begin{enumerate}[(a)] + \item \includegraphics[width=\textwidth]{voroni.jpg} + \item[(c)] \begin{tikzpicture}[auto,node distance=2.0cm] + \node[state] (A) {}; + \node[state] (B) [right of=A] {}; + \node[state] (C) [right of=B] {}; + \node[state] (D) [right of=C] {}; + \node[state] (E) [above of=D] {}; + \node[state] (F) [right of=E] {}; + \node (help) [below of=F] {}; + \node[state] (G) [below of=help] {}; + \node[state] (H) [left of=G] {}; + \node[state] (I) [below of=G] {}; + \node[state] (J) [left of=I] {}; + \node[state] (K) [below of=C] {}; + \node[state] (L) [below of=K] {}; + \node[state] (M) [left of=K] {}; + \node[state] (N) [below of=M] {}; + \node[state] (O) [left of=N] {}; + + \path + (A)edge(B)(B)edge(C)(C)edge(D)(D)edge(E)(E)edge(F)(F)edge(G)(G)edge(I)(I)edge(J)(J)edge(H)(H)edge(D) + (C)edge(K) + (K)edge(L) + (K)edge(M) + (M)edge(N) + (N)edge(O); + \end{tikzpicture} + \end{enumerate} +\end{document} +