\documentclass[aspectratio=169]{beamer}

\usefonttheme{professionalfonts}

\usetheme[
 numbering=fraction
]{metropolis}

\setmonofont{Iosevka sbruder}

\usepackage[ngerman]{babel}
\usepackage{appendixnumberbeamer}
\usepackage{array}

\title{Videoanalyse eines Chaospendels}
%\subtitle{}
\author{
 Eric Doberstein,
 Mai Zhou,
 Simon Bruder
}
\institute{Christian-von-Bomhard-Schule}
\usepackage{datetime}
\newdate{date}{3}{12}{2019}
\date{\displaydate{date}}

\begin{document}
 \maketitle

 \begin{frame}[noframenumbering]{Inhaltsüberblick}
  \tableofcontents
 \end{frame}

 \section{Chaospendel}
 \begin{frame}{Aufbau}
  \begin{center}
   \includegraphics[height=7cm]{img/aufbau}
  \end{center}
 \end{frame}

 \section{Tracking}
 \begin{frame}{Blender}
  \includegraphics[height=3em]{img/blender-logo}
  \begin{itemize}
   \item{Ursprünglich 3D-Animationsprogramm}
   \item{Deckt mittlerweile kompletten Arbeitsablauf für Filmproduktion ab}
  \end{itemize}
 \end{frame}

 \begin{frame}{Live-Demo}
  \hyperlink{blender-live-end}{\beamerskipbutton{Demo erfolgreich, Screenshots überspringen}} \\
 \end{frame}

 \begin{frame}
  \begin{center}
   % 0.825 = 1584 / 1920
   \includegraphics<1>[width=0.825\paperwidth]{img/blender-0}%
   \includegraphics<2>[width=0.825\paperwidth]{img/blender-1}%
   \includegraphics<3>[width=0.825\paperwidth]{img/blender-2}%
   \includegraphics<4>[width=0.825\paperwidth]{img/blender-3}%
  \end{center}
 \end{frame}

 \begin{frame}[label=blender-live-end]{Tracking-Ergebnisse}
  \tiny\begin{tabular}{>{\onslide <1>}r >{\onslide}r >{\onslide <1>}r >{\onslide}r >{\onslide <1>}r >{\onslide}r >{\onslide <1>}r}
time (frames)&$t$&x (px)&$x$          &y (px)         &$y$            &rotation\\
1 &0.04&560.4334759712&0.8302717976956&396.12247467041&0.5868480975057&0\\
2 &0.08&560.5243062973&0.8304063611386&396.20464324951&0.5869698287313&0.23773584383479\\
3 &0.12&560.4334759712&0.8302717976956&396.09981536865&0.5868145281705&0.35648843393869\\
4 &0.16&560.5022907257&0.8303737454777&396.15131378173&0.5868908221141&0.48422587123809\\
5 &0.20&560.4740309715&0.8303318791762&396.17752075195&0.5869296472543&0.27098651406572\\
6 &0.24&560.4189920425&0.8302503400240&396.10782623291&0.5868263961173&0.39046013035112\\
7 &0.28&560.4686236381&0.8303238683121&396.12590789794&0.5868531837686&0.47220017386621\\
8 &0.32&560.4391407966&0.8302801900294&396.14273071289&0.5868781064569&0.18822010173505\\
9 &0.36&560.4592895507&0.8303100400348&396.14913940429&0.5868876008143&0.19962089014342\\
10&0.40&560.4381752014&0.8302787595179&396.11011505126&0.5868297869592&0.49845554711816\\
11&0.44&560.4057955741&0.8302307897009&396.16344451904&0.5869087935764&0.39718314068488\\
12&0.48&560.4696536064&0.8303253941910&396.12739562988&0.5868553878159&0.85054854679435\\
13&0.52&560.3842306137&0.8301988416120&396.09958648681&0.5868141890863&0.41302134334785\\
14&0.56&560.4851031303&0.8303482823741&396.13220214843&0.5868625085839&0.21631585128005\\
15&0.60&560.4882574081&0.8303529553781&396.17912292480&0.5869320208437&0.55523747660242\\
\vdots&\vdots&\vdots  &\vdots         &\vdots         &\vdots         &\vdots          \\
  \end{tabular}
  \onslide<2->
 \end{frame}

 \section{Auswertung}
 \begin{frame}{Übersicht}
  \begin{columns}
   \begin{column}{0.5\textwidth}
    Gegeben
    \begin{itemize}
     \item{$t$}
     \item{$x$}
     \item{$y$}
    \end{itemize}
   \end{column}
   \begin{column}{0.5\textwidth}
    Gesucht
    \begin{itemize}
     \item{$s$}
     \item{$\overline{v}$}
     \item{$\overline{a}$}
    \end{itemize}
   \end{column}
  \end{columns}
 \end{frame}

 \begin{frame}{Strecke}
  \begin{columns}
   \begin{column}{0.5\textwidth}
    \begin{tikzpicture}[x=1cm, y=1cm]
     \draw[black,fill=black] (0, 0) circle (.5ex) node[below] {$P_1$};
     \draw[black,fill=black] (4, 3) circle (.5ex) node[right] {$P_2$};
     \draw (0, 0)
      -- (4, 3) node[midway,left=.5em] {$\Delta s$}
      -- (4, 0) node[midway,right] {$\Delta y$}
      -- cycle  node[midway,below] {$\Delta x$};
    \end{tikzpicture}
   \end{column}
   \begin{column}{0.5\textwidth}
    \begin{flalign}
     \Delta x_i &= x_i - x_{i-1} \\
     \Delta y_i &= y_i - y_{i-1} \\
     \Delta s_i &= \sqrt{\Delta x_i^2 + \Delta y_i^2} \\
     s_i &= \Delta s_i + s_{i-1}
    \end{flalign}
   \end{column}
  \end{columns}
 \end{frame}
 \begin{frame}{Geschwindigkeit}
  \begin{flalign}
   \Delta t_i &= t_i - t_{i-1} \\
   \overline{v_i} &= \frac{\Delta s_i}{\Delta t_i} \\
   \Delta \overline{v_i} &= \overline{v_i} - \overline{v}_{i-1}
  \end{flalign}
 \end{frame}
 \begin{frame}{Beschleunigung}
  \begin{flalign}
   \overline{a}_i &= \frac{\Delta \overline{v_i}}{\Delta t_i}
  \end{flalign}
 \end{frame}

 \section{Ergebnisse}
 \begin{frame}{Graphen \addfontfeatures{Numbers={Monospaced,Lining}}{(1/2)}}
  \includegraphics[width=\textwidth]{img/coole_bewegung_0}
 \end{frame}

 \begin{frame}{Graphen \addfontfeatures{Numbers={Monospaced,Lining}}{(2/2)}}
  \centering{\includegraphics[height=\textheight]{img/coole_bewegung_movement}}
 \end{frame}

 \appendix
 \begin{frame}{Weiterführende Informationen}
  \href{https://git.sbruder.de/simon/video-analysis}{\texttt{git.sbruder.de/simon/video-analysis}}
 \end{frame}
\end{document}
