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\documentclass[aspectratio=169]{beamer}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usetheme{Singapore}
\title{Galaxy Generation}
\subtitle{Jugend Forscht 2018}
\author{Emile Hansmaennel}
\institute{Theodor Fliedner Gymnasium}
\date{\today}
\begin{document}
\begin{frame}
\titlepage
\end{frame}
\begin{frame}
\tableofcontents
\end{frame}
\section{Point Cloud}
\subsection{Random generation of points}
\begin{frame}
\frametitle{Generating an evenly distributed point-cloud}
\begin{itemize}
\item numpy
\end{itemize}
\end{frame}
\subsection{Random-Sampling with the NFW-profile}
\begin{frame}
\frametitle{Random Sampling}
\begin{itemize}
\item Generate a random value in a range \( [r_{min};r_{max}] \)
\item Find out if the value is bigger or smaller than the NFW value
\end{itemize}
\end{frame}
\begin{frame}
\frametitle{The NFW-Profile}
\begin{itemize}
\item Returns a probability for a star to get generated
\end{itemize}
[insert nfw-distance function image]
\end{frame}
\subsection{Saving the stars}
\begin{frame}
\frametitle{Using the .csv file format}
\begin{itemize}
\item How do I use the csv format?
\end{itemize}
\end{frame}
\section{Forces}
\subsection{Generating a grid for subdividing the galaxy into cells}
\begin{frame}
\frametitle{Generating a grid for subdividing the galaxy}
\begin{itemize}
\item insert grid image without the spheres
\item problem (threshold)
\end{itemize}
\end{frame}
\subsubsection{Generating the spheres}
\begin{frame}
\frametitle{Generating the spheres on the vertices of the grid}
\begin{equation}
r = \sqrt{1^2 + 1^2 + 1^2}
\end{equation}
\begin{itemize}
\item insert grid image with the spheres
\item problem (threshold)
\end{itemize}
\end{frame}
\subsubsection{Finding out which star is in which spheres}
\begin{frame}
\frametitle{Which Star is in which sphere?}
\begin{itemize}
\item Method for finding this out
\end{itemize}
\end{frame}
\subsection{Calculate the forces acting inside of each sphere}
\begin{frame}
\frametitle{Forces acting in each sphere}
\begin{itemize}
\item cycle through all the stars in each sphere and calculate the forces
\end{itemize}
\end{frame}
\subsubsection{Calculation the Forces acting between one star and the rest}
\begin{frame}
\frametitle{Calculate the forces acting inbetween the individual stars
and the other stars}
\begin{itemize}
\item DO EPIC THINGS!
\end{itemize}
\end{frame}
\section{Extrapolation}
\subsection{Calculate where the stars are next}
\begin{frame}
\frametitle{Where are the stars after n seconds?}
\begin{itemize}
\item Force acting on star for n seconds equals a displacement of m
\end{itemize}
\end{frame}
\end{document}
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