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-rwxr-xr-x[-rw-r--r--]langfassung/docs/1_kurzfassung.tex0
-rw-r--r--langfassung/docs/2_einleitung.aux30
-rwxr-xr-x[-rw-r--r--]langfassung/docs/2_einleitung.tex0
-rw-r--r--langfassung/docs/3_hauptteil.aux67
-rwxr-xr-x[-rw-r--r--]langfassung/docs/3_hauptteil.tex0
-rw-r--r--langfassung/docs/4_ergebnisse.aux31
-rwxr-xr-x[-rw-r--r--]langfassung/docs/4_ergebnisse.tex0
-rw-r--r--langfassung/docs/5_quellen.aux32
-rwxr-xr-x[-rw-r--r--]langfassung/docs/5_quellen.tex2
-rwxr-xr-xlangfassung/docs/6_abgabe.tex273
-rwxr-xr-x[-rw-r--r--]langfassung/figs/Jugend_forscht.jpgbin107107 -> 107107 bytes
-rwxr-xr-x[-rw-r--r--]langfassung/figs/Untitled Diagram.xml0
-rw-r--r--langfassung/figs/all_forces_5000.pngbin0 -> 37154 bytes
-rwxr-xr-x[-rw-r--r--]langfassung/figs/galaxy.pngbin158503 -> 158503 bytes
-rwxr-xr-x[-rw-r--r--]langfassung/figs/galaxy_opengl.png (renamed from langfassung/figs/2018-01-07-122038_958x1041_scrot.png)bin184042 -> 184042 bytes
-rwxr-xr-x[-rw-r--r--]langfassung/figs/lookup_table_rho_r_function.pngbin19205 -> 19205 bytes
-rwxr-xr-x[-rw-r--r--]langfassung/figs/lookup_table_rho_r_function_grid.pngbin20668 -> 20668 bytes
-rwxr-xr-x[-rw-r--r--]langfassung/figs/lookup_table_speed.pngbin8277 -> 8277 bytes
-rwxr-xr-x[-rw-r--r--]langfassung/figs/runtime.png (renamed from langfassung/figs/2017-12-05-164935_374x65_scrot.png)bin8460 -> 8460 bytes
-rw-r--r--langfassung/figs/sphere_alignment.pngbin0 -> 169863 bytes
-rw-r--r--langfassung/figs/sphere_alignment_cc.jpgbin0 -> 264400 bytes
-rwxr-xr-x[-rw-r--r--]langfassung/figs/spiralgalaxy.pngbin321656 -> 321656 bytes
-rwxr-xr-x[-rw-r--r--]langfassung/master.aux349
-rwxr-xr-x[-rw-r--r--]langfassung/master.fdb_latexmk48
-rw-r--r--langfassung/master.fls19
-rwxr-xr-x[-rw-r--r--]langfassung/master.log527
-rwxr-xr-x[-rw-r--r--]langfassung/master.out18
-rwxr-xr-x[-rw-r--r--]langfassung/master.pdfbin578877 -> 878421 bytes
-rwxr-xr-x[-rw-r--r--]langfassung/master.pyg0
-rw-r--r--langfassung/master.synctex.gzbin111456 -> 142055 bytes
-rwxr-xr-x[-rw-r--r--]langfassung/master.tex54
-rwxr-xr-x[-rw-r--r--]langfassung/master.toc58
-rwxr-xr-x[-rw-r--r--]langfassung/master.x.gnuplot0
-rwxr-xr-x[-rw-r--r--]langfassung/references/Sampling_Design.pdfbin221160 -> 221160 bytes
-rwxr-xr-x[-rw-r--r--]langfassung/references/dissSchwarzmeier.pdfbin8834090 -> 8834090 bytes
-rwxr-xr-x[-rw-r--r--]langfassung/references/master(2).pdfbin133969 -> 133969 bytes
36 files changed, 1218 insertions, 290 deletions
diff --git a/langfassung/docs/1_kurzfassung.tex b/langfassung/docs/1_kurzfassung.tex
index b56b5a5..b56b5a5 100644..100755
--- a/langfassung/docs/1_kurzfassung.tex
+++ b/langfassung/docs/1_kurzfassung.tex
diff --git a/langfassung/docs/2_einleitung.aux b/langfassung/docs/2_einleitung.aux
new file mode 100644
index 0000000..44243d1
--- /dev/null
+++ b/langfassung/docs/2_einleitung.aux
@@ -0,0 +1,30 @@
+\relax 
+\providecommand\hyper@newdestlabel[2]{}
+\@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Themen}{3}{subsection.1.1}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Motivation}{3}{subsection.1.2}}
+\@setckpt{docs/2_einleitung}{
+\setcounter{page}{4}
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diff --git a/langfassung/docs/2_einleitung.tex b/langfassung/docs/2_einleitung.tex
index b450799..b450799 100644..100755
--- a/langfassung/docs/2_einleitung.tex
+++ b/langfassung/docs/2_einleitung.tex
diff --git a/langfassung/docs/3_hauptteil.aux b/langfassung/docs/3_hauptteil.aux
new file mode 100644
index 0000000..f598ad5
--- /dev/null
+++ b/langfassung/docs/3_hauptteil.aux
@@ -0,0 +1,67 @@
+\relax 
+\providecommand\hyper@newdestlabel[2]{}
+\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Generierung von elliptischen Galaxien}{5}{subsection.2.1}}
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.1.1}Das Navarro-Frenk-White Profil}{5}{subsubsection.2.1.1}}
+\newlabel{eq:NFW_profile}{{1}{5}{Das Navarro-Frenk-White Profil}{equation.2.1}{}}
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.1.2}Random Sampling}{5}{subsubsection.2.1.2}}
+\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Eine mit dem NFW-profil und der Random Sampling Methode generierte Galaxie\relax }}{6}{figure.caption.3}}
+\providecommand*\caption@xref[2]{\@setref\relax\@undefined{#1}}
+\newlabel{fig:galaxy}{{2}{6}{Eine mit dem NFW-profil und der Random Sampling Methode generierte Galaxie\relax }{figure.caption.3}{}}
+\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces  Die Rho Funktion im Intervall \( [~0~;~10^7 ~] \) geplottet mithilfe von Logarithmischen Achsen.   Die x-Achse beschreibt die Entfernung zum Mittelpunkt der Galaxie   Die y-Achse beschreibt die Warscheinlichkeit das ein Stern generiert wird \relax }}{6}{figure.caption.4}}
+\newlabel{fig:rho}{{3}{6}{Die Rho Funktion im Intervall \( [~0~;~10^7 ~] \) geplottet mithilfe von Logarithmischen Achsen. \\ Die x-Achse beschreibt die Entfernung zum Mittelpunkt der Galaxie \\ Die y-Achse beschreibt die Warscheinlichkeit das ein Stern generiert wird \relax }{figure.caption.4}{}}
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.1.3}Lookup Tabellen}{7}{subsubsection.2.1.3}}
+\newlabel{subsec:lookup}{{2.1.3}{7}{Lookup Tabellen}{subsubsection.2.1.3}{}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Generierung eines Dunkle-Materie Halos durch Anpassung des NFW-Profils}{7}{subsection.2.2}}
+\newlabel{eq:dark_matter}{{3}{7}{Generierung eines Dunkle-Materie Halos durch Anpassung des NFW-Profils}{equation.2.3}{}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {2.3}Stauchung und Streckung der Galaxie}{7}{subsection.2.3}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {2.4}Rechenaufwand}{8}{subsection.2.4}}
+\newlabel{subsec:big_o}{{2.4}{8}{Rechenaufwand}{subsection.2.4}{}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {2.5}Beschleunigung der Generation}{8}{subsection.2.5}}
+\newlabel{subsec:speeding_things_up}{{2.5}{8}{Beschleunigung der Generation}{subsection.2.5}{}}
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.5.1}Lookuptable}{8}{subsubsection.2.5.1}}
+\newlabel{subsec:lookuptable}{{2.5.1}{8}{Lookuptable}{subsubsection.2.5.1}{}}
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.5.2}Mehr Rechenleistung!}{9}{subsubsection.2.5.2}}
+\@writefile{toc}{\contentsline {paragraph}{\nonumberline Amazon Web Services}{9}{section*.5}}
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.5.3}Nichts in der Konsole ausgeben}{9}{subsubsection.2.5.3}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {2.6}Nutzung eines neuronalen Netzes zum unbeaufsichtigten generieren von Galaxien}{9}{subsection.2.6}}
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.6.1}Aufbau des neuronalen Netzes}{9}{subsubsection.2.6.1}}
+\@writefile{toc}{\contentsline {paragraph}{\nonumberline Neuronen und Synapsen}{10}{section*.6}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {2.7}Spiralgalaxien}{11}{subsection.2.7}}
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.7.1}Das n-K\IeC {\"o}rper Problem}{11}{subsubsection.2.7.1}}
+\newlabel{eq:n-body-2nd}{{10}{11}{Das n-Körper Problem}{equation.2.10}{}}
+\newlabel{eq:hamilton}{{11}{11}{Das n-Körper Problem}{equation.2.11}{}}
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.7.2}Unterteilung des Vektorraumes in verschiedene Zellen}{12}{subsubsection.2.7.2}}
+\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.7.3}Berechnung der wirkenden Kr\IeC {\"a}fte}{12}{subsubsection.2.7.3}}
+\newlabel{eq:gravitation_law}{{16}{12}{Berechnung der wirkenden Kräfte}{equation.2.16}{}}
+\@writefile{toc}{\contentsline {paragraph}{\nonumberline Masse der Sterne}{12}{section*.7}}
+\@writefile{toc}{\contentsline {paragraph}{\nonumberline Abstand der Sterne}{12}{section*.8}}
+\newlabel{eq:pytagoras}{{17}{12}{Abstand der Sterne}{equation.2.17}{}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {2.8}Weiteres}{12}{subsection.2.8}}
+\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces Eine Spiralgalaxie generiert mithilfe von Daten aus dem Max-Plank-Institut in Heidelberg\relax }}{13}{figure.caption.9}}
+\newlabel{fig:spiralgalaxy}{{4}{13}{Eine Spiralgalaxie generiert mithilfe von Daten aus dem Max-Plank-Institut in Heidelberg\relax }{figure.caption.9}{}}
+\@setckpt{docs/3_hauptteil}{
+\setcounter{page}{14}
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diff --git a/langfassung/docs/3_hauptteil.tex b/langfassung/docs/3_hauptteil.tex
index c3edf57..c3edf57 100644..100755
--- a/langfassung/docs/3_hauptteil.tex
+++ b/langfassung/docs/3_hauptteil.tex
diff --git a/langfassung/docs/4_ergebnisse.aux b/langfassung/docs/4_ergebnisse.aux
new file mode 100644
index 0000000..ec4d7a3
--- /dev/null
+++ b/langfassung/docs/4_ergebnisse.aux
@@ -0,0 +1,31 @@
+\relax 
+\providecommand\hyper@newdestlabel[2]{}
+\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Simulations Geschwindigkeit}{15}{subsection.3.1}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Lookuptabellen Geschwindigkeit}{15}{subsection.3.2}}
+\@writefile{toc}{\contentsline {subsection}{\numberline {3.3}Fazit}{15}{subsection.3.3}}
+\@setckpt{docs/4_ergebnisse}{
+\setcounter{page}{16}
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diff --git a/langfassung/docs/4_ergebnisse.tex b/langfassung/docs/4_ergebnisse.tex
index f398f55..f398f55 100644..100755
--- a/langfassung/docs/4_ergebnisse.tex
+++ b/langfassung/docs/4_ergebnisse.tex
diff --git a/langfassung/docs/5_quellen.aux b/langfassung/docs/5_quellen.aux
new file mode 100644
index 0000000..f7e47e9
--- /dev/null
+++ b/langfassung/docs/5_quellen.aux
@@ -0,0 +1,32 @@
+\relax 
+\providecommand\hyper@newdestlabel[2]{}
+\@writefile{toc}{\contentsline {paragraph}{\nonumberline Herrn J\IeC {\"o}rg Thar}{17}{section*.11}}
+\@writefile{toc}{\contentsline {paragraph}{\nonumberline Tim Tugendhat}{17}{section*.12}}
+\@writefile{toc}{\contentsline {paragraph}{\nonumberline Konstantin Bosbach}{17}{section*.13}}
+\@writefile{toc}{\contentsline {paragraph}{\nonumberline Tilman Hoffbauer}{17}{section*.14}}
+\@setckpt{docs/5_quellen}{
+\setcounter{page}{18}
+\setcounter{equation}{17}
+\setcounter{enumi}{0}
+\setcounter{enumii}{0}
+\setcounter{enumiii}{0}
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diff --git a/langfassung/docs/5_quellen.tex b/langfassung/docs/5_quellen.tex
index 9932028..6219a0a 100644..100755
--- a/langfassung/docs/5_quellen.tex
+++ b/langfassung/docs/5_quellen.tex
@@ -18,3 +18,5 @@ Die Einführung in die Mathematik bekam ich während meines Praktikums im Zentru
 
 \centering
 \vspace{0.5cm} \textbf{Außerdem gilt mein Dank allen, die mich auf jede nur erdenkliche Weise unterstützt haben.}
+
+\raggedright
diff --git a/langfassung/docs/6_abgabe.tex b/langfassung/docs/6_abgabe.tex
new file mode 100755
index 0000000..22fe221
--- /dev/null
+++ b/langfassung/docs/6_abgabe.tex
@@ -0,0 +1,273 @@
+% \subsection{Rotationsmatrizen}
+%
+% \begin{tabular}{ l | l }
+% I & II \\ \hline
+% IV & III \\
+% \end{tabular}
+%
+% \flushleft
+% \hfill
+% \begin{tabular}{l | l l}
+%   Clockwise & & \\ \hline
+%   I & + & + \\
+%   II & + & - \\
+%   III & - & - \\
+%   IV & - & +
+% \end{tabular}
+% \hfill
+% \begin{tabular}{l | l l}
+% Anticlockwise & & \\ \hline
+% I & - & - \\
+% II & - & + \\
+% III & + & + \\
+% IV & + & -
+% \end{tabular}
+% \hfill
+%
+% \subsection{Die Matrizen}
+%
+% \subsubsection{Rotation um die x-Achse}
+%
+% \begin{equation}
+%   R_x (\alpha) =
+%    \begin{pmatrix}
+%       1 & 0 & 0 \\
+%       0 & cos(\alpha) & -sin(\alpha) \\
+%       0 & sin(\alpha) & cos(\alpha)
+%     \end{pmatrix}
+% \end{equation}
+%
+% \subsubsection{Rotation um die y-Achse}
+%
+% \begin{equation}
+%   R_y (\alpha) =
+%    \begin{pmatrix}
+%       cos(\alpha) & 0 & sin(\alpha) \\
+%       0 & 1 & 0 \\
+%       -sin(\alpha) & 0 & cos(\alpha)
+%     \end{pmatrix}
+% \end{equation}
+%
+% \subsubsection{Rotation um die z-Achse}
+%
+% \begin{equation}
+%   R_z (\alpha) =
+%    \begin{pmatrix}
+%       cos(\alpha) & -sin(\alpha) & 0 \\
+%       sin(\alpha) & cos(\alpha) & 0 \\
+%       0 & 0 & 1
+%     \end{pmatrix}
+% \end{equation}
+
+\subsection{Spiralgalaxien}
+
+\subsection{Using Object Oriented Programming (OOP) techniques}
+
+In my case, the objects are galaxies.
+
+\subsubsection{Initialisation}
+
+The galaxy is initialised with the following objects:
+
+\begin{itemize}
+  \item A list storing the coordinates of each star
+  \begin{itemize}
+    \item X Coordinate
+    \item Y Coordinate
+    \item Z Coordinate
+  \end{itemize}
+
+  \item A list storing the individual forces acting on the stars
+  \begin{itemize}
+    \item X Force
+    \item Y Force
+    \item Z Force
+  \end{itemize}
+
+  \item A variable storing the number of stars generated in the galaxy
+
+  \item Newtons gravitational constant
+\end{itemize}
+
+\subsection{Generation of new stars}
+
+The function is given an integer defining the amount of stars that should be
+newly generated.
+
+The newly generated stars are then appended to the list storing the coordinates.
+
+The counter counting the amount of stars in the galaxy is incremented.
+
+\subsection{Printing all the coordinates}
+
+The function cycles through the list storing the star coordinates and prints
+them to the command line.
+
+\subsection{Calculating the Forces acting between the Stars}
+
+The function recieves two star objects and an axis on which the forces should
+be calculated and returns the force acting on the given axis. In case of a
+failture (The two given stars have got the same coordiantes), the function
+just goes on to the next Star.
+
+The Forces can be calculated using the equation (\ref{eq:gravitation_law}).
+
+\subsection{Calculating the forces acting between each star in the galaxy and
+each other star}
+
+To calculate the forces inbetween every star in the galaxy, the function cycles
+through every star, looks if the force that should be calculated hat not been
+calculated yet and calculates it. This includes testing if the force that should
+be calculated is not the force inbetween a star and itself.
+
+The results of the calculations are stored in a list storinf the forces.
+
+\subsection{Printing all the individual forces}
+
+The function is able to print all the forces acting inbetween the stars if no
+argument is given. If an argument n is given, the function print out the nth
+star in the list.
+
+\subsection{Spherical cells}
+
+
+\subsubsection{Testing if a point is inside or outside a sphere}
+
+In order to test is a point is inside a sphere, one just has to test if the
+following conditions are all true:
+
+\begin{equation}
+  \begin{split}
+    S_x - S_r \leq P_x \leq S_x + S_r \\
+    S_y - S_r \leq P_y \leq S_y + S_r \\
+    S_z - S_r \leq P_z \leq S_z + S_r
+  \end{split}
+\end{equation}
+
+\( P_x \) , \( P_y \) and \( P_z \) are the coordinates of the point to be tested,
+\( S_x \) , \( S_y \) and \( S_z \) are the coordinates of the midpoint of the sphere and
+\( S_r \) is the radius of the sphere.
+
+\subsubsection{Testing if a star is inside or outside of a sphere for a whole galaxy}
+
+While testting if a star is inside a sphere or not, because of the alignment
+of the spheres, a point can be in more than one sphere at the same time.
+To get rid of this problem, the software cycles over every star and searches
+for matches within the spheres. If a match is found, the next star is tested.
+This is pretty much as efficient as it can get.
+
+\begin{equation}
+  O(n) = n_{stars} \cdot n_{spheres}
+\end{equation}
+
+\subsubsection{Generate the position of the spheres}
+
+Generating the position of the spheres is accomplished in the following way:
+A 3D-grid is generated and the midpoints of the spheres are positioned on the
+gridpoints.
+
+[Include Graphic]
+
+The distance the spheres have to each other ist defined using the following
+function:
+
+\begin{equation} \label{sphere_distance}
+  \texttt{sphere\_distance} = \frac{\texttt{galaxy\_range}}{\texttt{sampling\_rate}}
+\end{equation}
+
+The higher the \texttt{sampling\_rate} is, the more spheres get generated.
+
+The next goal is to find out the ``sweet spot'' generating the spheres.
+When using a very low \texttt{sampling\_rate}, the reault gets inacurate, but
+when using a high \texttt{sampling\_rate}, the calculations are not affected
+in term of speed and efficiency. The Goal is therefor to find a sampling rate
+that enables the generation of accurate but fast results.
+
+By being able to controll the accuracy anf therefor the time, it is possible to
+teach the system to generate a galaxy in like one hour and it will automatically
+set the sampling rate so low that the simulation will finish perfectly in time.
+
+\subsubsection{The radius of the spheres}
+
+The Radius of the spheres is dynamicly allocated to ensure that the whole galaxy
+is covered.
+
+\begin{equation} \label{sphere_radius}
+  r = \sqrt{\texttt{sphere\_distance}^2 + \texttt{sphere\_distance}^2 + \texttt{sphere\_distance}^2}
+\end{equation}
+
+\begin{equation*}
+  1.7320508075688772 = \sqrt{1^2 + 1^2 + 1^2}
+\end{equation*}
+
+The equation (\ref{sphere_radius}) highly depends on the equation
+(\ref{sphere_distance}) and it's parameters.
+
+\begin{figure}
+  \includegraphics[width=1\textwidth]{figs/sphere_alignment_cc}
+  \caption{The Alignment of the spheres\\
+  Left: The perfect alignment covering the complete space\\
+  Right: A previously generated alignment using small spheres to cover the missing space
+  }
+  \label{sphere_alignment}
+\end{figure}
+
+\subsubsection{Calculate the forces acting on the spheres}
+
+In order to reduce the time that is needed to calculate the forces inbetween
+the stars, the stars are subdivided in different cells, in this case spheres.
+After all the forces acing inside one sphere are calculated, the forces are
+combined and applied to the midpoint of the sphere genrating a new coordinate:
+the mean force. The mean force inbetween all the cells can be calculated.
+
+[Include description binary tree]
+
+[Include graphic binary tree]
+
+\subsubsection{Calculate the forces acting on all the spheres together}
+
+This should be 0.
+
+\subsubsection{Benchmarks}
+
+\begin{tabular}{l | l | l | l}
+  Nr of Stars & Sample rate & Galaxy Range & Time (s) \\\hline
+
+
+  100         & 1           & 100          & 0.0814 \\
+  75          & 1           & 100          & 0.0499 \\
+  50          & 1           & 100          & 0.0295 \\
+  25          & 1           & 100          & 0.0116 \\ \hline
+
+  100         & 1           & 100          & 0.0828 \\
+  100         & 2           & 100          & 0.0909 \\
+  100         & 4           & 100          & 0.1832 \\
+  100         & 8           & 100          & 1.1114 \\
+  100         & 16          & 100          & 7.6944 \\
+  100         & 32          & 100          & 56.5731 \\
+  100         & 64          & 100          & 217.7768 \\ \hline
+
+  100         & 1           & 1            & 0.0809 \\
+  100         & 1           & 2            & 0.0844 \\
+  100         & 1           & 4            & 0.0782 \\
+  100         & 1           & 8            & 0.0758 \\
+  100         & 1           & 16           & 0.0847 \\
+  100         & 1           & 32           & 0.0815 \\
+  100         & 1           & 64           & 0.0770 \\
+
+\end{tabular}
+
+The sample rate is the factor that influences the time the most. Knowing this,
+it (the sample rate) can be used to controll the time in which a galaxy can
+be created.
+This is usefull in particular when using some very powerfull mashine with
+limited time.
+
+\subsection{Calculate the Position of a Star after a timestep}
+
+Not to be considered:
+\begin{itemize}
+  \item drag
+  \item any kind of resistance
+  \item acceleration
+\end{itemize}
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index 6d23e96..6d23e96 100644..100755
--- a/langfassung/figs/Jugend_forscht.jpg
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Binary files differdiff --git a/langfassung/figs/Untitled Diagram.xml b/langfassung/figs/Untitled Diagram.xml
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index 0728a61..4204fe5 100644..100755
--- a/langfassung/master.fdb_latexmk
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diff --git a/langfassung/master.fls b/langfassung/master.fls
index 6d9afd5..0ff9eba 100644
--- a/langfassung/master.fls
+++ b/langfassung/master.fls
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 INPUT /usr/share/texmf-dist/tex/latex/oberdiek/rerunfilecheck.sty
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 INPUT /usr/share/texmf-dist/tex/latex/graphics/graphicx.sty
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 INPUT docs/5_quellen.tex
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diff --git a/langfassung/master.log b/langfassung/master.log
index c9b4f76..f9b7036 100644..100755
--- a/langfassung/master.log
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diff --git a/langfassung/master.out b/langfassung/master.out
index a3a0f11..12deeab 100644..100755
--- a/langfassung/master.out
+++ b/langfassung/master.out
@@ -25,3 +25,21 @@
 \BOOKMARK [2][-]{subsection.3.2}{Lookuptabellen Geschwindigkeit}{section.3}% 25
 \BOOKMARK [2][-]{subsection.3.3}{Fazit}{section.3}% 26
 \BOOKMARK [1][-]{section.4}{Quellen und Hilfen}{}% 27
+\BOOKMARK [1][-]{section.5}{Nach der Abgabe...}{}% 28
+\BOOKMARK [2][-]{subsection.5.1}{Spiralgalaxien}{section.5}% 29
+\BOOKMARK [2][-]{subsection.5.2}{Using Object Oriented Programming \(OOP\) techniques}{section.5}% 30
+\BOOKMARK [3][-]{subsubsection.5.2.1}{Initialisation}{subsection.5.2}% 31
+\BOOKMARK [2][-]{subsection.5.3}{Generation of new stars}{section.5}% 32
+\BOOKMARK [2][-]{subsection.5.4}{Printing all the coordinates}{section.5}% 33
+\BOOKMARK [2][-]{subsection.5.5}{Calculating the Forces acting between the Stars}{section.5}% 34
+\BOOKMARK [2][-]{subsection.5.6}{Calculating the forces acting between each star in the galaxy and each other star}{section.5}% 35
+\BOOKMARK [2][-]{subsection.5.7}{Printing all the individual forces}{section.5}% 36
+\BOOKMARK [2][-]{subsection.5.8}{Spherical cells}{section.5}% 37
+\BOOKMARK [3][-]{subsubsection.5.8.1}{Testing if a point is inside or outside a sphere}{subsection.5.8}% 38
+\BOOKMARK [3][-]{subsubsection.5.8.2}{Testing if a star is inside or outside of a sphere for a whole galaxy}{subsection.5.8}% 39
+\BOOKMARK [3][-]{subsubsection.5.8.3}{Generate the position of the spheres}{subsection.5.8}% 40
+\BOOKMARK [3][-]{subsubsection.5.8.4}{The radius of the spheres}{subsection.5.8}% 41
+\BOOKMARK [3][-]{subsubsection.5.8.5}{Calculate the forces acting on the spheres}{subsection.5.8}% 42
+\BOOKMARK [3][-]{subsubsection.5.8.6}{Calculate the forces acting on all the spheres together}{subsection.5.8}% 43
+\BOOKMARK [3][-]{subsubsection.5.8.7}{Benchmarks}{subsection.5.8}% 44
+\BOOKMARK [2][-]{subsection.5.9}{Calculate the Position of a Star after a timestep}{section.5}% 45
diff --git a/langfassung/master.pdf b/langfassung/master.pdf
index 0575752..350b08d 100644..100755
--- a/langfassung/master.pdf
+++ b/langfassung/master.pdf
Binary files differdiff --git a/langfassung/master.pyg b/langfassung/master.pyg
index 05dd500..05dd500 100644..100755
--- a/langfassung/master.pyg
+++ b/langfassung/master.pyg
diff --git a/langfassung/master.synctex.gz b/langfassung/master.synctex.gz
index b15ecbc..02b0ae0 100644
--- a/langfassung/master.synctex.gz
+++ b/langfassung/master.synctex.gz
Binary files differdiff --git a/langfassung/master.tex b/langfassung/master.tex
index eedd29c..75e232f 100644..100755
--- a/langfassung/master.tex
+++ b/langfassung/master.tex
@@ -1,23 +1,43 @@
 \documentclass[a4paper,10pt]{scrartcl}
 \usepackage[top=2.5cm, bottom=2cm, left=2.5cm, right=2.5cm]{geometry}
+
+% UTF-8 support
 \usepackage[utf8]{inputenc}
+
+% german and english language support
 \usepackage[english,ngerman]{babel}
+
+% more math symbols
 \usepackage{amsmath}
+
+% advanced tables
 \usepackage{tabularx}
+
+% hide the hyperlinks
 \usepackage[hidelinks]{hyperref}
 
+% no newpage after include
+\usepackage{newclude}
+
+% fancy graphics
 \usepackage{graphicx}
+
+% more customizable captions
 \usepackage{caption}
+
+% nice font
 \usepackage{lmodern}
-\usepackage{textcomp}
-\usepackage[onehalfspacing]{setspace}
-\usepackage{setspace}
 
+% ???
+\usepackage{textcomp}
+% \usepackage[onehalfspacing]{setspace}
 % \linespread{0.95}
 
+% Tikz for designing graphics
 \usepackage{tikz}
 \usetikzlibrary{positioning}
 
+% code
 \usepackage{listings}
 \lstset{ %
   frame=single,	                   % adds a frame around the code
@@ -26,6 +46,7 @@
   stepnumber=1,                    % the step between two line-numbers. If it's 1, each line will be numbered
 }
 
+% hyperref / hyperlink settings
 \usepackage{hyperref}
 \hypersetup{
 colorlinks,
@@ -35,10 +56,12 @@ linkcolor=black,
 urlcolor=black
 }
 
+% renew some commands
 \newcommand{\bold}{\textbf}
 \renewcommand{\arraystretch}{1.5}
 \newcommand{ \rarrow }{\( \rightarrow \)}
 
+% redefine some parameters
 \setlength\parindent{0pt}
 \setlength\parskip{10pt}
 \setlength{\footskip}{30pt}
@@ -48,13 +71,16 @@ urlcolor=black
 
 \begin{document}
 
+% titlepage settings
 \title{Galaxy Generation}
 \subtitle{Jugend Forscht \the\year}
 \author{ Emile Hansmaennel \texttt{ emile.hansmaennel@gmail.com }}
 \date{\today}
 
+% generate the title using the informations given above
 \maketitle
 
+% include a nice image
 \begin{figure}[h]
   \centering
   \includegraphics[width=120mm, trim={0 8.5cm 0 8.5cm}, clip]{figs/galaxy}
@@ -62,33 +88,43 @@ urlcolor=black
   \caption{}
  \end{figure}
 
+% include the abstract
 \begin{abstract}
-\input{docs/1_kurzfassung}
+\include*{docs/1_kurzfassung}
 \end{abstract}
 
+% don't insert a page number on the first page
 \thispagestyle{empty}
 \clearpage
 \newpage
 \setcounter{page}{1}
 
+% generate a table of contents
 \tableofcontents
 \newpage
 
 \section{Einleitung} \label{Einleitung}
-\input{docs/2_einleitung}
+% \input{docs/2_einleitung}
+\include*{docs/2_einleitung}
 \newpage
 
 \section{Hauptteil} \label{Hauptteil}
-\input{docs/3_hauptteil}
+% \input{docs/3_hauptteil}
+\include*{docs/3_hauptteil}
 \newpage
 
 \section{Ergebnisse} \label{ergebnisse}
-\input{docs/4_ergebnisse}
+% \input{docs/4_ergebnisse}
+\include*{docs/4_ergebnisse}
 \newpage
 
 \section{Quellen und Hilfen} \label{quellen}
-\input{docs/5_quellen}
-
+% \input{docs/5_quellen}
+\include*{docs/5_quellen}
 \newpage
 
+\section{Nach der Abgabe...} \label{nach_der_abgabe}
+% \input{docs/6_abgabe}
+\include*{docs/6_abgabe}
+
 \end{document}
diff --git a/langfassung/master.toc b/langfassung/master.toc
index 4df4eba..4a85a0f 100644..100755
--- a/langfassung/master.toc
+++ b/langfassung/master.toc
@@ -5,32 +5,50 @@
 \contentsline {section}{\numberline {2}Hauptteil}{3}{section.2}
 \contentsline {subsection}{\numberline {2.1}Generierung von elliptischen Galaxien}{3}{subsection.2.1}
 \contentsline {subsubsection}{\numberline {2.1.1}Das Navarro-Frenk-White Profil}{3}{subsubsection.2.1.1}
-\contentsline {subsubsection}{\numberline {2.1.2}Random Sampling}{5}{subsubsection.2.1.2}
+\contentsline {subsubsection}{\numberline {2.1.2}Random Sampling}{3}{subsubsection.2.1.2}
 \contentsline {subsubsection}{\numberline {2.1.3}Lookup Tabellen}{5}{subsubsection.2.1.3}
 \contentsline {subsection}{\numberline {2.2}Generierung eines Dunkle-Materie Halos durch Anpassung des NFW-Profils}{5}{subsection.2.2}
-\contentsline {subsection}{\numberline {2.3}Stauchung und Streckung der Galaxie}{6}{subsection.2.3}
+\contentsline {subsection}{\numberline {2.3}Stauchung und Streckung der Galaxie}{5}{subsection.2.3}
 \contentsline {subsection}{\numberline {2.4}Rechenaufwand}{6}{subsection.2.4}
-\contentsline {subsection}{\numberline {2.5}Beschleunigung der Generation}{7}{subsection.2.5}
-\contentsline {subsubsection}{\numberline {2.5.1}Lookuptable}{7}{subsubsection.2.5.1}
+\contentsline {subsection}{\numberline {2.5}Beschleunigung der Generation}{6}{subsection.2.5}
+\contentsline {subsubsection}{\numberline {2.5.1}Lookuptable}{6}{subsubsection.2.5.1}
 \contentsline {subsubsection}{\numberline {2.5.2}Mehr Rechenleistung!}{7}{subsubsection.2.5.2}
 \contentsline {paragraph}{\nonumberline Amazon Web Services}{7}{section*.5}
-\contentsline {subsubsection}{\numberline {2.5.3}Nichts in der Konsole ausgeben}{8}{subsubsection.2.5.3}
-\contentsline {subsection}{\numberline {2.6}Nutzung eines neuronalen Netzes zum unbeaufsichtigten generieren von Galaxien}{8}{subsection.2.6}
-\contentsline {subsubsection}{\numberline {2.6.1}Aufbau des neuronalen Netzes}{8}{subsubsection.2.6.1}
+\contentsline {subsubsection}{\numberline {2.5.3}Nichts in der Konsole ausgeben}{7}{subsubsection.2.5.3}
+\contentsline {subsection}{\numberline {2.6}Nutzung eines neuronalen Netzes zum unbeaufsichtigten generieren von Galaxien}{7}{subsection.2.6}
+\contentsline {subsubsection}{\numberline {2.6.1}Aufbau des neuronalen Netzes}{7}{subsubsection.2.6.1}
 \contentsline {paragraph}{\nonumberline Neuronen und Synapsen}{8}{section*.6}
 \contentsline {subsection}{\numberline {2.7}Spiralgalaxien}{9}{subsection.2.7}
 \contentsline {subsubsection}{\numberline {2.7.1}Das n-K\IeC {\"o}rper Problem}{9}{subsubsection.2.7.1}
 \contentsline {subsubsection}{\numberline {2.7.2}Unterteilung des Vektorraumes in verschiedene Zellen}{10}{subsubsection.2.7.2}
-\contentsline {subsubsection}{\numberline {2.7.3}Berechnung der wirkenden Kr\IeC {\"a}fte}{11}{subsubsection.2.7.3}
-\contentsline {paragraph}{\nonumberline Masse der Sterne}{11}{section*.7}
-\contentsline {paragraph}{\nonumberline Abstand der Sterne}{11}{section*.8}
-\contentsline {subsection}{\numberline {2.8}Weiteres}{11}{subsection.2.8}
-\contentsline {section}{\numberline {3}Ergebnisse}{12}{section.3}
-\contentsline {subsection}{\numberline {3.1}Simulations Geschwindigkeit}{12}{subsection.3.1}
-\contentsline {subsection}{\numberline {3.2}Lookuptabellen Geschwindigkeit}{12}{subsection.3.2}
-\contentsline {subsection}{\numberline {3.3}Fazit}{13}{subsection.3.3}
-\contentsline {section}{\numberline {4}Quellen und Hilfen}{14}{section.4}
-\contentsline {paragraph}{\nonumberline Herrn J\IeC {\"o}rg Thar}{14}{section*.11}
-\contentsline {paragraph}{\nonumberline Tim Tugendhat}{14}{section*.12}
-\contentsline {paragraph}{\nonumberline Konstantin Bosbach}{14}{section*.13}
-\contentsline {paragraph}{\nonumberline Tilman Hoffbauer}{14}{section*.14}
+\contentsline {subsubsection}{\numberline {2.7.3}Berechnung der wirkenden Kr\IeC {\"a}fte}{10}{subsubsection.2.7.3}
+\contentsline {paragraph}{\nonumberline Masse der Sterne}{10}{section*.7}
+\contentsline {paragraph}{\nonumberline Abstand der Sterne}{10}{section*.8}
+\contentsline {subsection}{\numberline {2.8}Weiteres}{10}{subsection.2.8}
+\contentsline {section}{\numberline {3}Ergebnisse}{11}{section.3}
+\contentsline {subsection}{\numberline {3.1}Simulations Geschwindigkeit}{11}{subsection.3.1}
+\contentsline {subsection}{\numberline {3.2}Lookuptabellen Geschwindigkeit}{11}{subsection.3.2}
+\contentsline {subsection}{\numberline {3.3}Fazit}{11}{subsection.3.3}
+\contentsline {section}{\numberline {4}Quellen und Hilfen}{13}{section.4}
+\contentsline {paragraph}{\nonumberline Herrn J\IeC {\"o}rg Thar}{13}{section*.11}
+\contentsline {paragraph}{\nonumberline Tim Tugendhat}{13}{section*.12}
+\contentsline {paragraph}{\nonumberline Konstantin Bosbach}{13}{section*.13}
+\contentsline {paragraph}{\nonumberline Tilman Hoffbauer}{13}{section*.14}
+\contentsline {section}{\numberline {5}Nach der Abgabe...}{14}{section.5}
+\contentsline {subsection}{\numberline {5.1}Spiralgalaxien}{14}{subsection.5.1}
+\contentsline {subsection}{\numberline {5.2}Using Object Oriented Programming (OOP) techniques}{14}{subsection.5.2}
+\contentsline {subsubsection}{\numberline {5.2.1}Initialisation}{14}{subsubsection.5.2.1}
+\contentsline {subsection}{\numberline {5.3}Generation of new stars}{14}{subsection.5.3}
+\contentsline {subsection}{\numberline {5.4}Printing all the coordinates}{14}{subsection.5.4}
+\contentsline {subsection}{\numberline {5.5}Calculating the Forces acting between the Stars}{14}{subsection.5.5}
+\contentsline {subsection}{\numberline {5.6}Calculating the forces acting between each star in the galaxy and each other star}{15}{subsection.5.6}
+\contentsline {subsection}{\numberline {5.7}Printing all the individual forces}{15}{subsection.5.7}
+\contentsline {subsection}{\numberline {5.8}Spherical cells}{15}{subsection.5.8}
+\contentsline {subsubsection}{\numberline {5.8.1}Testing if a point is inside or outside a sphere}{15}{subsubsection.5.8.1}
+\contentsline {subsubsection}{\numberline {5.8.2}Testing if a star is inside or outside of a sphere for a whole galaxy}{15}{subsubsection.5.8.2}
+\contentsline {subsubsection}{\numberline {5.8.3}Generate the position of the spheres}{15}{subsubsection.5.8.3}
+\contentsline {subsubsection}{\numberline {5.8.4}The radius of the spheres}{16}{subsubsection.5.8.4}
+\contentsline {subsubsection}{\numberline {5.8.5}Calculate the forces acting on the spheres}{16}{subsubsection.5.8.5}
+\contentsline {subsubsection}{\numberline {5.8.6}Calculate the forces acting on all the spheres together}{17}{subsubsection.5.8.6}
+\contentsline {subsubsection}{\numberline {5.8.7}Benchmarks}{17}{subsubsection.5.8.7}
+\contentsline {subsection}{\numberline {5.9}Calculate the Position of a Star after a timestep}{17}{subsection.5.9}
diff --git a/langfassung/master.x.gnuplot b/langfassung/master.x.gnuplot
index 84fcd41..84fcd41 100644..100755
--- a/langfassung/master.x.gnuplot
+++ b/langfassung/master.x.gnuplot
diff --git a/langfassung/references/Sampling_Design.pdf b/langfassung/references/Sampling_Design.pdf
index 205839d..205839d 100644..100755
--- a/langfassung/references/Sampling_Design.pdf
+++ b/langfassung/references/Sampling_Design.pdf
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index b1b5d2b..b1b5d2b 100644..100755
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