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virtuelle Welt zu synchronisieren. +In dem Fall der Arbeit ist dieses Objekt wie bereits beschrieben ein Balken. + +Die Beam Kalibration ist für die Synchronisation des realen Balkens mit dem virtuellen Balken zuständig. +In der Entwicklungsphase gab es sehr viele Ansätze diese Synchronisation zu implementieren. +Hier ist zwischen Grundansätzen und Implementierungsansätze zu Unterscheiden. +Im Zuge dieser arbeit beschreibt ein Grundansatz die grundlegende Strategie das Problem zu lösen und ein Implementierungsansatz die Strategie einen Grundansatz zu lösen. + +\subsubsection{Grundansätze} + +Folgend werden zwei dieser Grundansätze beschrieben. + +\begin{itemize} + \item Tracker Ansatz + \item Marker Ansatz +\end{itemize} + +Der Initial Ansatz dieser Arbeit war der \emph{Tracker Ansatz}. +Dieser Ansatz war eine Lösung mit den bereits in Abschnitt~\ref{sec:vive-tracker} beschriebenen Tracker. +In diesem Lösungsansatz würde ein Tracker in die Mitte des Balkens platziert werden. +Durch diesen Tracker und die Dimensionen des Balkens würde es in der Theorie möglich sein die Position und größe des Balkens zu berechnen. + +Der Vorteil dieses Ansatzes wäre, dass der Balken wärend des Spielerlebnis verschiebbar ist, da die Position durch den Tracker aktualisiert werden kann. + +Leider besitzt dieser Ansatz den ein oder anderen Nachteil. +Einer dieser Nachteile ist, dass die Dimensionen des Balkens beim Initial Setup gemessen werden müssen. +Weiters muss der Tracker in der mitte des Balkens befestigt werden, da durch Änderungen der Position des Trackers auch Änderungen des virtuellen Balkens auftreten. +Schlussendlich muss auch die Mitte des Balkens gefunden werden um den Tracker dort zu plazieren. + +Da die Positionsänderung des Balkens während der Laufzeit in der BeamVR Applikation vernachlässigt werden kann wurde der zweite Lösungsansatz gewählt. + +Der zweite und finale Ansatz ist der \emph{Marker Ansatz}. +Für die BeamVR Applikation reicht es normal aus, dass die Skalierung, Position und Orientierung einmal vor dem Erlebnis ermittelt werden. +Wie bereits beschrieben ist dadurch die dynamische Änderung des virtuellen Balken vernachlässigbar. + +Für den Markenansatz wird kein zusätzlicher Tracker gebraucht. +Alles, was für diesen Ansatz wichtig ist, ist ein Controller und die restlichen VR Geräte. + +Das Prinzip diesem Ansatz ist, dass mit dem Controller die Ecken des Balkens markiert werden. +Diese Markierungen werden von der Applikation gespeichert und später in der Game-Szene verwendet, um den Balken richtig zu positionieren, skalieren und orientieren. +Da die Höhe durch das SteamVR Setup bekannt ist, müssen nur die oberen Ecken des Balkens. + +\begin{figure} + \centering + \includegraphics[scale=0.3]{pics/beam_mark} + \caption{Markierung Einer Ecke des Balkens} + \label{fig:beam-mark} +\end{figure} + +Eine dieser Markierung wird folgendermaßen durchgeführt. +Das runde ende des Controllers muss an der gewünschten Ecke anstoßen. +Daraufhin wird der Trigger gedrückt, welcher sich an der unteren seite des Controller befindet. +In Abb.~\ref{fig:beam-mark} ist dieser Vorgan Visualisiert visualisiert. + +\begin{figure} + \centering + \includegraphics[scale=0.25]{pics/beam-marking-sequence} + \caption{Reihenfolge der Markierungen} + \label{fig:beam-marking-sequence} +\end{figure} + + +Für die Markierung jeder Ecke gibt es eine gewisse Reihenfolge. +Diese Reihenfolge ist von der BeamVR Applikation vordefiniert und von der Position des Abgrunds abhängig. +In Abb.~\ref{fig:beam-marking-sequence} ist die Reihenfolge ersichtlich. + +\subsubsection{Implementierungsansatz} + +Für den Marker Ansatz gibt es wiederum zwei verschiedene Implementierunsansätze. +Diese beinhalten: + +\begin{itemize} + \item Beam Transformation Ansatz + \item World Transformation Ansatz +\end{itemize} + +Der einfachere Ansatz ist der Beam Transformation Ansatz. +Bei diesem Ansatz passen wir den virtuellen Balken an den realen Balken an. + +\begin{figure} + \centering + \includegraphics[scale=0.25]{pics/beam-point-labeling} + \caption{Beschriftungen des Balkens} + \label{fig:beam-point-labeling} +\end{figure} + + +Durch die Postionen der Ecken kann die Mitte berechnet werden, da davon ausgegangen werden kann, dass der Balken ein Quader ist. +In Abb.~\ref{fig:beam-point-labeling} sind die Ecken der oberen Seite des Balken mit $P_{1}, P_{2}, P_{3}, P_{4}$ beschriftet. +Die Mitte der oberen Decke kann mit folgender Formel beschrieben werden. + +$$ + +D = (P_{4} - P_{1}) + +M = P_{1} + \frac{D}{2} + +$$ + \subsection{Schwerkraft} \label{subsec:gravity}