deletions | additions       diff --git a/Methodology Complimentary Data.tex b/Methodology Complimentary Data.tex  index abd71a8..e086836 100644  --- a/Methodology Complimentary Data.tex  +++ b/Methodology Complimentary Data.tex 
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Trajectory clustering is the first step in scenery interpretation. Trajectory clustering is an abstract representation of movements along prototypical paths through a scene, called alignments. This is the foundation for relating spatial position with road geometry and, in particular, position of moving objects in relation to lanes and sidewalks. The alignment is represented as a simple series of points with a begining and end, typically in the same direction is the majority of flows along this path. This process introduces a new coordinate system which maps a position of a moving object in cartesian space to a position in curvilinear space  \begin{equation} \label{eqn:coordinate-transform} (x,y)\to(S,\gamma). (x,y)\to(l,S,\gamma).  \end{equation} where a point located at ($x$,$y$) in cartesian space is snapped to the nearest position on the nearest alignment, alignment $l$,  and is represented by the curvilinear distance $S$ along this alignment from its begining and the offset \( \gammma \), orthogonal to this alignment, measuring the distance between the original point and it's snapped position. These coordinates are useful for measuring following behaviour, lane changes, and lane deflection. Many approaches exist to trajectory clustering, some are produced manually, some are learned automatically. Manual trajectory clustering is labour intensive and potentially a source of bias, but allows for tight control of scenery description and analysis oversight. Larned clustering is systematic but naive as this form of clustering can only make use of trajectory data to infer position. The methodology is primarily based in manual trajectory clustering (called alignments), although a hybrid approach, which refines spatial positioning of manually defined alignments through traditional clustering approaches, is proposed for future work.  \subsubsection{Network Topology}  Once trajectories are clustered, a network topology is constructed in order to in be able to propogate future positions of moving objects across multiple paths. In simple networks, these movements are implicitly defined simply by observing lane change ratios, but larger networks might involve multiple lane changes and require a more general definition.  \subsubsection{Geometric data/inventory}