current TeX

competition/tex/chapters/graph.tex

@@ -1,7 +1,31 @@
 \subsection{Transition}
 	
-	a graph based on the building's floorplan
-	uses prior knowledge (floorplan + desired destination [if known])
-	uses random-walks to perform the transition
-	uses imo (acc,gyro) for the random-walk (distance/direction)
-	calculated offline
+	To enhance the quality of the proposal distribution, the transition step is 
+	based on a \SI{20}{\centimeter}-gridded graph $G = (V,E)$
+	with vertices $v_i \in V$ and undirected edges $e_{i,j} \in E$
+	derived from the buildings floorplan. This ensures that only valid
+	movements can be sampled from the previous state.%
+	
+	\todo{wenn platz dann bild?}
+	
+	The graph is built once and offline using the floorplan created by our editor.
+	Besides realistic stairwells, additional semantic information (e.g. doors)
+	can be included. Hereafter, the built graph is transmitted to the smartphone
+	and is used during the online phase.
+	
+	If the pedestrian's destination is know beforehand, this information can
+	be included as prior knowledge into the transition step. A shortest-path
+	calculation imposes additional constraints to the transition by favouring
+	movements that approach the desired destination (pedestrian sticking to the shortest path)
+	over movements that depart from the destination.
+	
+	To ensure that the calculated shortest path is realistic (resembled human walking paths)
+	each node within the graph contains a weight, denoting the likelyhood for being visited
+	by the pedestrian. Using this approach, nodes near to walls receive a lower likelyhood.
+	During the path-calculation this importance is used to artificially increase/decrease the
+	weight $\delta(\mEdgeAB)$ between two nodes. This ensures that the resulting path is 
+	farther away from obstacles and looks much more realistic
+	
+	\todo{wenn platz dann bild?}
+	
+