From 4ee0e752a0b9e24d469281fbc0e2a1c331853981 Mon Sep 17 00:00:00 2001 From: FrankE Date: Wed, 10 Feb 2016 08:53:58 +0100 Subject: [PATCH] grid changes only --- tex/chapters/grid.tex | 9 ++++++--- 1 file changed, 6 insertions(+), 3 deletions(-) diff --git a/tex/chapters/grid.tex b/tex/chapters/grid.tex index 88ef73a..f662236 100644 --- a/tex/chapters/grid.tex +++ b/tex/chapters/grid.tex @@ -73,6 +73,7 @@ route calculation. \subsection{wall avoidance} + \label{sec:wallAvoidance} As already mentioned, shortest-path calculation usually sticks close to walls to reduce the path's length. Pedestrian's however, walk either somewhere near (but not close to) a wall or, for larger hallways/rooms, @@ -100,6 +101,7 @@ \subsection{door detection} + \label{sec:doorDetection} Doors are usually anchored between two (thin) walls and have a normed width. Examining only a limited region around the door, its surrounding walls describe a flat ellipse with the same center as the door itself. It is thus @@ -210,9 +212,10 @@ \newcommand{\pathRef}{v_{\hat{x},\hat{y},\hat{z}}} This center is used as starting-point for the shortest path. As it is not necessarily part of - the grid, its nearest-grid-neighbor is used instead. - The resulting node already knows its way to the pedestrian's destination, but is located somewhere - within the deviation of the sample set. After slightly advancing it by a fixed value of about \SI{5}{\meter} + the grid, its nearest-grid-neighbor is determined and used instead. + The resulting vertex already knows its way to the pedestrian's destination, but is located somewhere + within the sample-set. We thus calculate the standard deviation for the distance + of all states from the center. After advancing the starting-vertex by three times the deviation we get a new point outside of the sample-set and closer to the desired destination. This new reference node $\pathRef$ serves as a comparison base: