FrankE
c5a5acbbf6
started working on eval-graphics ned helper methods tested some new aspects some fixes and changes added some graphics new test-floorplan many cleanups
54 lines
2.4 KiB
TeX
54 lines
2.4 KiB
TeX
\section{Floorplan/Path/whatever (RENAME)}
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\subsection{wall avoidance}
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\begin{figure}
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\includegraphics[angle=-90, width=\columnwidth, trim=15 15 15 15]{floorplan_importance}
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\end{figure}
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\subsection{door detection}
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invert grid,
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find k-NN within inversion
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calculate centroid, covariance and eigenvalues
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when centroid OK and eigenvalues OK: is door/passage
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\commentByFrank {
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doors serve 3 purposes:
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- reverting the downvote due to "near walls"
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- hint for a pathless-movement-model how to leave rooms
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- also detecting narrow passages (center the path)
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}
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Doors are usually anchored between two (thin) walls and have a normed width. Examining only a limited region
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around the door, its surrounding walls describe a flat ellipse with the same center as the door itself. It is thus
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possible to detect doors within the floorplan using the PCA \todo{cite}. To describe the surroundings of a door,
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we create and inverted version of our grid whereby the contained nodes denote walls and other obstacles.
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To decide whether a node within the (non-inverted) grid belongs to a door, we use $k$-NN \todo{cite} to fetch its
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$k$ nearest neighbors within the inverted grid. If the distance \todo{equation} between the centroid of those neighbors
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and the node-in-question is above certain threshold, the node does not belong to a door. Assuming the distance was fine,
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we compare the two eigenvalues $\{e_1, e_2 \mid e_1 > e_2\}$ , determined by the PCA. If their ratio $\frac{e_1}{e_2}$ is above
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a certain threshold (flat ellipse)
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the node-in-question belongs to a door. Fig. \ref{fig:doorPCA} depicts all three cases where the node is part of a door (left),
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the distance between node and k-NN centroid is above the threshold (middle) and the ration between $e_1$ and $e_2$ is below the
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threshold (right).
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\begin{figure}
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\includegraphics[width=\columnwidth]{door_pca}
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\caption{Detect doors within the floorplan using k-NN and PCA. While the white nodes are walkable, the black ones represent walls. The grey node is the one in question.}
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\label{fig:doorPCA}
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\end{figure}
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\subsection{pathfinding}
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\begin{figure}
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\includegraphics[angle=-90, width=\columnwidth, trim=15 15 15 15]{floorplan_paths}
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\end{figure}
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\begin{figure}
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\includegraphics[angle=-90, width=\columnwidth, trim=15 15 15 15]{floorplan_dijkstra_heatmap}
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\end{figure}
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