chapter 4 almost rewritten
changed gfx
This commit is contained in:
@@ -68,19 +68,19 @@
|
||||
% error development over time while walking along a path
|
||||
\begin{figure}
|
||||
\input{gfx/eval/error_timed_nexus}
|
||||
\caption{Development of the error while walking along
|
||||
%path 1 (upper) and
|
||||
path 4 (lower) using the Motorola Nexus 6.
|
||||
Path 4 shows increasing errors for our methods when leaving the shortest path (3) and when facing multimodalities between two
|
||||
staircases just before the destination (9).}
|
||||
\caption{Development of the error while walking along Path 4 using the Motorola Nexus 6.
|
||||
When leaving the suggested route (3), the error of shortest path \refeq{eq:transShortestPath}
|
||||
and multipath \refeq{eq:transMultiPath} increases.
|
||||
The same issues arise when facing multimodalities between two staircases just before the destination (9).}
|
||||
\label{fig:errorTimedNexus}
|
||||
\end{figure}
|
||||
% detailed analysis of path 4
|
||||
\begin{figure}
|
||||
\input{gfx/eval/path_nexus_detail}
|
||||
\caption{Detailed path analysis depicting the individual segments of path 4. Their corresponding error contribution can
|
||||
be seen in fig. \ref{fig:errorTimedNexus}. Even though the shortest path suggested by the system is ignored multiple
|
||||
times ($3'$ and $3''$) our approach is still able to improve the overall localisation error.}
|
||||
\caption{Detailed path analysis depicting the individual segments of path 4 using \refeq{eq:transMultiPath}.
|
||||
Their corresponding error can be seen in fig. \ref{fig:errorTimedNexus}. Even though the shortest path
|
||||
suggested by the system is ignored multiple times ($3'$ and $3''$) our approach is still able to improve
|
||||
the overall localisation error.}
|
||||
\label{fig:nexusPathDetails}
|
||||
\end{figure}
|
||||
%
|
||||
|
||||
@@ -7,11 +7,11 @@
|
||||
|
||||
To sample only transitions that are actually feasible
|
||||
within the environment, we utilize a \SI{20}{\centimeter}-gridded graph
|
||||
$G = (V,E)$, $v_{x,y,z} \in V$, $e_{v_{x,y,z}}^{v_{x',y',z'}} \in E$
|
||||
$G = (V,E)$ with vertices $v \in V$ and undirected edges $e \in E$
|
||||
derived from the buildings floorplan as described in section \ref{sec:relatedWork}.
|
||||
However, we add improved $z$-transitions by also modelling realistic
|
||||
stairwells using nodes and edges, depicted in fig. \ref{fig:gridStairs}.
|
||||
%
|
||||
|
||||
\begin{figure}
|
||||
\centering
|
||||
\input{gfx/grid/grid}
|
||||
@@ -24,40 +24,45 @@
|
||||
\end{figure}
|
||||
%
|
||||
Stairs are defined using three points $\vec{\spoint}_1, \vec{\spoint}_2, \vec{\spoint}_3 \in \R^3$ whereby the segment
|
||||
$[ \vec{\spoint}_1 \vec{\spoint}_2 ]$ describes the starting-edge, and $[ \vec{\spoint}_2 \vec{\spoint}_3 ]$ the stair's direction
|
||||
(see fig. \ref{fig:gridStairs}). The grid-vertices corresponding to the starting-edge are determined using an intersection of
|
||||
the segment $[ \vec{\spoint}_1 \vec{\spoint}_2 ]$ with the \SI{20}{\centimeter} bounding-box around each vertex.
|
||||
$[ \vec{\spoint}_1 \vec{\spoint}_2 ]$ describes the starting-edge, and $[ \vec{\spoint}_2 \vec{\spoint}_3 ]$ the stair's
|
||||
direction (see fig. \ref{fig:gridStairs}). The grid-vertices corresponding to the starting-edge are determined using an
|
||||
intersection of the segment $[ \vec{\spoint}_1 \vec{\spoint}_2 ]$ with the \SI{20}{\centimeter} bounding-box around each
|
||||
node's centre $\fPos{v} = (x,y,z)^T$.
|
||||
|
||||
|
||||
To reduce the system's memory footprint, we search for the largest connected region within the graph and
|
||||
remove all nodes and edges that are not connected to this region.
|
||||
|
||||
Walking the grid is now possible by moving along adjacent nodes into a given walking-direction
|
||||
until a desired distance $\gDist$ is reached \cite{Ebner-15}.
|
||||
In order to use meaningful headings $\gHead$ and distances $\gDist$
|
||||
(matching the pedestrian's real heading and walking speed) for each transition,
|
||||
we use the current sensor-readings $\mObsVec_{t}$ for hinted instead of randomized adjustments:
|
||||
%
|
||||
New states $\mStateVec_{t}$ may now be sampled by starting at the vertex for $\fPos{\mStateVec_{t-1}}$ and
|
||||
walking along adjacent nodes into a given walking-direction $\gHead$ until a distance $\gDist$ is
|
||||
reached \cite{Ebner-15}.
|
||||
Both, heading and distance, are supplied by the current sensor readings $\mObsVec_{t}$
|
||||
and thus reflect the pedestrian's real heading and walking speed including uncertainty.
|
||||
Working with relative sensor readings, the state's heading is updated during each transition:
|
||||
%
|
||||
\begin{align}
|
||||
\mState_{t}^{\mStateHeading} = \gHead &= \mState_{t-1}^{\mStateHeading} + \mObs_t^{\mObsHeading} + \mathcal{N}(0, \sigma_{\gHead}^2) \\
|
||||
\gDist &= \mObs_t^{\mObsSteps} \cdot \SI{0.7}{\meter} + \mathcal{N}(0, \sigma_{\gDist}^2)
|
||||
\gHead &= \mState_{t}^{\mStateHeading} = \mState_{t-1}^{\mStateHeading} + \mObs_t^{\mObsHeading} + \mathcal{N}(0, \sigma_{\gHead}^2) \\
|
||||
\gDist &= \mObs_t^{\mObsSteps} \cdot \SI{0.7}{\meter} + \mathcal{N}(0, \sigma_{\gDist}^2)
|
||||
.
|
||||
\end{align}
|
||||
%
|
||||
During a walk, each edge has an assigned probability $p(e)$ which depends on
|
||||
the its direction $\angle e$ and the current heading $\gHead$.
|
||||
We will use $p(e)$ to incorporate prior path knowledge to
|
||||
favour some vertices/edges. For each single movement on the graph,
|
||||
we calculate $p(e)$ for all adjacent edges, and, hereafter, randomly draw the
|
||||
to-be-walked edge depending on those probabilities. The random walk ends,
|
||||
as soon as the distance $d$ is reached. $d$ depends on the number of detected steps
|
||||
$\mObsVec_t^{\mObsSteps}$ and assumes an average step-size of \SI{0.7}{\meter}.
|
||||
During the random walk, each edge has its own probability $p(e)$
|
||||
which e.g. depends on the edge's direction $\angle e$ and the
|
||||
pedestrian's current heading $\gHead$.
|
||||
Furthermore, $p(e)$ is used to incorporate prior path knowledge to
|
||||
favour edges leading towards the pedestrian's desired target.
|
||||
|
||||
For comparison purpose we define a simple weighting method that assigns a probability to each edge
|
||||
just based on the deviation from the currently estimated heading $\gHead$ omitting additional prior knowledge:
|
||||
|
||||
\commentByFrank{das erste $=$ ist komisch. ideen?}
|
||||
\commentByToni{Find ich jetzt nicht tragisch. Eher notwendig fuers Verstaendnis.}
|
||||
For each single movement on the graph, we calculate $p(e)$ for all edges
|
||||
connected to a vertex $v$, and, hereafter, randomly draw the to-be-walked edge
|
||||
depending on those probabilities. This step is repeated until the sum
|
||||
of the length of all used edges exceeds $d$. The latter depends on the number of
|
||||
detected steps $\mObs_t^{\mObsSteps}$ and assumes an average
|
||||
step-size of \SI{0.7}{\meter}.
|
||||
|
||||
To quantify the improvement prior knowledge is able to provide,
|
||||
we define a simple reference for $p(e)$ that assigns a probability to each edge
|
||||
just based on its deviation from the currently estimated heading $\gHead$:
|
||||
%
|
||||
\begin{equation}
|
||||
p(e) = p(e \mid \gHead) = \mathcal{N} (\angle e \mid \gHead, \sigma_\text{dev}^2).
|
||||
\label{eq:transSimple}
|
||||
@@ -79,34 +84,24 @@
|
||||
\label{sec:wallAvoidance}
|
||||
|
||||
As discussed in section \ref{sec:relatedWork}, simply applying a shortest-path algorithm such as Dijkstra or
|
||||
A* using the previously created graph would obviously lead to non-realistic paths sticking to the walls and
|
||||
walking many diagonals. Pedestrian's however, walk either somewhere near (but not close to) a wall or, for
|
||||
larger open spaces, somewhere far from the walls. In order to calculate paths that resemble such a walking
|
||||
behaviour, an importance-factor is derived for each vertex within the graph. Those will be used to
|
||||
adjust the distance-weight between two vertices, needed by the shortest-path algorithm.
|
||||
A* using the previously created graph would obviously lead to non-realistic paths sticking to walls and
|
||||
walking many diagonals. Pedestrian's however, will probably keep a small gap between themselves and
|
||||
nearby walls. To calculate paths that resemble this behaviour, an importance-factor is derived for
|
||||
each vertex. Those will be used to modify the euclidean distance $\fDistance{u}{v}$ between two vertices
|
||||
$u,v$, examined by the shortest-path algorithm.
|
||||
|
||||
To downvote vertices near walls, we need to get the distance of each vertex from its nearest wall.
|
||||
We therefore build an inverted version $G' = (V', E')$ of the graph $G$, just containing walls and other obstacles.
|
||||
A nearest-neighbour search \cite{Cover1967}
|
||||
%$\mNN(v_{x,y,z}, G')$
|
||||
will then provide the nearest wall-vertex
|
||||
$v'_{x,y,z} \in V'$ from the inverted graph. To get a smooth gradient, the wall avoidance
|
||||
is calculated using a normal distribution with the distance from the nearest wall
|
||||
and a deviation of \SI{0.5}{\meter}:
|
||||
%
|
||||
%\begin{equation}
|
||||
% d_{v, v'} = \| v_{x,y,z}, v'_{x,y,z}, \enskip 0.0 < d_{v, v'} < 2.2 \\
|
||||
%\end{equation}
|
||||
%\begin{equation}
|
||||
%\begin{array}{ll}
|
||||
% \text{wa}_{x,y,z} = & - 0.30 \cdot \mathcal{N}(d_{v, v'} \mid 0.0, 0.5^2) \\
|
||||
% & + 0.15 \cdot \mathcal{N}(d_{v, v'} \mid 0.9, 0.5^2) \\
|
||||
% & + 0.15 \cdot \mathcal{N}(d_{v, v'} \mid 2.2, 0.5^2)
|
||||
%\end{array}
|
||||
%\label{eq:wallAvoidance}
|
||||
%\end{equation}
|
||||
To downvote vertices near walls, we need to determine the distance of each vertex from its nearest wall.
|
||||
We therefore derive an inverted version $G' = (V', E')$ of the graph $G$, just describing walls and other
|
||||
obstacles. A nearest-neighbour search \cite{Cover1967} within $V'$ provides the vertex $v'$
|
||||
nearest to $v$:
|
||||
\begin{equation}
|
||||
\text{wa}_{x,y,z} = \mathcal{N}( \| v_{x,y,z} - v'_{x,y,z} \| \mid 0.0, 0.5^2) \\
|
||||
v' = \fNN{v}{V'} \enskip .
|
||||
\end{equation}
|
||||
To get a smooth gradient around walls, the avoidance-factor
|
||||
is derived using a normal distribution with a deviation of \SI{0.5}{\meter}:
|
||||
%
|
||||
\begin{equation}
|
||||
\fWA{v} = \mathcal{N}( \fDistance{v}{\fNN{v}{V'}} \mid 0.0, 0.5^2) \\
|
||||
\label{eq:wallAvoidance}
|
||||
\end{equation}
|
||||
%
|
||||
@@ -114,9 +109,9 @@
|
||||
%While this approach provides good results for most areas, doors are downvoted by
|
||||
%\refeq{eq:wallAvoidance}, as they have only vertices that are close to walls.
|
||||
%Door detection and upvoting thus is the next conducted step.
|
||||
While effectively rendering wall-regions less likely, \refeq{eq:wallAvoidance}
|
||||
will obviously have the same effect on all doors located within the building.
|
||||
Therefore, a door-detection is necessary, to upvote them again.
|
||||
While rendering wall-regions less likely, \refeq{eq:wallAvoidance}
|
||||
will obviously have the same effect on doors as they are just a small gap between
|
||||
consecutive walls. Therefore, a door-detection is necessary, to upvote them again.
|
||||
|
||||
|
||||
|
||||
@@ -124,90 +119,103 @@
|
||||
\label{sec:doorDetection}
|
||||
|
||||
To automatically detect doors within the floorplan, we utilize the fact that doors are usually
|
||||
anchored between two (straight) walls and have a normed width. Examining the region directly
|
||||
around it, the door and its surrounding walls describe a flat ellipse with the door as its
|
||||
centre.
|
||||
anchored between two straight walls and have a normed width. Examining the region directly
|
||||
around it, the door and its surrounding walls thus describe a flat ellipse with the door as its centre.
|
||||
%It is thus possible to detect doors within the floorplan using a PCA.
|
||||
|
||||
To decide whether a vertex $v_{x,y,z}$ within the (non-inverted) grid $G$ belongs to a door,
|
||||
we use $k$-NN to fetch its $k$ nearest neighbours $\hat{V}$ within the inverted grid $G'$,
|
||||
describing the walls nearby. Hereafter we determine the centroid $\vec{c} \in \R^3$
|
||||
and 2D covariance $(x,y)$ for those vertices.
|
||||
To decide whether a vertex $v$ belongs to a door, we use \mbox{$k$-NN} to fetch its $k$ nearest neighbours
|
||||
$\{v'_1, v'_2, \dots, v'_k\} \in V'$ within the inverted grid $G'$, denoting nearby walls.
|
||||
%Hereafter we determine the centroid $\vec{c} \in \R^3$
|
||||
%and 2D covariance $(x,y)$ for those vertices.
|
||||
Hereafter we determine their centroid $\vec{c}$ and covariance $\mat{\Sigma}$:
|
||||
\begin{equation}
|
||||
\vec{c} = \frac{1}{k}\sum_{i=1}^{k} \fPos{v_i}
|
||||
,\smallskip
|
||||
\mat{\Sigma} = \frac{1}{k} \sum_{i=1}^{k} \varphi \cdot \varphi^T
|
||||
,\smallskip
|
||||
\varphi = \fPos{v_i}-\vec{c} \enskip.
|
||||
\end{equation}
|
||||
%
|
||||
Using the PCA, we examine the two eigenvalues $\{\lambda_1, \lambda_2 \mid \lambda_1 > \lambda_2\}$,
|
||||
for the covariance matrix. If their ratio $\frac{\lambda_1}{\lambda_2}$ is above a certain
|
||||
threshold, the neighbourhood describes a flat ellipse and thus either a straight wall or door.
|
||||
For $\mat{\Sigma}$, the two largest eigenvalues $\{\lambda_1, \lambda_2 \mid \lambda_1 > \lambda_2\}$
|
||||
are calculated. If their ratio $^{\lambda_1}/_{\lambda_2}$ is above a certain
|
||||
threshold, the neighbourhood describes a flat ellipse and thus either a door or a straight wall
|
||||
%
|
||||
To prevent a vertex $v_{x,y,z}$ adjacent to such straight walls from also being detected,
|
||||
we ensure the distance $\| \vec{c} - v_{x,y,z} \|$ between the centroid and the vertex is
|
||||
below a certain threshold. Hereafter, only vertices located within the door itself remain.
|
||||
To filter the latter, we enforce the euclidean distance \mbox{$\| \fPos{v} - \vec{c} \|$} between
|
||||
the centroid and the vertex to be very small. Hereafter, only vertices located directly within a
|
||||
door itself remain.
|
||||
%
|
||||
\begin{figure}
|
||||
\includegraphics[width=\columnwidth]{door_pca}
|
||||
\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.}
|
||||
\caption{Detect doors within the floorplan using $k$-NN to get the centroid $\vec{c}$ and covariance $\mat{\Sigma}$
|
||||
of the wall-vertices (black) near $v$. While the left version is fine, the $v$ in the middle is too far
|
||||
from $\vec{c}$ and the right one has an invalid eigenvalue-ratio.}
|
||||
\label{fig:doorPCA}
|
||||
\end{figure}
|
||||
%
|
||||
Fig. \ref{fig:doorPCA} depicts all three cases where
|
||||
(left) the vertex is part of a door,
|
||||
(middle) the distance between node and centroid is above the threshold and
|
||||
(right) the ration between $\lambda_1$ and $\lambda_2$ is below the threshold.
|
||||
(right) the ratio between $\lambda_1$ and $\lambda_2$ is below the threshold.
|
||||
|
||||
For smooth importance-gradients around doors, we again use a distribution based on
|
||||
the distance of a vertex $v_{x,y,z}$ from its nearest door and a deviation
|
||||
of \SI{1.0}{\meter} to determine its importance-factor:
|
||||
For smooth gradients around doors, we again use a distribution based on
|
||||
the distance of a vertex $v$ from its nearest door and a deviation
|
||||
of \SI{1.0}{\meter}:
|
||||
%
|
||||
%\commentByFrank{distanzrechnung: formel ok?}
|
||||
\begin{equation}
|
||||
\text{dd}_{x,y,z} = \mathcal{N}( \| \vec{c} - v_{x,y,z} \| \mid 0.0, 1.0^2 )
|
||||
\fDD{v} = \mathcal{N}( \| \fPos{v} - \vec{c} \| \mid 0.0, 1.0^2 )
|
||||
\label{eq:doorDetection}
|
||||
\end{equation}
|
||||
|
||||
The final importance for each node is now calculated using \refeq{eq:wallAvoidance}
|
||||
%
|
||||
The final importance combines \refeq{eq:wallAvoidance}
|
||||
and \refeq{eq:doorDetection}:
|
||||
%
|
||||
\begin{equation}
|
||||
\text{imp}_{x,y,z} = 1.0 - \text{wa}_{x,y,z} + \text{dd}_{x,y,z} \enspace .
|
||||
\fImp{v} = 1.0 - \fWA{v} + \fDD{v} \enspace .
|
||||
\label{eq:finalImp}
|
||||
\end{equation}
|
||||
%
|
||||
While most vertices receive a factor of $1.0$, wall-regions get lower and
|
||||
While most nodes receive a neutral factor of $1.0$, wall-regions get lower and
|
||||
door-regions higher values, depicted in fig. \ref{fig:importance}.
|
||||
%
|
||||
\begin{figure}
|
||||
\includegraphics[width=\columnwidth]{floorplan_importance}
|
||||
\caption{The calculated importance-factor for each vertex. While the black wall-elements denote
|
||||
a small importance, the yellow door-regions receive much higher values.}
|
||||
\caption{The calculated importance-factor \refeq{eq:finalImp} for each vertex.
|
||||
While the dark wall-elements denote a small importance, the yellow areas around doors and narrow
|
||||
passages depict a high importance.}
|
||||
\label{fig:importance}
|
||||
\end{figure}
|
||||
|
||||
\subsection{Path Estimation}
|
||||
\label{sec:pathEstimation}
|
||||
|
||||
|
||||
\commentByFrank{ueberleitung}
|
||||
To estimate the shortest path to the pedestrian's desired target, we use a modified version
|
||||
of Dijkstra's algorithm. Instead of calculating the shortest path from the start to the end,
|
||||
we swap start/end and do not terminate the calculation until every single node was evaluated.
|
||||
Thus, every node in the grid knows the shortest path to the pedestrian's target.
|
||||
For routing the pedestrian towards his desired target, a modified version
|
||||
of Dijkstra's algorithm is used. Instead of calculating the shortest path from the start to the end,
|
||||
the direction is inverted and the calculated terminates as soon as every single node was evaluated.
|
||||
Hereafter, every node in the grid knows the distance and shortest path to the pedestrian's target.
|
||||
|
||||
As weighting-function we use
|
||||
To get realistic path suggestions, we use the importance-factors to adjust the edge-weight
|
||||
$\delta(v_1, v_2)$ for the Dijkstra:
|
||||
%
|
||||
\begin{equation}
|
||||
\begin{split}
|
||||
\text{weight}(v_{x,y,z}, v_{x',y',z'}) =
|
||||
\delta(v_1, v_2) =
|
||||
\frac
|
||||
{ \| v_{x,y,z} - v_{x',y',z'} \| }
|
||||
{ \text{imp}_{x',y',z'} }
|
||||
.
|
||||
{ \| v_1 - v_2 \| }
|
||||
{ \fImp{v_2} }
|
||||
\enskip.
|
||||
\end{split}
|
||||
\label{eq:edgeWeight}
|
||||
\end{equation}
|
||||
%
|
||||
Eq. \eqref{eq:edgeWeight} artificially increases the euclidean distance between $v_1, v_2$ when
|
||||
$v_2$ approaches a wall and decreases it when encountering a door.
|
||||
%
|
||||
%whereby $\text{stretch}(\cdots)$ is a scaling function (linear or non-linear) used to adjust
|
||||
%the impact of the previously calculated importance-factors.
|
||||
%
|
||||
Fig. \ref{fig:multiHeatMap} depicts the difference between the shortest path calculated without (dashed) and
|
||||
with importance-factors (solid), where the latter version is clearly more realistic.
|
||||
with importance-factors (solid), where the latter is clearly more realistic.
|
||||
|
||||
%\begin{figure}
|
||||
% \includegraphics[angle=-90, width=\columnwidth, trim=20 19 17 9, clip]{floorplan_paths}
|
||||
@@ -219,101 +227,89 @@
|
||||
|
||||
\subsection{Guidance}
|
||||
|
||||
Based on the previous calculations, we propose two approaches to utilize the prior
|
||||
knowledge within the transition model.
|
||||
Based on the previous considerations, we propose two approaches to utilize prior
|
||||
knowledge within the transition.
|
||||
|
||||
\subsubsection{Shortest Path}
|
||||
|
||||
Before every transition, the centroid $\vec{c}$ of the current sample-set $\Upsilon_{t-1}$,
|
||||
representing the posterior distribution at time $t-1$, is calculated:
|
||||
%
|
||||
\begin{equation}
|
||||
\vec{c} = \frac
|
||||
%{ \sum_{\mStateVec_{t-1}} (\mState_{t-1}^x, \mState_{t-1}^y, \mState_{t-1}^z)^T }
|
||||
{ \sum_{i=1}^N \Upsilon_{t-1}^{x,y,z} }
|
||||
{N}
|
||||
\end{equation}
|
||||
\newcommand{\pathCentroid}{{\vec{\overline{c}}_{t-1}}}
|
||||
\newcommand{\pathDev}{\sigma_{t-1}}
|
||||
\newcommand{\pathRef}{\hat{v}}
|
||||
|
||||
Before every transition, the centroid $\pathCentroid$ of the current
|
||||
sample-set, representing the posterior distribution at time $t-1$, is calculated.
|
||||
%
|
||||
oder
|
||||
%
|
||||
\begin{equation}
|
||||
\vec{c} = \frac
|
||||
{ \sum_{i=1}^N \{(\mState_{t-1}^x, \mState_{t-1}^y, \mState_{t-1}^z)^T\}^i }
|
||||
{N}
|
||||
\end{equation}
|
||||
%\commentByFrank{avg-state vom sample-set. frank d. meinte ja hier muessen wir aufpassen. bin noch unschluessig wie.}
|
||||
%\commentByToni{Das ist gar nicht so einfach... wir haben nie ein Sample Set eingefuehrt. Nicht mal einen Sample. Wir haben immer nur diesen State... Man könnte natuerlich einfach sagen das $\Upsilon_t$ an set of random samples representing the posterior distribution ist oder einfach nur ein set von partikeln. habs mal eingefuegt wie ich denke}
|
||||
%
|
||||
oder: the centroid $\vec{c}$ of the current sample-set's 3D positions $\Upsilon_{t-1}^i = \{(\mState_{t-1}^x, \mState_{t-1}^y, \mState_{t-1}^z)^T\}_{i=0}^N$ is calculated:
|
||||
This centre serves as the starting point for the shortest-path calculation.
|
||||
As it is not necessarily part of the grid, its nearest-grid-neighbour is determined and used instead.
|
||||
This vertex is located somewhere within the sample-set and already knows the way to the pedestrian's destination.
|
||||
%
|
||||
\begin{equation}
|
||||
\vec{c} = \frac
|
||||
%{ \sum_{\mStateVec_{t-1}} (\mState_{t-1}^x, \mState_{t-1}^y, \mState_{t-1}^z)^T }
|
||||
{ \sum_{i=1}^N \Upsilon_{t-1}^{i} }
|
||||
{N}
|
||||
\end{equation}
|
||||
|
||||
\newcommand{\pathRef}{v_{\hat{x},\hat{y},\hat{z}}}
|
||||
\commentByFrank{avg-state vom sample-set. frank d. meinte ja hier muessen wir aufpassen. bin noch unschluessig wie.}
|
||||
\commentByToni{Das ist gar nicht so einfach... wir haben nie ein Sample Set eingefuehrt. Nicht mal einen Sample. Wir haben immer nur diesen State... Man könnte natuerlich einfach sagen das $\Upsilon_t$ an set of random samples representing the posterior distribution ist oder einfach nur ein set von partikeln. habs mal eingefuegt wie ich denke}
|
||||
|
||||
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 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 samples from the centre. After advancing the starting-vertex by three times this deviation
|
||||
we get a new point that is: part of the shortest path, outside of the sample-set and closer to the
|
||||
desired destination.
|
||||
This new reference node $\pathRef$ serves as a comparison base:
|
||||
\commentByToni{Allgemein mal zur Schreibweise der Vertices. Irgendwie finde ich dieses $v_{x,y,z}$ nicht so gut. Ich denke jeder sieht das wir 3D haben und deswegen könntem man doch schlicht $v$, $v'$, $\hat{v}$ ... nutzen, oder was denkst du?}
|
||||
\commentByFrank{war der vorschlag von frank d. letztes mal, weil man an vertices nicht einfach attribute (x,y,z) anhaengen kann wie wir es bei $\mObsVec$, $\mStateVec$ haben.}
|
||||
As new states $\mStateVec_{t}$ should approach the pedestrian's destination
|
||||
we use a reference $\pathRef$ all states try to reach. This references must
|
||||
both, part of the shortest path and located somewhere outside of the sample-set.
|
||||
%
|
||||
We thus calculate the standard deviation of the distance of all samples from the centre
|
||||
$\pathCentroid$. After advancing the starting-vertex by three times this deviation
|
||||
we get a new point $\pathRef$ that is: part of the shortest path, outside of the sample-set
|
||||
and closer (but not too close) to the desired destination.
|
||||
%
|
||||
Hereafter, the simple transition \refeq{eq:transSimple} is combined with a second probability,
|
||||
downvoting all grid-steps that depart from $\pathRef$.
|
||||
Finally, \refeq{eq:transShortestPath} provides a metric tending towards the reference while
|
||||
still allowing the pedestrian to leave the shortest path:
|
||||
%
|
||||
\begin{equation}
|
||||
\begin{split}
|
||||
p(e) &=
|
||||
p(v_{x',y',z'} \mid v_{x,y,z})\\
|
||||
&= \mathcal{N} (\angle [ v_{x,y,z} v_{x',y',z'} ] \mid \gHead, \sigma_\text{dev}^2) \cdot \alpha \\
|
||||
p(v' \mid v) =
|
||||
\mathcal{N} (\angle e \mid \gHead, \sigma_\text{dev}^2) \cdot \alpha \\
|
||||
\alpha &=
|
||||
\begin{cases}
|
||||
0.9 & \| v_{x',y',z'} - \pathRef \| < \| v_{x,y,z} - \pathRef \| \\
|
||||
0.9 & \| v' - \pathRef \| < \| v - \pathRef \| \\
|
||||
0.1 & \text{else}
|
||||
\end{cases}
|
||||
\end{split}
|
||||
.
|
||||
\label{eq:transShortestPath}
|
||||
\end{equation}
|
||||
%
|
||||
Eq. \eqref{eq:transShortestPath} combines the simple transition \refeq{eq:transSimple} with
|
||||
a second probability, downvoting all nodes that are farther away from the reference $\pathRef$
|
||||
than the previous step. Put another way: grid-steps increasing the distance to the reference
|
||||
are unlikely but not impossible.
|
||||
|
||||
|
||||
|
||||
\subsubsection{Multipath}
|
||||
|
||||
The shortest-path algorithm mentioned in \ref{sec:pathEstimation} already calculated the
|
||||
cumulative distance $\text{cdist}_{x,y,z}$ to the pedestrian's target for each vertex.
|
||||
We thus apply the same assumption as above and downvote grid-steps not decreasing
|
||||
the distance to the destination:
|
||||
|
||||
$\fLength{v}{\dot{v}}$ % = \sum_{i=s}^{e-1} \| v_{i} - v_{i+1} \| $
|
||||
for the path from $v$ to the pedestrian's destination $\dot{v}$.
|
||||
We thus apply the same assumption as \refeq{eq:transShortestPath} and downvote edges
|
||||
not decreasing the distance to the destination:
|
||||
%
|
||||
\begin{equation}
|
||||
\begin{split}
|
||||
p(e) &=
|
||||
p(v_{x',y',z'} \mid v_{x,y,z})\\
|
||||
& = \mathcal{N} (\angle [ v_{x,y,z} v_{x',y',z'} ] \mid \gHead, \sigma_\text{dev}^2) \cdot \alpha \\
|
||||
p(v' \mid v) =
|
||||
\mathcal{N} (\angle e \mid \gHead, \sigma_\text{dev}^2) \cdot \alpha \\
|
||||
\alpha &=
|
||||
\begin{cases}
|
||||
0.9 & \text{cdist}_{x',y',z'} < \text{cdist}_{x,y,z} \\
|
||||
0.9 & \fLength{v'}{\dot{v}} < \fLength{v}{\dot{v}} \\
|
||||
0.1 & \text{else}
|
||||
\end{cases}
|
||||
\end{split}
|
||||
\label{eq:transMultiPath}
|
||||
\end{equation}
|
||||
|
||||
Fig. \ref{fig:multiHeatMap} shows the heat-map of visited vertices after several \SI{125}{\meter}
|
||||
walks simulating slight, random heading changes.
|
||||
|
||||
%
|
||||
Fig. \ref{fig:multiHeatMap} shows a heat-map of how often vertices were visited after several
|
||||
\SI{125}{\meter} walks. The colours from cold to hot indicate that both possible paths
|
||||
are covered and slight deviations from the shortest version are possible.
|
||||
%
|
||||
\begin{figure}
|
||||
\includegraphics[width=\columnwidth]{floorplan_dijkstra_heatmap}
|
||||
\caption{Heat-Map of visited vertices after several walks using \refeq{eq:transMultiPath}.
|
||||
Additionally shows the shortest path calculation without (dashed) and with (solid) importance-factors
|
||||
\includegraphics[width=\columnwidth, trim=4 8 4 4]{floorplan_dijkstra_heatmap}
|
||||
\caption{Heat-Map of visited vertices after several walks using \refeq{eq:transMultiPath} with colours
|
||||
from cold to hot. Both possible paths are covered and slight deviations are possible.
|
||||
Additionally shows the shortest-path calculation without (dashed) and with (solid) importance-factors
|
||||
used for edge-weight-adjustment.}
|
||||
\label{fig:multiHeatMap}
|
||||
\end{figure}
|
||||
|
||||
@@ -1,10 +1,10 @@
|
||||
%!PS-Adobe-3.0 EPSF-3.0
|
||||
%%Creator: cairo 1.14.4 (http://cairographics.org)
|
||||
%%CreationDate: Wed Feb 3 18:26:16 2016
|
||||
%%CreationDate: Wed Feb 17 20:50:33 2016
|
||||
%%Pages: 1
|
||||
%%DocumentData: Clean7Bit
|
||||
%%LanguageLevel: 2
|
||||
%%BoundingBox: 3 2 356 37
|
||||
%%BoundingBox: 0 -1 359 39
|
||||
%%EndComments
|
||||
%%BeginProlog
|
||||
save
|
||||
@@ -60,53 +60,283 @@ save
|
||||
/d1 { setcachedevice } bind def
|
||||
%%EndProlog
|
||||
%%BeginSetup
|
||||
%%BeginResource: font LiberationSerif-BoldItalic
|
||||
11 dict begin
|
||||
/FontType 42 def
|
||||
/FontName /LiberationSerif-BoldItalic def
|
||||
/PaintType 0 def
|
||||
/FontMatrix [ 1 0 0 1 0 0 ] def
|
||||
/FontBBox [ 0 0 0 0 ] def
|
||||
/Encoding 256 array def
|
||||
0 1 255 { Encoding exch /.notdef put } for
|
||||
Encoding 99 /c put
|
||||
/CharStrings 2 dict dup begin
|
||||
/.notdef 0 def
|
||||
/c 1 def
|
||||
end readonly def
|
||||
/sfnts [
|
||||
<000100000009008000030010637674205a045c31000001b8000002406670676d73d323b00000
|
||||
03f800000705676c79667f4da6240000009c0000011c6865616405f2afde00000b0000000036
|
||||
686865610f5f063300000b3800000024686d74780679006200000b5c000000086c6f6361008e
|
||||
002c00000b64000000066d6178700422074f00000b6c00000020707265705992daf000000b8c
|
||||
000004520002004400000264055500030007002eb101002f3cb207041ded32b10605dc3cb203
|
||||
021ded3200b103002f3cb205041ded32b207061efc3cb201021ded3233112111252111214402
|
||||
20fe240198fe680555faab4404cd00000001001effec036f03c50027004d40197707011a032a
|
||||
03020a020111101023200f600f700f800f040fb8ffc04014161c480f291a4705154f4011800a
|
||||
10221f500016003ffdc63f1acc1aed012fed10d62b5dce33113331305d5d5d05222e0235343e
|
||||
0233321e02170323272e0123220e0215141e0233323637170e0301875a885a2d619dc7662854
|
||||
4f441731480e1947323a6c54321b2e40244b7b392c1b4e617214335d804e9ceea051080d1008
|
||||
fee0ab1c204d8ac0743f5a391a36283f18362e1f0000058d00150051053d000f006f053d054c
|
||||
000000000000000000000000000003ac001900a20000ffec00000000ffec00000000ffecfee3
|
||||
fe4cfffa00000000000000000000000000000000000000000000000000000000000000000000
|
||||
0000000000000000000000000000000000000000000000000000000000000000000000000000
|
||||
000000000800000000000000010a00da00fa0133000000000000005a0064007c009400860133
|
||||
00000000000000000000000001290137005a007d01000064006e008d01040000000000000000
|
||||
0000000000000000000000000000010d00fc005a00f2009e0064006e007d00cd005500000000
|
||||
0000000000000000000000000000000000560109013300f0004c00d500630079007100c50131
|
||||
013300f000a4014600ad00c00071005501bc014c015a00cd00ee0054014c0066006f008c010e
|
||||
00000000000000000000000000000000026a012d008f004b010c008f007b0068010c00000000
|
||||
02ef00c1029d005e02e3000000ae005e006a010a023900ee006a01a200ec018b005a00be00b4
|
||||
0000000000540048000000000000000000000000ff10ff0100c200fa01060070009000a40000
|
||||
000000000000054002160546020a00a000b40000000000490052007b008e0000000000000064
|
||||
00ea01840000000000ea00fcfeee0000000000560068007c000000000748036a02b60202fd93
|
||||
0000009100670091006101d90000028d034101ce030e030100bafe51fe67056e000000d20088
|
||||
00d40102019400d8007800e8fe8c02140136009e00e90044051101b440455958555453525150
|
||||
4f4e4d4c4b4a494847464544434241403f3e3d3c3b3a393837363531302f2e2d2c2827262524
|
||||
2322211f181411100f0e0d0b0a090807060504030201002c4523466020b02660b00426234848
|
||||
2d2c452346236120b02661b004262348482d2c45234660b0206120b04660b004262348482d2c
|
||||
4523462361b0206020b02661b02061b004262348482d2c45234660b0406120b06660b0042623
|
||||
48482d2c4523462361b0406020b02661b04061b004262348482d2c0110203c003c2d2c204523
|
||||
20b0cd442320b8015a51582320b08d44235920b0ed51582320b04d44235920b0042651582320
|
||||
b00d44235921212d2c20204518684420b001602045b04676688a4560442d2c01b10b0a432343
|
||||
650a2d2c00b10a0b4323430b2d2c00b0282370b101283e01b0282370b10228453ab10200080d
|
||||
2d2c2045b00325456164b050515845441b2121592d2c49b00e23442d2c2045b0004360442d2c
|
||||
01b00643b00743650a2d2c2069b04061b0008b20b12cc08a8cb8100062602b0c642364615c58
|
||||
b00361592d2c8a03458a8a87b0112bb0292344b0297ae4182d2c4565b02c234445b02b23442d
|
||||
2c4b525845441b2121592d2c4b515845441b2121592d2c01b005251023208af500b0016023ed
|
||||
ec2d2c01b005251023208af500b0016123edec2d2c01b0062510f500edec2d2c462346608a8a
|
||||
462320468a608a61b8ff8062232010238ab10c0c8a70456020b0005058b00161b8ffba8b1bb0
|
||||
468c59b0106068013a2d2c2045b0032546524bb013515b58b0022546206861b00325b003253f
|
||||
2321381b2111592d2c2045b00325465058b0022546206861b00325b003253f2321381b211159
|
||||
2d2c00b00743b006430b2d2c21210c6423648bb84000622d2c21b08051580c6423648bb82000
|
||||
621bb200402f2b59b002602d2c21b0c051580c6423648bb81555621bb200802f2b59b002602d
|
||||
2c0c6423648bb84000626023212d2c4b53588ab004254964234569b0408b61b08062b020616a
|
||||
b00e23442310b00ef61b21238a121120392f592d2c4b535820b0032549646920b00526b00625
|
||||
49642361b08062b020616ab00e2344b0042610b00ef68a10b00e2344b00ef6b00e2344b00eed
|
||||
1b8ab00426111220392320392f2f592d2c4523456023456023456023766818b08062202d2cb0
|
||||
482b2d2c2045b0005458b040442045b04061441b2121592d2c45b1302f4523456160b0016069
|
||||
442d2c4b5158b02f2370b01423421b2121592d2c4b515820b0032545695358441b2121591b21
|
||||
21592d2c45b01443b0006063b0016069442d2cb02f45442d2c452320458a60442d2c45234560
|
||||
442d2c4b235158b90033ffe0b134201bb3330034005944442d2cb0164358b00326458a586466
|
||||
b01f601b64b020606620581b21b04059b001615923586559b02923442310b029e01b21212121
|
||||
21592d2cb0024354584b53234b515a58381b2121591b21212121592d2cb0164358b004254564
|
||||
b020606620581b21b04059b0016123581b6559b0292344b00525b00825082058021b0359b004
|
||||
2510b005252046b0042523423cb00425b0072508b0072510b006252046b00425b0016023423c
|
||||
2058011b0059b0042510b00525b029e0b02920456544b0072510b00625b029e0b00525b00825
|
||||
082058021b0359b00525b003254348b00425b0072508b00625b00325b0016043481b21592121
|
||||
21212121212d2c02b00425202046b004252342b0052508b003254548212121212d2c02b00325
|
||||
20b0042508b0022543482121212d2c452320451820b00050205823652359236820b040505821
|
||||
b04059235865598a60442d2c4b53234b515a5820458a60441b2121592d2c4b545820458a6044
|
||||
1b2121592d2c4b53234b515a58381b2121592d2cb000214b5458381b2121592d2cb002435458
|
||||
b0462b1b21212121592d2cb002435458b0472b1b212121592d2cb002435458b0482b1b212121
|
||||
21592d2cb002435458b0492b1b212121592d2c208a08234b538a4b515a5823381b2121592d2c
|
||||
00b0022549b000535820b04038111b21592d2c014623466023466123201020468a61b8ff8062
|
||||
8ab140408a704560683a2d2c208a2349648a2353583c1b21592d2c4b52587d1b7a592d2cb012
|
||||
004b014b54422d2cb1020042b123018851b1400188535a58b910000020885458b20201024360
|
||||
4259b12401885158b920000040885458b2020202436042b12401885458b2022002436042004b
|
||||
014b5258b2020802436042591bb940000080885458b202040243604259b94000008063b80100
|
||||
885458b202080243604259b94000010063b80200885458b202100243604259b94000020063b8
|
||||
0400885458b202400243604259595959592d2c451868234b51582320452064b04050587c5968
|
||||
8a6059442d2cb00016b00225b0022501b001233e00b002233eb10102060cb00a236542b00b23
|
||||
4201b001233f00b002233fb10102060cb006236542b0072342b00116012d2c7a8a104523f518
|
||||
2d00000000010000000111eb6e6c067c5f0f3cf5001f080000000000cf7aa9c500000000cf7a
|
||||
a9c5fe93fd93093407d9000300080002000000000000000100000721fe4500570902fe93fe86
|
||||
09340064001d000000000000000000000000000202ec0044038d001e0000002c008e00000001
|
||||
0000000201520054006f000500020010002f005a00000359055b00030002bf00500107000100
|
||||
2f0107000100af0104404601d0fd01bffd0110fd016ffb0140fb01f21ac81ff75f331ff65fff
|
||||
1ff54eff1ff1f0331f3ff04ff002e7e6331f0fe60100e610e602e5e4ff1fe4ab331fe1e0321f
|
||||
9fe0afe002b9010a0109400b331fdfdd331fde03331f1f41190109002f010900020000010900
|
||||
100109003001090060010900d0010900050010010900300109004001090060010900b0010940
|
||||
3705bfdd010fdd3fdd4fdd7fdd8fddafddbfddcfddffdd09dc03331fd7d61f1fd55fff1fd4d4
|
||||
ff1fc9c8ff1fc8c3fe1fc5c4ff1fd1d0331fb8ffc0406fd0090c4640c001c1472b1fbc47ff1f
|
||||
be472b1fafbdbfbd02bfbdcfbd025fbd6fbd7fbdafbd0440bd090c46ba5fff1fb9adff1f0fb7
|
||||
3fb702b64eff1f7fb5afb5022fb33fb3bfb3030fb33fb35fb3efb30490b001a0b001b0b0c0b0
|
||||
02afad1f1faead341f90ac01a0ac01b0acc0ac02b8010eb203181fb8010d401f1bff1fa0a9b0
|
||||
a902a99b331f9d5fff1f9c5fff1f309b409b02d09b010f9b01b8011ab2961c1fb80113402099
|
||||
331f9f47ff1f3f99010098109820980360980197961c1f3096409602d09601b8010cb31bff1f
|
||||
60410d0115000100800114000100400114005001140060011400e0011440290494931f1f7092
|
||||
8092909203918f331f908c331f8e85ff1f8d84ff1f2f8c015f8c010f8c1f8c7f8c03b8010b40
|
||||
0a8b331f308a408a508a03b8ffc0400c891a1e468882331f8682ff1fb8ffc0404d84090c4677
|
||||
4e3c1f00761076a0760360767076807603755f201f7460ff1f735fff1f6f727f72029f72af72
|
||||
0271471e1f6f6e341f6e47321f001a101a021a01185519331855073303550603ff1fb9ffc001
|
||||
1bb2141c46b80117b262341fb80116b35f341f00410a0110001001100020011000a001100004
|
||||
ffc00110b20f1346b8ffc0409362143446615f341f605f341f5f4f1f1f0f5e1f5e2f5e9f5eaf
|
||||
5e055b5a2b1f605ad05a020f5a1f5a02140112551333125505010355043303550f032f033f03
|
||||
5f037f03af0306005310538053038051016f4e7f4e8f4e03804a014a470a1f4947331f4f485f
|
||||
48020f471f47020f471f472f479f47af47051d011b551c481b551633155511010f5510330f55
|
||||
0201005501330055b8011840191b331f2f0fff0f020f0f5f0f7f0f030f003f00028016010501
|
||||
b80190b154532b2b4bb807ff524bb007505bb00188b02553b00188b040515ab00688b000555a
|
||||
5b58b101018e59858d8d00421d4bb0325358b0601d594bb0645358b0401d594bb0805358b010
|
||||
1db1160042597373742b2b2b2b2b2b2b2b017374732b2b7300747573732b2b2b2b0173742b73
|
||||
002b2b2b2b2b742b2b2b2b2b2b2b73012b2b2b7374002b2b2b73742b012b2b2b2b742b007374
|
||||
752b2b2b2b732b7374732b0173742b7374732b2b2b007373742b2b2b752b2b01737475002b2b
|
||||
73747573740173002b732b2b2b737475012b2b002b0173002b2b012b002b2b012b002b2b2b73
|
||||
747374752b2b2b01732b002b2b74752b01732b002b2b2b2b73737373730173737318000000>
|
||||
] def
|
||||
/f-0-0 currentdict end definefont pop
|
||||
%%EndResource
|
||||
%%BeginResource: font LiberationSerif-Italic
|
||||
11 dict begin
|
||||
/FontType 42 def
|
||||
/FontName /LiberationSerif-Italic def
|
||||
/PaintType 0 def
|
||||
/FontMatrix [ 1 0 0 1 0 0 ] def
|
||||
/FontBBox [ 0 0 0 0 ] def
|
||||
/Encoding 256 array def
|
||||
0 1 255 { Encoding exch /.notdef put } for
|
||||
Encoding 118 /v put
|
||||
/CharStrings 2 dict dup begin
|
||||
/.notdef 0 def
|
||||
/v 1 def
|
||||
end readonly def
|
||||
/sfnts [
|
||||
<00010000000900800003001063767420516347b6000001d0000002406670676d73d323b00000
|
||||
041000000705676c79660817154b0000009c00000134686561640574afde00000b1800000036
|
||||
686865610ee205ae00000b5000000024686d74780679006000000b74000000086c6f6361009a
|
||||
002c00000b7c000000066d617870049a069d00000b840000002070726570c8e9076c00000ba4
|
||||
000003e40002004400000264055500030007002eb101002f3cb20704e6ed32b10605dc3cb203
|
||||
02e6ed3200b103002f3cb20504e6ed32b207061efc3cb20102e6ed3233112111252111214402
|
||||
20fe240198fe680555faab4404cd00000001001cffec038d03ac0015008b405e061201090f01
|
||||
290f010f100152141514471110141111105415011515110baf03cf03020303173f175f177f17
|
||||
03d411e41102bb11cb1102af11019b110100111011021114114f07130f401550150214152415
|
||||
341503801501741501151016003f335d5d71713f33ed33012f5d5d5d5d5d5d11332f5dcd1139
|
||||
192f5d8718102b872bc401325d31305d5d013e013534262737331e0115140607012303273721
|
||||
1302af231d2a1808be09112033fe5949bd71090100910266396226252c072d082215206b51fd
|
||||
5b037a192dfd2400058d00150000053d000f006f053d054c0000000000000000000000000000
|
||||
03ac001900000000ffec00000000ffec00000000ffecfee3fe4cfffa00000000000000000000
|
||||
0000000000000000000000000000000000000000000000000000000000000000000000000000
|
||||
00000000000000000000000000000000000000000000000000000000080000000000000000a6
|
||||
00af009300d900c6000000000000004600500069007d00d900000000000000000000000000c1
|
||||
00c800af007700500050005a00aa000000000000000000000000000000000000000000000000
|
||||
00ac00b8005a0000000000500060008200990000000000000000000000000000000000000000
|
||||
000000cb003700d70050009b00b4000000000000000000c9007b006d008d00d9005000460058
|
||||
0132014600f200b2006a00da00c500f2004d000000000000ffe3009c00d4020e00fe00000000
|
||||
0000053d0000006600000000006600c002db0000000000000000009802a0004a02e400000099
|
||||
00660050000000000042004201a8009c019f0046008e0000000000000046003c000000000000
|
||||
00000000000000000000007d008900000052006800760087000000000000054202170552020a
|
||||
007e008e006c0000003a0056004400670070030e0301000000a9017f018b000000b000a50000
|
||||
000000000056002efe4cfeee00000748036a02b60202fd930000009100670091006101d90000
|
||||
028d034100000000022fff10009c00c40030ff00fe67fe5801c901d60082004600e8017200b4
|
||||
006e008dfe9c006a01aa051101b4404559585554535251504f4e4d4c4b4a4948474645444342
|
||||
41403f3e3d3c3b3a393837363531302f2e2d2c28272625242322211f181411100f0e0d0b0a09
|
||||
0807060504030201002c4523466020b02660b004262348482d2c452346236120b02661b00426
|
||||
2348482d2c45234660b0206120b04660b004262348482d2c4523462361b0206020b02661b020
|
||||
61b004262348482d2c45234660b0406120b06660b004262348482d2c4523462361b0406020b0
|
||||
2661b04061b004262348482d2c0110203c003c2d2c20452320b0cd442320b8015a51582320b0
|
||||
8d44235920b0ed51582320b04d44235920b0042651582320b00d44235921212d2c2020451868
|
||||
4420b001602045b04676688a4560442d2c01b10b0a432343650a2d2c00b10a0b4323430b2d2c
|
||||
00b0282370b101283e01b0282370b10228453ab10200080d2d2c2045b00325456164b0505158
|
||||
45441b2121592d2c49b00e23442d2c2045b0004360442d2c01b00643b00743650a2d2c2069b0
|
||||
4061b0008b20b12cc08a8cb8100062602b0c642364615c58b00361592d2c8a03458a8a87b011
|
||||
2bb0292344b0297ae4182d2c4565b02c234445b02b23442d2c4b525845441b2121592d2c4b51
|
||||
5845441b2121592d2c01b005251023208af500b0016023edec2d2c01b005251023208af500b0
|
||||
016123edec2d2c01b0062510f500edec2d2c462346608a8a462320468a608a61b8ff80622320
|
||||
10238ab10c0c8a70456020b0005058b00161b8ffba8b1bb0468c59b0106068013a2d2c2045b0
|
||||
032546524bb013515b58b0022546206861b00325b003253f2321381b2111592d2c2045b00325
|
||||
465058b0022546206861b00325b003253f2321381b2111592d2c00b00743b006430b2d2c2121
|
||||
0c6423648bb84000622d2c21b08051580c6423648bb82000621bb200402f2b59b002602d2c21
|
||||
b0c051580c6423648bb81555621bb200802f2b59b002602d2c0c6423648bb84000626023212d
|
||||
2c4b53588ab004254964234569b0408b61b08062b020616ab00e23442310b00ef61b21238a12
|
||||
1120392f592d2c4b535820b0032549646920b00526b0062549642361b08062b020616ab00e23
|
||||
44b0042610b00ef68a10b00e2344b00ef6b00e2344b00eed1b8ab00426111220392320392f2f
|
||||
592d2c4523456023456023456023766818b08062202d2cb0482b2d2c2045b0005458b0404420
|
||||
45b04061441b2121592d2c45b1302f4523456160b0016069442d2c4b5158b02f2370b0142342
|
||||
1b2121592d2c4b515820b0032545695358441b2121591b2121592d2c45b01443b0006063b001
|
||||
6069442d2cb02f45442d2c452320458a60442d2c45234560442d2c4b235158b90033ffe0b134
|
||||
201bb3330034005944442d2cb0164358b00326458a586466b01f601b64b020606620581b21b0
|
||||
4059b001615923586559b02923442310b029e01b2121212121592d2cb0024354584b53234b51
|
||||
5a58381b2121591b21212121592d2cb0164358b004254564b020606620581b21b04059b00161
|
||||
23581b6559b0292344b00525b00825082058021b0359b0042510b005252046b0042523423cb0
|
||||
0425b0072508b0072510b006252046b00425b0016023423c2058011b0059b0042510b00525b0
|
||||
29e0b02920456544b0072510b00625b029e0b00525b00825082058021b0359b00525b0032543
|
||||
48b00425b0072508b00625b00325b0016043481b2159212121212121212d2c02b00425202046
|
||||
b004252342b0052508b003254548212121212d2c02b0032520b0042508b0022543482121212d
|
||||
2c452320451820b00050205823652359236820b040505821b04059235865598a60442d2c4b53
|
||||
234b515a5820458a60441b2121592d2c4b545820458a60441b2121592d2c4b53234b515a5838
|
||||
1b2121592d2cb000214b5458381b2121592d2cb002435458b0462b1b21212121592d2cb00243
|
||||
5458b0472b1b212121592d2cb002435458b0482b1b21212121592d2cb002435458b0492b1b21
|
||||
2121592d2c208a08234b538a4b515a5823381b2121592d2c00b0022549b000535820b0403811
|
||||
1b21592d2c014623466023466123201020468a61b8ff80628ab140408a704560683a2d2c208a
|
||||
2349648a2353583c1b21592d2c4b52587d1b7a592d2cb012004b014b54422d2cb1020042b123
|
||||
018851b1400188535a58b910000020885458b202010243604259b12401885158b92000004088
|
||||
5458b2020202436042b12401885458b2022002436042004b014b5258b2020802436042591bb9
|
||||
40000080885458b202040243604259b94000008063b80100885458b202080243604259b94000
|
||||
010063b80200885458b202100243604259b94000020063b80400885458b20240024360425959
|
||||
5959592d2c451868234b51582320452064b04050587c59688a6059442d2cb00016b00225b002
|
||||
2501b001233e00b002233eb10102060cb00a236542b00b234201b001233f00b002233fb10102
|
||||
060cb006236542b0072342b00116012d2c7a8a104523f5182d00000000010000000111eb905c
|
||||
fa345f0f3cf5001f080000000000cf7aa9c500000000cf7aa9c5fe96fd9308b407d900020008
|
||||
0002000000000000000100000721fe450057086bfe96fe9808b40064001d0000000000000000
|
||||
00000000000202ec0044038d001c0000002c009a000000010000000201520054007900050002
|
||||
0010002f005a000003d1049f00030002bf005001070001002f0107000100af0104401101d0fd
|
||||
01bffd0110fd016ffb0140fb01f8b8010f4012291ff71bff1ff650281ff5503c1ff1f03c1fb9
|
||||
0113011240843c1feeed3c1fec47ff1fe850291fe750291fe6e43c1fe550351fe450351fe1b4
|
||||
331fe0b41a1feae9331fdfdd331fde03331f2fe95fe97fe9afe9040fe95fe9afe9ffe9040900
|
||||
dd013c2fdd3fdd7fddbfdd042fdd3fdd4fddafddbfddcfddffdd070fdd01dc03331fd8501c1f
|
||||
d7501c1fd6501c1fd550ff1fc9c83d1fc84f3c1fc34f291fb9010b010f4012291f2fc2013fc2
|
||||
8fc202c1a1ff1fbf50291fb8010db247121fb8010cb7a1ff1fbe5e291f0fb8010a400901bbad
|
||||
341fbaadff1fb8ffc04033b9242846b950241f3fb701b650291fbfb4010faf5faf6faf9faf04
|
||||
70ae80ae90ae0320ae30ae40aed0aee0aef0ae06ad50291fbc0111003d011000550110b21b3c
|
||||
1fb8010e402e2903550fa3012fa2018fa201ffa20160a270a280a203a912ff1fa803ff1fa033
|
||||
12559c50291f9b533c1fa44a3c1fb8ffc04015a12124469fa1afa1029a47121f994aff1f964a
|
||||
3c1fbc011d01170029001f0118b353291f3fba0117004f0117404a0295943c1f0f947f940209
|
||||
93503d1f92503d1f9150ff1f908c3d1f8f8d291f8e8d3d1f008d013b0f8d018c533c1f878229
|
||||
1f84823c1f708280820276753c1ff0750174732a1f7350291fb80115401b70291f6f6e2b1f6e
|
||||
472a1f1a0b1b5519331855073303550603ff1fbc011a01140029001f0119b35f331f40b80114
|
||||
b2242746b8ffc0b3612b3046b8ffc0400c611f2346605f401f5f50291fb8ffc0409a5d1a1e46
|
||||
5c47201f5b5a301f5a47291f140112551333125505010355043303550f032f033f035f037f03
|
||||
af03066053705380530352512f1f5150291fe050f050020f4f1f4f2f4f034b47331f4a47121f
|
||||
49473c1f4847381f0f471f472f47cf47df47ef47069f47011d011b551c481b55163315551101
|
||||
0f5510330f5502010055013300552f0fff0f020f0f5f0f7f0f030f003f00028016010501b801
|
||||
90b154532b2b4bb807ff524bb009505bb00188b02553b00188b040515ab00688b000555a5b58
|
||||
b101018e59858d8d00421d4bb0325358b0601d594bb0645358b0401d594bb0805358b0101db1
|
||||
160042597373742b2b2b2b2b2b2b0173752b2b2b2b0075742b2b73732b2b2b2b012b2b2b2b00
|
||||
2b2b2b2b2b2b2b2b2b2b2b012b2b2b002b2b742b01732b2b002b755e732b2b2b2b2b2b5e732b
|
||||
732b2b012b2b2b732b2b002b2b2b2b2b73737475732b2b2b2b7475730173002b732b2b2b2b73
|
||||
012b2b2b002b2b73742b012b002b2b2b2b2b2b2b7373745e735e73742b2b2b012b2b002b2b2b
|
||||
2b2b012b002b2b012b002b2b2b2b7373737373017373731800>
|
||||
] def
|
||||
/f-1-0 currentdict end definefont pop
|
||||
%%EndResource
|
||||
%%EndSetup
|
||||
%%Page: 1 1
|
||||
%%BeginPageSetup
|
||||
%%PageBoundingBox: 3 2 356 37
|
||||
%%PageBoundingBox: 0 -1 359 39
|
||||
%%EndPageSetup
|
||||
q 3 2 353 35 rectclip q
|
||||
1 0.501961 0.501961 rg
|
||||
281.602 19.201 m 281.602 10.365 273.004 3.201 262.398 3.201 c 251.797 3.201
|
||||
243.199 10.365 243.199 19.201 c 243.199 28.037 251.797 35.201 262.398 35.201
|
||||
c 273.004 35.201 281.602 28.037 281.602 19.201 c h
|
||||
281.602 19.201 m f
|
||||
q 0 -1 359 40 rectclip q
|
||||
0.501961 g
|
||||
0 0.002 m 12.801 0.002 l 12.801 12.798 l 38.398 12.798 l 38.398 25.599
|
||||
l 12.801 25.599 l 12.801 38.4 l 0 38.4 l h
|
||||
0 0.002 m f*
|
||||
89.602 25.599 25.598 -12.801 re f*
|
||||
121.602 38.4 m 121.602 0.002 l 134.398 0.002 l 134.398 12.798 l 160 12.798
|
||||
l 160 25.599 l 134.398 25.599 l 134.398 38.4 l h
|
||||
121.602 38.4 m f*
|
||||
211.199 25.599 25.602 -12.801 re f*
|
||||
243.199 38.4 m 243.199 0.002 l 256 0.002 l 256 12.798 l 281.602 12.798
|
||||
l 281.602 25.599 l 256 25.599 l 256 38.4 l h
|
||||
243.199 38.4 m f*
|
||||
332.801 25.599 25.598 -12.801 re f*
|
||||
0 g
|
||||
0.8 w
|
||||
0 J
|
||||
0 j
|
||||
[ 0.8 0.8] 0 d
|
||||
4 M q 1 0 0 -1 0 38.400002 cm
|
||||
281.602 19.199 m 281.602 28.035 273.004 35.199 262.398 35.199 c 251.797
|
||||
35.199 243.199 28.035 243.199 19.199 c 243.199 10.363 251.797 3.199 262.398
|
||||
3.199 c 273.004 3.199 281.602 10.363 281.602 19.199 c h
|
||||
281.602 19.199 m S Q
|
||||
0.501961 1 0.501961 rg
|
||||
115.199 19.201 m 115.199 15.666 92.277 12.798 64 12.798 c 35.723 12.798
|
||||
12.801 15.666 12.801 19.201 c 12.801 22.736 35.723 25.599 64 25.599 c 92.277
|
||||
25.599 115.199 22.736 115.199 19.201 c h
|
||||
115.199 19.201 m f
|
||||
0 g
|
||||
[ 0.8 0.8] 0 d
|
||||
q 1 0 0 -1 0 38.400002 cm
|
||||
115.199 19.199 m 115.199 22.734 92.277 25.602 64 25.602 c 35.723 25.602
|
||||
12.801 22.734 12.801 19.199 c 12.801 15.664 35.723 12.801 64 12.801 c 92.277
|
||||
12.801 115.199 15.664 115.199 19.199 c h
|
||||
115.199 19.199 m S Q
|
||||
1 0.501961 0.501961 rg
|
||||
236.801 19.201 m 236.801 15.666 216.742 12.798 192 12.798 c 167.258 12.798
|
||||
147.199 15.666 147.199 19.201 c 147.199 22.736 167.258 25.599 192 25.599
|
||||
c 216.742 25.599 236.801 22.736 236.801 19.201 c h
|
||||
236.801 19.201 m f
|
||||
0 g
|
||||
[ 0.8 0.8] 0 d
|
||||
q 1 0 0 -1 0 38.400002 cm
|
||||
236.801 19.199 m 236.801 22.734 216.742 25.602 192 25.602 c 167.258 25.602
|
||||
147.199 22.734 147.199 19.199 c 147.199 15.664 167.258 12.801 192 12.801
|
||||
c 216.742 12.801 236.801 15.664 236.801 19.199 c h
|
||||
236.801 19.199 m S Q
|
||||
0.501961 g
|
||||
[] 0.0 d
|
||||
4 M q 1 0 0 -1 0 38.400002 cm
|
||||
118.398 0 m 118.398 38.398 l S Q
|
||||
q 1 0 0 -1 0 38.400002 cm
|
||||
240 0 m 240 38.398 l S Q
|
||||
0.501961 g
|
||||
q 1 0 0 -1 0 38.400002 cm
|
||||
48 19.199 m 48 20.969 46.566 22.398 44.801 22.398 c 43.031 22.398 41.602
|
||||
20.969 41.602 19.199 c 41.602 17.434 43.031 16 44.801 16 c 46.566 16 48
|
||||
@@ -251,14 +481,17 @@ q 1 0 0 -1 0 38.400002 cm
|
||||
30.232 3.199 32.002 c 3.199 33.767 4.633 35.201 6.398 35.201 c 8.168 35.201
|
||||
9.602 33.767 9.602 32.002 c h
|
||||
9.602 32.002 m f
|
||||
0 0 1 rg
|
||||
q 1 0 0 -1 0 38.400002 cm
|
||||
64 19.199 m 64 12.801 l S Q
|
||||
q 1 0 0 -1 0 38.400002 cm
|
||||
64 19.199 m 12.801 19.199 l S Q
|
||||
0 0 0.752941 rg
|
||||
[ 0.8 0.8] 0 d
|
||||
q 1 0 0 -1 0 38.400002 cm
|
||||
64 19.199 m 70.398 6.398 l S Q
|
||||
0.501961 g
|
||||
[] 0.0 d
|
||||
q 1 0 0 -1 0 38.400002 cm
|
||||
169.602 19.199 m 169.602 20.969 168.168 22.398 166.398 22.398 c 164.633
|
||||
22.398 163.199 20.969 163.199 19.199 c 163.199 17.434 164.633 16 166.398
|
||||
@@ -391,14 +624,17 @@ q 1 0 0 -1 0 38.400002 cm
|
||||
227.199 8.168 227.199 6.398 c 227.199 4.633 228.633 3.199 230.398 3.199
|
||||
c 232.168 3.199 233.602 4.633 233.602 6.398 c h
|
||||
233.602 6.398 m S Q
|
||||
0 0 1 rg
|
||||
q 1 0 0 -1 0 38.400002 cm
|
||||
192 19.199 m 192 12.801 l S Q
|
||||
q 1 0 0 -1 0 38.400002 cm
|
||||
192 19.199 m 147.199 19.199 l S Q
|
||||
0 0 0.752941 rg
|
||||
[ 0.8 0.8] 0 d
|
||||
q 1 0 0 -1 0 38.400002 cm
|
||||
192 19.199 m 230.398 6.398 l S Q
|
||||
0.501961 g
|
||||
[] 0.0 d
|
||||
q 1 0 0 -1 0 38.400002 cm
|
||||
291.199 19.199 m 291.199 20.969 289.766 22.398 288 22.398 c 286.234 22.398
|
||||
284.801 20.969 284.801 19.199 c 284.801 17.434 286.234 16 288 16 c 289.766
|
||||
@@ -537,14 +773,52 @@ q 1 0 0 -1 0 38.400002 cm
|
||||
8.168 284.801 6.398 c 284.801 4.633 286.234 3.199 288 3.199 c 289.766 3.199
|
||||
291.199 4.633 291.199 6.398 c h
|
||||
291.199 6.398 m S Q
|
||||
0 g
|
||||
0 0 1 rg
|
||||
q 1 0 0 -1 0 38.400002 cm
|
||||
262.398 19.199 m 243.199 19.199 l S Q
|
||||
q 1 0 0 -1 0 38.400002 cm
|
||||
262.398 19.199 m 262.398 3.199 l S Q
|
||||
0 0 0.752941 rg
|
||||
[ 0.8 0.8] 0 d
|
||||
q 1 0 0 -1 0 38.400002 cm
|
||||
262.398 19.199 m 275.199 6.398 l S Q
|
||||
1 0 0 rg
|
||||
2.4 w
|
||||
[] 0.0 d
|
||||
q 1 0 0 -1 0 38.400002 cm
|
||||
281.602 19.199 m 281.602 28.035 273.004 35.199 262.398 35.199 c 251.797
|
||||
35.199 243.199 28.035 243.199 19.199 c 243.199 10.363 251.797 3.199 262.398
|
||||
3.199 c 273.004 3.199 281.602 10.363 281.602 19.199 c h
|
||||
281.602 19.199 m S Q
|
||||
0 0.768627 0 rg
|
||||
q 1 0 0 -1 0 38.400002 cm
|
||||
115.199 19.199 m 115.199 22.734 92.277 25.602 64 25.602 c 35.723 25.602
|
||||
12.801 22.734 12.801 19.199 c 12.801 15.664 35.723 12.801 64 12.801 c 92.277
|
||||
12.801 115.199 15.664 115.199 19.199 c h
|
||||
115.199 19.199 m S Q
|
||||
1 0 0 rg
|
||||
q 1 0 0 -1 0 38.400002 cm
|
||||
236.801 19.199 m 236.801 22.734 216.742 25.602 192 25.602 c 167.258 25.602
|
||||
147.199 22.734 147.199 19.199 c 147.199 15.664 167.258 12.801 192 12.801
|
||||
c 216.742 12.801 236.801 15.664 236.801 19.199 c h
|
||||
236.801 19.199 m S Q
|
||||
0 g
|
||||
BT
|
||||
8 0 0 8 260.60459 11.289333 Tm
|
||||
/f-0-0 1 Tf
|
||||
(c)Tj
|
||||
-24.839723 0.312057 Td
|
||||
(c)Tj
|
||||
16.477159 0.142513 Td
|
||||
(c)Tj
|
||||
/f-1-0 1 Tf
|
||||
-16.332804 2.339562 Td
|
||||
(v)Tj
|
||||
20.127616 0.00947022 Td
|
||||
(v)Tj
|
||||
6.908234 -0.0220971 Td
|
||||
(v)Tj
|
||||
ET
|
||||
Q Q
|
||||
showpage
|
||||
%%Trailer
|
||||
|
||||
@@ -206,11 +206,11 @@
|
||||
borderopacity="1.0"
|
||||
inkscape:pageopacity="0.0"
|
||||
inkscape:pageshadow="2"
|
||||
inkscape:zoom="1.979899"
|
||||
inkscape:cx="232.59995"
|
||||
inkscape:cy="65.182272"
|
||||
inkscape:zoom="2.8284271"
|
||||
inkscape:cx="265.88479"
|
||||
inkscape:cy="23.442037"
|
||||
inkscape:document-units="px"
|
||||
inkscape:current-layer="layer4"
|
||||
inkscape:current-layer="layer5"
|
||||
showgrid="true"
|
||||
units="px"
|
||||
inkscape:window-width="1600"
|
||||
@@ -241,30 +241,48 @@
|
||||
</metadata>
|
||||
<g
|
||||
inkscape:groupmode="layer"
|
||||
id="layer5"
|
||||
inkscape:label="ellipse2"
|
||||
transform="translate(0,-132)">
|
||||
<ellipse
|
||||
style="fill:#ff8080;fill-opacity:1;stroke:#000000;stroke-width:1;stroke-miterlimit:4;stroke-dasharray:1, 1;stroke-dashoffset:0;stroke-opacity:1"
|
||||
id="path4385-3"
|
||||
cx="328"
|
||||
cy="156"
|
||||
rx="24"
|
||||
ry="20" />
|
||||
<ellipse
|
||||
style="fill:#80ff80;fill-opacity:1;stroke:#000000;stroke-width:1;stroke-miterlimit:4;stroke-dasharray:1, 1;stroke-dashoffset:0;stroke-opacity:1"
|
||||
id="path4385"
|
||||
cx="80"
|
||||
cy="156"
|
||||
rx="64"
|
||||
ry="8" />
|
||||
<ellipse
|
||||
style="fill:#ff8080;fill-opacity:1;stroke:#000000;stroke-width:1;stroke-miterlimit:4;stroke-dasharray:1, 1;stroke-dashoffset:0;stroke-opacity:1"
|
||||
id="path4385-7"
|
||||
cx="240"
|
||||
cy="156"
|
||||
rx="56"
|
||||
ry="8" />
|
||||
id="layer7"
|
||||
inkscape:label="lines">
|
||||
<path
|
||||
style="fill:#808080;fill-rule:evenodd;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;fill-opacity:1"
|
||||
d="M 0,48 16,48 16,32 48,32 48,16 16,16 16,0 0,0 Z"
|
||||
id="path4358"
|
||||
inkscape:connector-curvature="0" />
|
||||
<path
|
||||
style="fill:#808080;fill-rule:evenodd;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;fill-opacity:1"
|
||||
d="m 112,16 0,16 32,0 0,-16 z"
|
||||
id="path4360"
|
||||
inkscape:connector-curvature="0" />
|
||||
<path
|
||||
style="fill:#808080;fill-rule:evenodd;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;fill-opacity:1"
|
||||
d="m 152,0 0,48 16,0 0,-16 32,0 0,-16 -32,0 0,-16 -16,0 z"
|
||||
id="path4362"
|
||||
inkscape:connector-curvature="0" />
|
||||
<path
|
||||
style="fill:#808080;fill-rule:evenodd;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;fill-opacity:1"
|
||||
d="m 264,16 0,16 32,0 0,-16 -32,0 z"
|
||||
id="path4364"
|
||||
inkscape:connector-curvature="0" />
|
||||
<path
|
||||
style="fill:#808080;fill-rule:evenodd;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;fill-opacity:1"
|
||||
d="m 304,0 0,48 16,0 0,-16 32,0 0,-16 -32,0 0,-16 z"
|
||||
id="path4366"
|
||||
inkscape:connector-curvature="0" />
|
||||
<path
|
||||
style="fill:#808080;fill-rule:evenodd;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;fill-opacity:1"
|
||||
d="m 416,16 0,16 32,0 0,-16 -32,0 0,0 z"
|
||||
id="path4368"
|
||||
inkscape:connector-curvature="0" />
|
||||
<path
|
||||
style="fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
|
||||
d="m 148,0 0,48"
|
||||
id="path4370"
|
||||
inkscape:connector-curvature="0" />
|
||||
<path
|
||||
style="fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
|
||||
d="m 300,0 0,48"
|
||||
id="path4372"
|
||||
inkscape:connector-curvature="0" />
|
||||
</g>
|
||||
<g
|
||||
inkscape:label="Layer 1"
|
||||
@@ -460,19 +478,19 @@
|
||||
inkscape:label="ellipse"
|
||||
transform="translate(0,-96)">
|
||||
<path
|
||||
style="display:inline;fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
|
||||
style="display:inline;fill:none;fill-rule:evenodd;stroke:#0000ff;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
|
||||
d="m 80,120 0,-8"
|
||||
id="path4387"
|
||||
inkscape:connector-curvature="0"
|
||||
sodipodi:nodetypes="cc" />
|
||||
<path
|
||||
style="display:inline;fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
|
||||
style="display:inline;fill:none;fill-rule:evenodd;stroke:#0000ff;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
|
||||
d="m 80,120 -64,0"
|
||||
id="path4389"
|
||||
inkscape:connector-curvature="0"
|
||||
sodipodi:nodetypes="cc" />
|
||||
<path
|
||||
style="fill:none;fill-rule:evenodd;stroke:#0000c0;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
|
||||
style="fill:none;fill-rule:evenodd;stroke:#0000c0;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;stroke-miterlimit:4;stroke-dasharray:1,1;stroke-dashoffset:0"
|
||||
d="m 80,120 8,-16"
|
||||
id="path5147"
|
||||
inkscape:connector-curvature="0"
|
||||
@@ -634,19 +652,19 @@
|
||||
cy="104"
|
||||
r="4" />
|
||||
<path
|
||||
style="display:inline;fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
|
||||
style="display:inline;fill:none;fill-rule:evenodd;stroke:#0000ff;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
|
||||
d="m 240,120 0,-8"
|
||||
id="path4387-4"
|
||||
inkscape:connector-curvature="0"
|
||||
sodipodi:nodetypes="cc" />
|
||||
<path
|
||||
style="display:inline;fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
|
||||
style="display:inline;fill:none;fill-rule:evenodd;stroke:#0000ff;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
|
||||
d="m 240,120 -56,0"
|
||||
id="path4389-2"
|
||||
inkscape:connector-curvature="0"
|
||||
sodipodi:nodetypes="cc" />
|
||||
<path
|
||||
style="fill:none;fill-rule:evenodd;stroke:#0000c0;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
|
||||
style="fill:none;fill-rule:evenodd;stroke:#0000c0;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;stroke-miterlimit:4;stroke-dasharray:1,1;stroke-dashoffset:0"
|
||||
d="m 240,120 48,-16"
|
||||
id="path5371"
|
||||
inkscape:connector-curvature="0"
|
||||
@@ -814,21 +832,125 @@
|
||||
cy="104"
|
||||
r="4" />
|
||||
<path
|
||||
style="display:inline;fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
|
||||
style="display:inline;fill:none;fill-rule:evenodd;stroke:#0000ff;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
|
||||
d="m 328,120 -24,0"
|
||||
id="path4389-7"
|
||||
inkscape:connector-curvature="0"
|
||||
sodipodi:nodetypes="cc" />
|
||||
<path
|
||||
style="display:inline;fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
|
||||
style="display:inline;fill:none;fill-rule:evenodd;stroke:#0000ff;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
|
||||
d="m 328,120 0,-20"
|
||||
id="path4387-5"
|
||||
inkscape:connector-curvature="0"
|
||||
sodipodi:nodetypes="cc" />
|
||||
<path
|
||||
style="fill:none;fill-rule:evenodd;stroke:#0000c0;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
|
||||
style="fill:none;fill-rule:evenodd;stroke:#0000c0;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;stroke-miterlimit:4;stroke-dasharray:1,1;stroke-dashoffset:0"
|
||||
d="m 328,120 16,-16"
|
||||
id="path6160"
|
||||
inkscape:connector-curvature="0" />
|
||||
</g>
|
||||
<g
|
||||
inkscape:groupmode="layer"
|
||||
id="layer5"
|
||||
inkscape:label="ellipse2"
|
||||
transform="translate(0,-132)">
|
||||
<ellipse
|
||||
style="fill:none;fill-opacity:1;stroke:#ff0000;stroke-width:3;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
|
||||
id="path4385-3"
|
||||
cx="328"
|
||||
cy="156"
|
||||
rx="24"
|
||||
ry="20" />
|
||||
<ellipse
|
||||
style="fill:none;fill-opacity:1;stroke:#00c400;stroke-width:3;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
|
||||
id="path4385"
|
||||
cx="80"
|
||||
cy="156"
|
||||
rx="64"
|
||||
ry="8" />
|
||||
<ellipse
|
||||
style="fill:none;fill-opacity:1;stroke:#ff0000;stroke-width:3;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
|
||||
id="path4385-7"
|
||||
cx="240"
|
||||
cy="156"
|
||||
rx="56"
|
||||
ry="8" />
|
||||
<text
|
||||
xml:space="preserve"
|
||||
style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
|
||||
x="325.75574"
|
||||
y="165.88834"
|
||||
id="text4264-7-1"
|
||||
sodipodi:linespacing="125%"><tspan
|
||||
sodipodi:role="line"
|
||||
id="tspan4266-7-3"
|
||||
x="325.75574"
|
||||
y="165.88834"
|
||||
style="font-style:italic;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:10px;font-family:'Liberation Serif';-inkscape-font-specification:'Liberation Serif Bold Italic'">c</tspan></text>
|
||||
</g>
|
||||
<g
|
||||
inkscape:groupmode="layer"
|
||||
id="layer6"
|
||||
inkscape:label="txt">
|
||||
<text
|
||||
xml:space="preserve"
|
||||
style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
|
||||
x="77.358505"
|
||||
y="30.767767"
|
||||
id="text4264"
|
||||
sodipodi:linespacing="125%"><tspan
|
||||
sodipodi:role="line"
|
||||
id="tspan4266"
|
||||
x="77.358505"
|
||||
y="30.767767"
|
||||
style="font-size:10px;-inkscape-font-specification:'Liberation Serif Bold Italic';font-family:'Liberation Serif';font-weight:bold;font-style:italic;font-stretch:normal;font-variant:normal">c</tspan></text>
|
||||
<text
|
||||
xml:space="preserve"
|
||||
style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
|
||||
x="242.1301"
|
||||
y="29.342638"
|
||||
id="text4264-7"
|
||||
sodipodi:linespacing="125%"><tspan
|
||||
sodipodi:role="line"
|
||||
id="tspan4266-7"
|
||||
x="242.1301"
|
||||
y="29.342638"
|
||||
style="font-style:italic;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:10px;font-family:'Liberation Serif';-inkscape-font-specification:'Liberation Serif Bold Italic'">c</tspan></text>
|
||||
<text
|
||||
xml:space="preserve"
|
||||
style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
|
||||
x="78.802055"
|
||||
y="5.947021"
|
||||
id="text4264-7-9"
|
||||
sodipodi:linespacing="125%"><tspan
|
||||
sodipodi:role="line"
|
||||
id="tspan4266-7-6"
|
||||
x="78.802055"
|
||||
y="5.947021"
|
||||
style="font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10px;font-family:'Liberation Serif';-inkscape-font-specification:'Liberation Serif Italic'">v</tspan></text>
|
||||
<text
|
||||
xml:space="preserve"
|
||||
style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
|
||||
x="280.07822"
|
||||
y="5.8523188"
|
||||
id="text4264-7-9-6"
|
||||
sodipodi:linespacing="125%"><tspan
|
||||
sodipodi:role="line"
|
||||
id="tspan4266-7-6-7"
|
||||
x="280.07822"
|
||||
y="5.8523188"
|
||||
style="font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10px;font-family:'Liberation Serif';-inkscape-font-specification:'Liberation Serif Italic'">v</tspan></text>
|
||||
<text
|
||||
xml:space="preserve"
|
||||
style="font-style:normal;font-weight:normal;font-size:40px;line-height:125%;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
|
||||
x="349.16055"
|
||||
y="6.0732894"
|
||||
id="text4264-7-9-9"
|
||||
sodipodi:linespacing="125%"><tspan
|
||||
sodipodi:role="line"
|
||||
id="tspan4266-7-6-4"
|
||||
x="349.16055"
|
||||
y="6.0732894"
|
||||
style="font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10px;font-family:'Liberation Serif';-inkscape-font-specification:'Liberation Serif Italic'">v</tspan></text>
|
||||
</g>
|
||||
</svg>
|
||||
|
||||
|
Before Width: | Height: | Size: 29 KiB After Width: | Height: | Size: 35 KiB |
@@ -1,7 +1,7 @@
|
||||
%!PS-Adobe-2.0 EPSF-2.0
|
||||
%%Title: error_timed_nexus.tex
|
||||
%%Creator: gnuplot 5.0 patchlevel 1
|
||||
%%CreationDate: Tue Feb 16 19:06:27 2016
|
||||
%%CreationDate: Wed Feb 17 14:47:42 2016
|
||||
%%DocumentFonts:
|
||||
%%BoundingBox: 50 50 294 150
|
||||
%%EndComments
|
||||
@@ -441,7 +441,7 @@ SDict begin [
|
||||
/Author (kazu)
|
||||
% /Producer (gnuplot)
|
||||
% /Keywords ()
|
||||
/CreationDate (Tue Feb 16 19:06:27 2016)
|
||||
/CreationDate (Wed Feb 17 14:47:42 2016)
|
||||
/DOCINFO pdfmark
|
||||
end
|
||||
} ifelse
|
||||
|
||||
@@ -83,9 +83,9 @@ set object 10 rectangle from 142,0 to 150,15 fs solid noborder fc rgb "#dddddd"
|
||||
set label 10 "\\footnotesize{10}" at 146,10 center rotate by 0 front
|
||||
|
||||
set object 900 rectangle at graph 0.5, 0.94 size graph 0.65,0.12 fs solid fc rgb "#ffffff" lc rgb "#000000"
|
||||
set label 901 "\\textcolor[rgb]{0,0,0}{\\footnotesize{simple \\eqref{eq:transSimple}}}" at graph 0.28, 0.94 center front
|
||||
set label 902 "\\textcolor[rgb]{0,0,0.8}{\\footnotesize{multi \\eqref{eq:transMultiPath}}}" at graph 0.49, 0.94 center front
|
||||
set label 903 "\\textcolor[rgb]{0.8,0,0}{\\footnotesize{shortest \\eqref{eq:transShortestPath}}}" at graph 0.71, 0.94 center front
|
||||
set label 901 "\\textcolor[rgb]{0,0,0}{\\footnotesize{simple}}" at graph 0.28, 0.94 center front
|
||||
set label 902 "\\textcolor[rgb]{0,0,0.8}{\\footnotesize{multi}}" at graph 0.49, 0.94 center front
|
||||
set label 903 "\\textcolor[rgb]{0.8,0,0}{\\footnotesize{shortest}}" at graph 0.71, 0.94 center front
|
||||
|
||||
unset key
|
||||
set yrange[0:13]
|
||||
|
||||
@@ -110,9 +110,9 @@
|
||||
\put(4057,1559){\makebox(0,0){\strut{}\footnotesize{8}}}%
|
||||
\put(4421,1559){\makebox(0,0){\strut{}\footnotesize{9}}}%
|
||||
\put(4702,1559){\makebox(0,0){\strut{}\footnotesize{10}}}%
|
||||
\put(1793,1846){\makebox(0,0){\strut{}\textcolor[rgb]{0,0,0}{\footnotesize{simple \eqref{eq:transSimple}}}}}%
|
||||
\put(2682,1846){\makebox(0,0){\strut{}\textcolor[rgb]{0,0,0.8}{\footnotesize{multi \eqref{eq:transMultiPath}}}}}%
|
||||
\put(3614,1846){\makebox(0,0){\strut{}\textcolor[rgb]{0.8,0,0}{\footnotesize{shortest \eqref{eq:transShortestPath}}}}}%
|
||||
\put(1793,1846){\makebox(0,0){\strut{}\textcolor[rgb]{0,0,0}{\footnotesize{simple}}}}%
|
||||
\put(2682,1846){\makebox(0,0){\strut{}\textcolor[rgb]{0,0,0.8}{\footnotesize{multi}}}}%
|
||||
\put(3614,1846){\makebox(0,0){\strut{}\textcolor[rgb]{0.8,0,0}{\footnotesize{shortest}}}}%
|
||||
}%
|
||||
\gplbacktext
|
||||
\put(0,0){\includegraphics{error_timed_nexus}}%
|
||||
|
||||
@@ -70,7 +70,7 @@ set multiplot layout 1,1 scale 2.4,2.4 offset 0,0.1
|
||||
splot \
|
||||
"data/floors.dat" with lines lc rgb "#cccccc" notitle,\
|
||||
"data/est_bergwerk_path4_nexus_multi.dat" using 1:2:3:(f4(column(0))) with lines lw 8 palette notitle,\
|
||||
"data/est_bergwerk_path4_nexus_multi.dat" with lines lw 2 lc rgb "#000099" title "\\footnotesize{multi \\eqref{eq:transMultiPath}}",\
|
||||
"data/est_bergwerk_path4_nexus_multi.dat" with lines lw 2 lc rgb "#000099" title "\\footnotesize{multi}",\
|
||||
"data/path4.dat" with lines title "\\footnotesize{ground truth}" dashtype 3 lw 2 lc rgb "#000000"
|
||||
|
||||
unset multiplot
|
||||
|
||||
@@ -1,7 +1,7 @@
|
||||
%!PS-Adobe-2.0 EPSF-2.0
|
||||
%%Title: path_nexus_detail.tex
|
||||
%%Creator: gnuplot 5.0 patchlevel 1
|
||||
%%CreationDate: Tue Feb 16 19:12:37 2016
|
||||
%%CreationDate: Wed Feb 17 14:45:48 2016
|
||||
%%DocumentFonts:
|
||||
%%BoundingBox: 50 50 302 226
|
||||
%%EndComments
|
||||
@@ -441,7 +441,7 @@ SDict begin [
|
||||
/Author (kazu)
|
||||
% /Producer (gnuplot)
|
||||
% /Keywords ()
|
||||
/CreationDate (Tue Feb 16 19:12:37 2016)
|
||||
/CreationDate (Wed Feb 17 14:45:48 2016)
|
||||
/DOCINFO pdfmark
|
||||
end
|
||||
} ifelse
|
||||
@@ -553,14 +553,14 @@ stroke
|
||||
LTb
|
||||
LCb setrgbcolor
|
||||
LTb
|
||||
103 89 N
|
||||
1687 89 N
|
||||
0 440 V
|
||||
1409 0 V
|
||||
-175 0 V
|
||||
0 -440 V
|
||||
103 89 L
|
||||
175 0 V
|
||||
Z stroke
|
||||
103 529 M
|
||||
1409 0 V
|
||||
1687 529 M
|
||||
-175 0 V
|
||||
stroke
|
||||
0.80 0.80 0.80 C 2555 1288 M
|
||||
-50 -15 V
|
||||
@@ -4668,19 +4668,19 @@ LC2 setrgbcolor
|
||||
221 0 V
|
||||
stroke
|
||||
LCw setrgbcolor
|
||||
1.000 103 89 1409 440 BoxColFill
|
||||
1.000 1687 89 -175 440 BoxColFill
|
||||
1.000 UL
|
||||
LTb
|
||||
LCb setrgbcolor
|
||||
LTb
|
||||
103 89 N
|
||||
1687 89 N
|
||||
0 440 V
|
||||
1409 0 V
|
||||
-175 0 V
|
||||
0 -440 V
|
||||
103 89 L
|
||||
175 0 V
|
||||
Z stroke
|
||||
103 529 M
|
||||
1409 0 V
|
||||
1687 529 M
|
||||
-175 0 V
|
||||
stroke
|
||||
0.80 0.80 0.80 C 1.000 UL
|
||||
LTb
|
||||
|
||||
@@ -84,11 +84,11 @@
|
||||
}%
|
||||
\gplgaddtomacro\gplfronttext{%
|
||||
\csname LTb\endcsname%
|
||||
\put(1027,419){\makebox(0,0)[r]{\strut{}\footnotesize{multi \eqref{eq:transMultiPath}}}}%
|
||||
\put(1027,419){\makebox(0,0)[r]{\strut{}\footnotesize{multi}}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(1027,199){\makebox(0,0)[r]{\strut{}\footnotesize{ground truth}}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(1027,419){\makebox(0,0)[r]{\strut{}\footnotesize{multi \eqref{eq:transMultiPath}}}}%
|
||||
\put(1027,419){\makebox(0,0)[r]{\strut{}\footnotesize{multi}}}%
|
||||
\csname LTb\endcsname%
|
||||
\put(1027,199){\makebox(0,0)[r]{\strut{}\footnotesize{ground truth}}}%
|
||||
\csname LTb\endcsname%
|
||||
|
||||
@@ -41,6 +41,13 @@
|
||||
|
||||
\newcommand{\mNN}{\text{nn}}
|
||||
\newcommand{\mKNN}{\text{knn}}
|
||||
\newcommand{\fPos}[1]{\textbf{pos}(#1)}
|
||||
\newcommand{\fDistance}[2]{\delta(#1, #2)}
|
||||
\newcommand{\fWA}[1]{\text{wa}(#1)}
|
||||
\newcommand{\fDD}[1]{\text{dd}(#1)}
|
||||
\newcommand{\fImp}[1]{\text{imp}(#1)}
|
||||
\newcommand{\fNN}[2]{\text{nn}(#1, #2)}
|
||||
\newcommand{\fLength}[2]{\text{length}(#1, #2)}
|
||||
|
||||
%\newcommand{\docIBeacon}{iBeacon}
|
||||
|
||||
|
||||
Reference in New Issue
Block a user