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bends

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Motiejus Jakštys 2020-05-27 13:41:27 +03:00
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II/Referatas/mj-referatas.tex
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@ -160,21 +160,21 @@ page~\pageref{fig:zeimena}) will be used as inputs to the generalization
algorithms, because the river exhibits both both straight and curved shape, is
a combination of two curly rivers, and author's familiarity with the location.
Since the map area is large (approx. 20km by 28km, scale $1:150 000$), we will
Since the map area is large (approx. 20km by 28km, scale $1:300 000$), we will
also review a subset of the area of approx 2200m by 1575m. The zoomed-in
version will help explain some of the deficiencies in the reviewed algorithms.
\begin{figure}[h]
\centering
\includegraphics[width=67.5mm]{zeimena}
\caption{Lakaja and Žeimena, with marked river crossing area, $1:300000$}
\caption{Lakaja and Žeimena, with marked river crossing area, $1:300 000$}
\label{fig:zeimena}
\end{figure}
\begin{figure}[h]
\centering
\includegraphics[width=74mm]{crossing}
\caption{River crossing area zoomed in, $1:30000$}
\caption{River crossing area zoomed in, $1:30 000$}
\label{fig:crossing}
\end{figure}
@ -196,7 +196,7 @@ researched.
As can be observed in table~\ref{tab:comparison-zeimena} on
page~\pageref{tab:comparison-zeimena}, both simplication algorithms convert
bends to chopped lines. This is especially visible in tolerances 250 and 500.
bends to chopped lines. This is especially visible in tolerances 256 and 512.
In a more robust simplification algorithm, the larger tolerance, the larger the
bends on the original map should be retained.
@ -215,7 +215,7 @@ bends on the original map should be retained.
\includegraphics[width=.5\linewidth]{zeimena-douglas-256} &
\includegraphics[width=.5\linewidth]{zeimena-visvalingam-256} \tabularnewline \hline
512/ 262144 &
512/262144 &
\includegraphics[width=.25\linewidth]{zeimena-douglas-512} &
\includegraphics[width=.25\linewidth]{zeimena-visvalingam-512} \tabularnewline \hline
@ -235,8 +235,22 @@ bends on the original map should be retained.
\label{tab:comparison-zeimena}
\end{figure}
Let's zoom in to the river crossing area for some of the algorithms.
Let's zoom in to the river crossing area for some of the algorithms; see
table~\ref{tab:comparison-crossing} on page~\pageref{tab:comparison-crossing}.
Both {\VW} and {\DP} simplify "blunt" bends (a "blunt" bent looks like a cutout
from a large circle, see figure~\ref{blunt-bent} on page~\pageref{blunt-bent}.
\begin{figure}[h]
\centering
\begin{tikzpicture}
\draw (-5,0) -- (-3, 0) ;
\draw (0,0) arc (60:120:3) ;
\draw (0,0) -- (2, 0) ;
\end{tikzpicture}
\caption{Blunt bent}
\label{fig:blunt-bent}
\end{figure}
\begin{figure}[h]
\renewcommand{\tabularxcolumn}[1]{>{\center\small}m{#1}}
@ -249,22 +263,20 @@ Let's zoom in to the river crossing area for some of the algorithms.
\includegraphics[width=\linewidth]{overlaid-zeimena-douglas-64} &
\includegraphics[width=\linewidth]{overlaid-zeimena-visvalingam-64} \tabularnewline \hline
125/15625 &
128/16384 &
\includegraphics[width=\linewidth]{overlaid-zeimena-douglas-128} &
\includegraphics[width=\linewidth]{overlaid-zeimena-visvalingam-128} \tabularnewline \hline
250/62500 &
256/65536 &
\includegraphics[width=\linewidth]{overlaid-zeimena-douglas-256} &
\includegraphics[width=\linewidth]{overlaid-zeimena-visvalingam-256} \tabularnewline \hline
\end{tabularx}
\caption{{\DP} and {\VW} on river crossing area}
\label{tab:comparison-zoomed}
\label{tab:comparison-crossing}
\end{figure}
To sum up, both {\VW} and {\DP} simplify the lines, but their cartographic
output poorly represents lines and bends. Where to look for better output?