more explanations
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Motiejus Jakštys
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@ -18,7 +18,7 @@
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\input{version}
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\newcommand{\DP}{Douglas \& Peucker}
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\newcommand{\VW}{Visvalingam-Whyatt}
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\newcommand{\VW}{Visvalingam--Whyatt}
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\title{
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Cartografic Generalization of Lines \\
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@ -111,22 +111,22 @@ general public:
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\href{https://postgis.net/docs/ST_SimplifyVW.html}{PostGIS SimplifyVW}.
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\end{itemize}
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For comparison reasons, this article will be using Lakaja and large part of Žeimena
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(see figure~\ref{fig:zeimena} on page~\pageref{fig:zeimena}). This location was
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This article will be using Lakaja and large part of Žeimena (see
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figure~\ref{fig:zeimena} on page~\pageref{fig:zeimena}). This location was
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chosen because the river exhibits both both straight and curved shape, is a
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combination of two curly rivers, and author's familiarity with the location.
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\begin{figure}
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\begin{figure}[h]
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\centering
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\includegraphics[width=148mm]{zeimena-pretty}
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\caption{Lakaja and Žeimena}
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\label{fig:zeimena}
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\end{figure}
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\section{Mathematical and geometrical algorithms}
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\section{Visually comparing {\DP} and {\VW}}
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To visually evaluate the sample above, we created a few examples for {\DP}
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and {\VW} using the following parameters:
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To visually evaluate the Žeimena sample, a few examples for {\DP} and {\VW}
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were created using the following parameters:
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\begin{enumerate}[label=(\Roman*)]
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\item {\DP} tolerance: $tolerance := 125 * 2^n, n = 0,1,...,5$.
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@ -135,41 +135,52 @@ and {\VW} using the following parameters:
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Item~\ref{itm:2} requires explanation. Tolerance for {\DP} is specified in
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linear units, in this case, meters. Tolerance for {\VW} is specified in areal
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units, in this case, square meters $m^2$. As author was not able to locate
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formal comparisons between the two (i.e. how to calculate one tolerance value
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from another, so the results are comparable?), {\DP} tolerance was arbitrarily
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squared. To the author's understanding, this provides reasonalbe results.
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units, in this case, $m^2$. As author was not able to locate formal comparisons
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between the two (i.e. how to calculate one tolerance value from the other, so
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the results are comparable?), {\DP} tolerance was arbitrarily squared and fed
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to {\VW}. To author's eye, this provides comparable and reasonable results,
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though could be researched.
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\renewcommand{\tabularxcolumn}[1]{>{\center\small}m{#1}}
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\begin{tabularx}{\textwidth}{ p{1.5cm} | X | X | }
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Tolerance &
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Douglas \& Peucker &
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Visvalingam-Whyatt \tabularnewline \hline
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As can be observed in table~\ref{tab:dp-vs-vw} on page~\pageref{tab:dp-vs-vw},
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both simplication algorithms convert bends to chopped lines. This is especially
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visible in tolerances 250 and 500. In a more robust simplification algorithm,
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the larger tolerance, the larger the bends on the original map should be
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retained.
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125 &
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\includegraphics[width=\linewidth]{douglas-125} &
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\includegraphics[width=\linewidth]{visvalingam-125} \tabularnewline \hline
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\begin{figure}[h]
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\renewcommand{\tabularxcolumn}[1]{>{\center\small}m{#1}}
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\begin{tabularx}{\textwidth}{ p{1.5cm} | X | X | }
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Tolerance &
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Douglas \& Peucker &
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Visvalingam-Whyatt \tabularnewline \hline
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250 &
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\includegraphics[width=.5\linewidth]{douglas-250} &
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\includegraphics[width=.5\linewidth]{visvalingam-250} \tabularnewline \hline
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125 &
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\includegraphics[width=\linewidth]{douglas-125} &
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\includegraphics[width=\linewidth]{visvalingam-125} \tabularnewline \hline
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500 &
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\includegraphics[width=.25\linewidth]{douglas-500} &
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\includegraphics[width=.25\linewidth]{visvalingam-500} \tabularnewline \hline
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250 &
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\includegraphics[width=.5\linewidth]{douglas-250} &
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\includegraphics[width=.5\linewidth]{visvalingam-250} \tabularnewline \hline
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1000 &
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\includegraphics[width=.125\linewidth]{douglas-1000} &
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\includegraphics[width=.125\linewidth]{visvalingam-1000} \tabularnewline \hline
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500 &
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\includegraphics[width=.25\linewidth]{douglas-500} &
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\includegraphics[width=.25\linewidth]{visvalingam-500} \tabularnewline \hline
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2000 &
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\includegraphics[width=.0625\linewidth]{douglas-2000} &
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\includegraphics[width=.0625\linewidth]{visvalingam-2000} \tabularnewline \hline
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1000 &
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\includegraphics[width=.125\linewidth]{douglas-1000} &
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\includegraphics[width=.125\linewidth]{visvalingam-1000} \tabularnewline \hline
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4000 &
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\includegraphics[width=.0625\linewidth]{douglas-4000} &
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\includegraphics[width=.0625\linewidth]{visvalingam-4000} \tabularnewline \hline
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\end{tabularx}
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2000 &
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\includegraphics[width=.0625\linewidth]{douglas-2000} &
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\includegraphics[width=.0625\linewidth]{visvalingam-2000} \tabularnewline \hline
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4000 &
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\includegraphics[width=.0625\linewidth]{douglas-4000} &
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\includegraphics[width=.0625\linewidth]{visvalingam-4000} \tabularnewline \hline
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\end{tabularx}
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\label{tab:dp-vs-vw}
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\caption{{\DP} and {\VW} side-by-side visual comparison.}
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\end{figure}
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\section{Algorithms based on cartographical knowledge}
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