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