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II/Referatas/mj-referatas.tex
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@ -18,7 +18,7 @@
\input{version}
\newcommand{\DP}{Douglas \& Peucker}
\newcommand{\VW}{Visvalingam-Whyatt}
\newcommand{\VW}{Visvalingam--Whyatt}
\title{
Cartografic Generalization of Lines \\
@ -111,22 +111,22 @@ general public:
\href{https://postgis.net/docs/ST_SimplifyVW.html}{PostGIS SimplifyVW}.
\end{itemize}
For comparison reasons, this article will be using Lakaja and large part of Žeimena
(see figure~\ref{fig:zeimena} on page~\pageref{fig:zeimena}). This location was
This article will be using Lakaja and large part of Žeimena (see
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
combination of two curly rivers, and author's familiarity with the location.
\begin{figure}
\begin{figure}[h]
\centering
\includegraphics[width=148mm]{zeimena-pretty}
\caption{Lakaja and Žeimena}
\label{fig:zeimena}
\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}
and {\VW} using the following parameters:
To visually evaluate the Žeimena sample, a few examples for {\DP} and {\VW}
were created using the following parameters:
\begin{enumerate}[label=(\Roman*)]
\item {\DP} tolerance: $tolerance := 125 * 2^n, n = 0,1,...,5$.
@ -135,11 +135,19 @@ and {\VW} using the following parameters:
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
units, in this case, square meters $m^2$. As author was not able to locate
formal comparisons between the two (i.e. how to calculate one tolerance value
from another, so the results are comparable?), {\DP} tolerance was arbitrarily
squared. To the author's understanding, this provides reasonalbe results.
units, in this case, $m^2$. As author was not able to locate formal comparisons
between the two (i.e. how to calculate one tolerance value from the other, so
the results are comparable?), {\DP} tolerance was arbitrarily squared and fed
to {\VW}. To author's eye, this provides comparable and reasonable results,
though could be researched.
As can be observed in table~\ref{tab:dp-vs-vw} on page~\pageref{tab:dp-vs-vw},
both simplication algorithms convert bends to chopped lines. This is especially
visible in tolerances 250 and 500. In a more robust simplification algorithm,
the larger tolerance, the larger the bends on the original map should be
retained.
\begin{figure}[h]
\renewcommand{\tabularxcolumn}[1]{>{\center\small}m{#1}}
\begin{tabularx}{\textwidth}{ p{1.5cm} | X | X | }
Tolerance &
@ -170,6 +178,9 @@ squared. To the author's understanding, this provides reasonalbe results.
\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}