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@ -103,12 +103,12 @@
\vfill \vfill
Šiuo metu prieinami linijų supaprastinimo algoritmai yra kilę iš Šiuo metu esami linijų supaprastinimo algoritmai yra kilę iš matematikos ir
matematikos ir geometrijos, bei yra netinkami lankstiems geografiniams geometrijos, bet nėra tinkami lankstiems geografiniams objektams, tokiems
objektams, tokiems kaip upės ir pakrantės. {\WirM} ištyrė, kaip kartografai kaip upės ir pakrantės, atvaizduoti. {\WirM} ištyrė, kaip kartografai
vykdo upių generalizaciją, ir sukūrė algoritmą. Mes realizavome šį atlieka upių generalizaciją, ir sukūrė algoritmą. Mes realizavome šį
algoritmą ir išsamiai jį dokumentavome. Mūsų {\WM} realizacija ir algoritmą ir išsamiai jį dokumentavome. Mūsų {\WM} realizacija ir
dokumentacija yra nemokami ir laisvai prieinami naudojant PostGIS dokumentacija yra nemokamos ir laisvai prieinamos, naudojant PostGIS
platformą. platformą.
\end{abstract} \end{abstract}
@ -164,7 +164,7 @@ viewed as a task of finding a delicate balance between two competing goals:
\end{itemize} \end{itemize}
Given the discussed complexities with natural features, a fine line between Given the discussed complexities with natural features, a fine line between
under-simplification (leaving object as-is) and over-simplification (making a under-simplification (leaving an object as-is) and over-simplification (making a
straight line) needs to be found. Therein lies the complexity of simplification straight line) needs to be found. Therein lies the complexity of simplification
algorithms: all have different trade-offs. algorithms: all have different trade-offs.
@ -265,7 +265,7 @@ Same rivers, unprocessed but in higher scales (1:\numprint{50000} and
river features are so compact that a reasonably thin line depicting the river river features are so compact that a reasonably thin line depicting the river
is touching itself, creating a thicker line. We can assume that some is touching itself, creating a thicker line. We can assume that some
simplification for scale 1:\numprint{50000} and especially for simplification for scale 1:\numprint{50000} and especially for
1:\numprint{250000} are worthwhile. 1:\numprint{250000} is worthwhile.
\begin{figure}[ht] \begin{figure}[ht]
\centering \centering
@ -484,7 +484,7 @@ Lack of robust openly available generalization algorithm implementations poses
a problem for map creation with free software: there is no high-quality a problem for map creation with free software: there is no high-quality
simplification algorithm to create down-scaled maps, so any cartographic work, simplification algorithm to create down-scaled maps, so any cartographic work,
which uses line generalization as part of its processing, will be of sub-par which uses line generalization as part of its processing, will be of sub-par
quality. We believe that availability of high-quality open-source tools is an quality. We believe that the availability of high-quality open-source tools is an
important foundation for future cartographic experimentation and development, important foundation for future cartographic experimentation and development,
thus it benefits the cartographic society as a whole. thus it benefits the cartographic society as a whole.
@ -785,7 +785,7 @@ code.
Besides testing for specific cases, an automated test suite ensures future Besides testing for specific cases, an automated test suite ensures future
stability and longevity of the implementation itself: when new contributors stability and longevity of the implementation itself: when new contributors
start changing code, they have higher assurance they have not broken start changing code, they have higher assurance they have not broken
already-working code. an already-working code.
\subsection{Reproducibility} \subsection{Reproducibility}
\label{sec:reproducing-the-paper} \label{sec:reproducing-the-paper}
@ -811,7 +811,7 @@ example reference for anyone willing to start using the algorithm.
\section{Algorithm Implementation} \section{Algorithm Implementation}
Like alluded in section~\ref{sec:introduction}, {\WM} paper skims over As alluded in section~\ref{sec:introduction}, {\WM} paper skims over
certain details which are important to implement the algorithm. This section certain details which are important to implement the algorithm. This section
goes through each algorithm stage, illustrating the intermediate steps and goes through each algorithm stage, illustrating the intermediate steps and
explaining the author's desiderata for a more detailed description. explaining the author's desiderata for a more detailed description.
@ -912,7 +912,7 @@ purpose of each column in \textsc{wm\_debug} is described below:
When debug mode is turned off (that is, \textsc{dbgname} is left unspecified), When debug mode is turned off (that is, \textsc{dbgname} is left unspecified),
\textsc{wm\_debug} is empty and the algorithm runs slightly faster. \textsc{wm\_debug} is empty and the algorithm runs slightly faster.
\subsection{Merging Pieces of the River into One} \subsection{Merging Pieces of a River into One}
Example river geometries were sourced from OpenStreetMap\cite{openstreetmap} Example river geometries were sourced from OpenStreetMap\cite{openstreetmap}
and NŽT\cite{nzt}. Rivers in both data sources are stored in shorter line and NŽT\cite{nzt}. Rivers in both data sources are stored in shorter line
@ -988,7 +988,7 @@ table~\ref{table:scale-halfcirlce-diameter}.
\subsection{Definition of a Bend} \subsection{Definition of a Bend}
\label{sec:definition-of-a-bend} \label{sec:definition-of-a-bend}
The original article describes a bend as: The original article describes a bend as follows:
\begin{displaycquote}{wang1998line} \begin{displaycquote}{wang1998line}
A bend can be defined as that part of a line which contains a number of A bend can be defined as that part of a line which contains a number of
@ -1359,7 +1359,7 @@ of exaggeration operator:
\end{description} \end{description}
Both functions are inter-change-able and can be found in listing~\ref{lst:wm.sql}. Both functions are interchangeable and can be found in listing~\ref{lst:wm.sql}.
Figure~\ref{fig:isolated-1-exaggerated} illustrates an exaggerated bend using Figure~\ref{fig:isolated-1-exaggerated} illustrates an exaggerated bend using
\textsc{wm\_exaggerate\_bend2}. \textsc{wm\_exaggerate\_bend2}.
@ -1371,9 +1371,9 @@ generalization, and suggests specific improvements.
One of our goals is to compare the generalized lines with the official One of our goals is to compare the generalized lines with the official
generalized dataset\cite{nzt}. Therefore, we have selected the target scales generalized dataset\cite{nzt}. Therefore, we have selected the target scales
that the official sources offer too: 1:\numprint{50000} and that the official sources offer, too: 1:\numprint{50000} and
1:\numprint{250000}. The \textsc{dhalfcircle} values for the subset are as 1:\numprint{250000}. The \textsc{dhalfcircle} values for the subset are as
follows: follow:
\begin{table}[ht] \begin{table}[ht]
\centering \centering
@ -1394,7 +1394,7 @@ Our generalized results are viewed from the following angles:
\subsection{Generalization Results of Analyzed Rivers} \subsection{Generalization Results of Analyzed Rivers}
\label{sec:generalization-results-of-analyzed-rivers} \label{sec:generalization-results-of-analyzed-rivers}
\subsubsection{Medium-scale (1:\numprint{50000})} \subsubsection{Medium-Scale (1:\numprint{50000})}
\label{sec:analyzed-medium-scale} \label{sec:analyzed-medium-scale}
\begin{figure}[h!] \begin{figure}[h!]
@ -1427,7 +1427,7 @@ Figure's~\ref{fig:salvis-wm75--grpk10-1x50k} left part is clipped to
Figure~\ref{fig:salvis-wm75--grpk10-1x50ktl}. As one can see, some bends were well Figure~\ref{fig:salvis-wm75--grpk10-1x50ktl}. As one can see, some bends were well
exaggerated, and some bends were eliminated. exaggerated, and some bends were eliminated.
Top--right side (clipped in Figure~\ref{fig:salvis-wm75--grpk10-1x50ktl}) some jagged Top--right side (clipped in Figure~\ref{fig:salvis-wm75--grpk10-1x50ktl}), some jagged
and sharp bends appear. These will become more pronounced in even larger-scale and sharp bends appear. These will become more pronounced in even larger-scale
simplification in the next section. simplification in the next section.
@ -1436,7 +1436,7 @@ sharp edges for others.
\clearpage \clearpage
\subsubsection{Large-scale (1:\numprint{250000})} \subsubsection{Large-Scale (1:\numprint{250000})}
\label{sec:analyzed-large-scale} \label{sec:analyzed-large-scale}
As visible in Figure~\ref{fig:salvis-wm220-10x}, for large-scale map, some of the As visible in Figure~\ref{fig:salvis-wm220-10x}, for large-scale map, some of the
@ -1470,7 +1470,7 @@ simplification and overlays the original.
A conglomeration of bends is visible, especially in top--right side of the A conglomeration of bends is visible, especially in top--right side of the
illustration. We assume this was caused by two bends significantly exaggerated, illustration. We assume this was caused by two bends significantly exaggerated,
leaving no space to exaggerate for those between the two. leaving no space to exaggerate those between the two.
\subsubsection{Discussion} \subsubsection{Discussion}
@ -1495,17 +1495,17 @@ future research and improvement:
\subsubsection{Background} \subsubsection{Background}
There are a few datasets used in this comparison: GRPK10, GRPK50 and There are a few datasets used in this comparison: GRPK10, GRPK50 and
GRPK250. They are vector datasets, which include rivers. They can be GRPK250. They are vector datasets which include rivers. They can be
downloaded for free from \cite{nzt}. Here are the meanings of the codenames: downloaded for free from \cite{nzt}. Here are the meanings of the codenames:
\begin{description} \begin{description}
\item[GRPK10] is dataset of highest detail. Suited for maps of scale \item[GRPK10] is a dataset of highest detail. Suited for maps of scale
1:\numprint{10000}. 1:\numprint{10000}.
\item[GRPK50] is suited for maps of scale 1:\numprint{50000}. \item[GRPK50] is suited for maps of scale 1:\numprint{50000}.
\item[GRPK250] offers least detail, and is suited for maps of \item[GRPK250] offers the least detail, and is suited for maps of
scale 1:\numprint{250000}. scale 1:\numprint{250000}.
\end{description} \end{description}
@ -1515,7 +1515,7 @@ During the analysis, we ran {\WM} on GRPK10 for 2 destination scales:
detailed in section~\ref{sec:bend-scaling-and-dimensions}.} This section detailed in section~\ref{sec:bend-scaling-and-dimensions}.} This section
compares the resulting {\WM}--generalized rivers to GRPK50 and GRPK250. compares the resulting {\WM}--generalized rivers to GRPK50 and GRPK250.
\subsubsection{Medium-scale (1:\numprint{50000})} \subsubsection{Medium-Scale (1:\numprint{50000})}
For our research location, the national dataset GRPK10 is almost equivalent to For our research location, the national dataset GRPK10 is almost equivalent to
GRPK50, with a few nuances. Figure~\ref{fig:salvis-wm75-grpk50-grpk10-1x50k} GRPK50, with a few nuances. Figure~\ref{fig:salvis-wm75-grpk50-grpk10-1x50k}
@ -1552,7 +1552,7 @@ implementation.
\clearpage \clearpage
\subsubsection{Large-scale (1:\numprint{250000})} \subsubsection{Large-Scale (1:\numprint{250000})}
\label{sec:national-large-scale} \label{sec:national-large-scale}
Figure~\ref{fig:salvis-wm220} illustrates the original GRPK250 and the Figure~\ref{fig:salvis-wm220} illustrates the original GRPK250 and the
@ -1582,7 +1582,7 @@ desired in section~\ref{sec:future-suggestions}.
\subsection{Comparison with {\DP} and {\VW}} \subsection{Comparison with {\DP} and {\VW}}
It is time to visually compare our implementation with the classical It is time to visually compare our implementation with the classical
algorithms: {\DP}, {\VW} and Chaikin. Since we have established more work is algorithms: {\DP}, {\VW} and Chaikin. Since we have established that more work is
needed for small-scale maps (1:\numprint{250000}), we will limit the comparison needed for small-scale maps (1:\numprint{250000}), we will limit the comparison
in this section to 1:\numprint{50000}. in this section to 1:\numprint{50000}.
@ -1675,9 +1675,9 @@ implementation:
limits are necessary. limits are necessary.
\item Research when bends should be marked as \textsc{isolated}. As is \item Research when bends should be marked as \textsc{isolated}. As is
seen from examples, the current criteria is not robust enough. seen from examples, the current criteria are not robust enough.
\item Once the points above yield a satisfactory result, efficiency of the \item Once the points above yield a satisfactory result, the efficiency of the
algorithm could be improved to work on the lines in "streaming" fashion algorithm could be improved to work on the lines in "streaming" fashion
(more details in section~\ref{sec:algorithm-implementation-process}). (more details in section~\ref{sec:algorithm-implementation-process}).
@ -1716,7 +1716,7 @@ This section contains code listings of the {\WM} algorithm.
\subsection{Re-Generating This Paper} \subsection{Re-Generating This Paper}
\label{sec:code-regenerate} \label{sec:code-regenerate}
Like explained in section~\ref{sec:reproducing-the-paper}, illustrations in As explained in section~\ref{sec:reproducing-the-paper}, illustrations in
this paper are generated from a small list of sample geometries. To observe this paper are generated from a small list of sample geometries. To observe
the source geometries or regenerate this paper, run this script (assuming the source geometries or regenerate this paper, run this script (assuming
the name of this document is \textsc{mj-msc-full.pdf}). the name of this document is \textsc{mj-msc-full.pdf}).