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Motiejus Jakštys 2021-05-19 22:57:48 +03:00 committed by Motiejus Jakštys
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mj-msc.tex
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@ -48,7 +48,7 @@
\newcommand{\DP}{Douglas \& Peucker}
\newcommand{\VW}{Visvalingam--Whyatt}
\newcommand{\WM}{Wang--M{\"u}ller}
% {\WM} algoritmo realizacija kartografinei upių generalizacijai vykdyti (PostGIS programinės įrangos pagrindu)
% {\WM} algoritmo realizacija kartografinei upių generalizacijai
\newcommand{\MYTITLE}{{\WM} algorithm realization for cartographic line generalization}
\newcommand{\MYAUTHOR}{Motiejus Jakštys}
@ -80,12 +80,15 @@
\begin{abstract}
\label{sec:abstract}
Current open-source line generalization solutions have their roots in
mathematics and geometry, and are not fit for natural objects like rivers
and coastlines. This paper discusses our implementation of {\WM}'s algorithm
under and open-source license, explains things that we would had
appreciated in the original paper and compares our results to different
generalization algorithms.
Currently available line simplification algorithms are rooted in mathematics
and geometry, and are not fit bendy natural features like rivers and
coastlines. This paper discusses our implementation of {\WM} algorithm,
with notes that we would have been appreciated before starting the
re-implementation endeavor. This paper accompanies our implementation of
{\WM} algorithm and will be helpful to anyone trying to understand the
original {\WM} paper, or our implementation.
\end{abstract}
\newpage
@ -268,18 +271,34 @@ figure~\onpage{fig:salvis-generalized-chaikin-50k}.
\label{fig:salvis-overlaid-generalized-chaikin-50k}
\end{figure}
There are a few problems with {\VW} and {\DP} immediately visible in
figure~\onpage{fig:salvis-generalized-chaikin-50k}:
The resulting generalized and smoothened example
(figure~\onpage{fig:salvis-generalized-chaikin-50k}) yields a more
aesthetically pleasant result, however, it obscures natural river features.
Given the absence of rocks, the only natural features that influence the river
direction are topographic:
\begin{itemize}
\item problem 1
\item problem 2
\item Relatively straight river (completely straight or with small-angled
bends over a relatively long distance) implies greater slope, more
water, and/or faster flow.
\item Bendy river, on the contrary, implies slower flow, smaller slope,
and/or less water.
\end{itemize}
Therefore, a more robust generalization algorithm is worthwhile for lookout.
Both {\VW} and {\DP} have a tendency to remove the small bends altogether,
which is a valuable characterization of the river. Therefore, a more robust
generalization algorithm is worthwhile for lookout.
\subsubsection{Modern approaches}
% TODO:
% https://pdfs.semanticscholar.org/e80b/1c64345583eb8f7a6c53834d1d40852595d5.pdf
% A New Algorithm for Cartographic Simplification of Streams and Lakes Using
% Deviation Angles and Error Bands
Due to their simplicity and ubiquity, {\DP} and {\VW} have been established as
go-to algorithms for line generalization. During recent years, alternatives
have emerged. These modern replacements fall into roughly two categories: