diff --git a/IV/mj-msc.tex b/IV/mj-msc.tex index 6f80bff..633cf66 100644 --- a/IV/mj-msc.tex +++ b/IV/mj-msc.tex @@ -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: