From f63e4ce252a2718b38afae36fe8a8a8180401a47 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Motiejus=20Jak=C5=A1tys?= Date: Wed, 19 May 2021 22:57:50 +0300 Subject: [PATCH] add wang125 --- mj-msc.tex | 117 +++++++++++++++++++++++++++++----------------------- wang125.png | Bin 0 -> 86831 bytes 2 files changed, 65 insertions(+), 52 deletions(-) create mode 100644 wang125.png diff --git a/mj-msc.tex b/mj-msc.tex index bd7a834..ff9193b 100644 --- a/mj-msc.tex +++ b/mj-msc.tex @@ -160,7 +160,8 @@ different trade-offs. \section{Literature Review and Problematic} \label{sec:literature-review-problematic} -\subsection{Simplification, Cartographic Simplification and Generalization} +\subsection{From Simplification to Generalization} +\label{sec:from-simplification-to-generalization} It is important to note the distinction between simplification, line generalization and cartographic generalization. @@ -173,65 +174,47 @@ but lose some shapes that define it. For example: \begin{itemize} \item Low-water rivers in slender slopes have many small bends next to each - other. A non-cartographic line simplification may remove all of them, thus - losing an important river's characteristic feature. + other. A non-cartographic line simplification may remove all of them, + thus losing an important river's characteristic feature: after such + simplification, it will be hard to tell that the original river was + low-water in a slender slope. - \item Insignificant river bend river over a long distance differs - significantly from a completely straight canal. Non-cartographic line - simplification may replace a long and small bend with a straight line, - making the river more similar to a canal than a river. + \item Low-angle river bend river over a long distance differs significantly + from a completely straight canal. Non-cartographic line simplification + may replace a that bend with a straight line, making the river more + similar to a canal than a river. \end{itemize} -In other words, simplification simplifies the line ignoring its cartographic +In other words, simplification processes the line ignoring its geographic features. It is works well when the features are man-made (e.g., roads, -administrative boundaries, buildings) +administrative boundaries, buildings). There is a number of freely available +non-cartographic line simplification algorithms, which this paper will review. +Contrary to line simplification, Cartographic Generalization does not focus +into a single feature class (e.g., rivers), but the whole map. For example, +line simplification may change river bends in a way that bridges (and roads to +the bridges) become misplaced. While line simplification is limited to a single +feature class, cartographic generalization is not. Fully automatic cartographic +generalization is not yet a solved problem . -Line simplification solves a - -Simplification is most frequently used when the topology -mismatches are invisible or not a concern (huge scale maps), or when creating, -for example, river-only maps. - -Conversely, cartographic generalization takes into account the surrounding -object's topology. That way, when a river is generalized, objects around it are -generalized with it. Keeping the river as an example: - -\begin{itemize} - - \item "Minor" bridges will be removed. Important bridges will be generalized - together with the river and remain on the river. Roads or railways that - cross the bridge will be generalized together, and will make sense (a - railway will be relatively straight when crossing the river). - - \item Towns will either disappear (if they are too small for the given - scale), or retain in the correct river side. - -\end{itemize} - -"Cartographic Line Generalization" is in the middle: it accepts - -In essence, cartographic generalization cannot be done in isolation. However, -full automatic feature generalization is not yet a solved problem . This paper examines {\WM}'s \titlecite{wang1998line}, which -has "generalization" in its title, but is a simplification following the rules -above. - -A number of cartographic line generalization algorithms have been researched. -The "classical" ones are {\DP}\cite{douglas1973algorithms} and -{\VW}\cite{visvalingam1993line} in combination with -Chaikin's\cite{chaikin1974algorithm}. - -This section reviews the classical ones, which, besides being around for a long -time, offer easily accessible implementations, as well as more modern ones, -which only theorize, but do not provide an implementation. +Cartographic line generalization falls in between the two: it does more than +line simplification, and less than cartographic generalization. Cartographic +line generalization deals with a single feature class, but takes into account +its geographic properties. This paper examines {\WM}'s +\titlecite{wang1998line}, a cartographic line generalization algorithm. \subsection{Available algorithms} +This section reviews the classical line simplification algorithms, which, +besides being around for a long time, offer easily accessible implementations, +as well as more modern ones, which only theorize, but do not provide an +implementation. + \subsection{Simplification requirements} \subsubsection{{\DP}, {\VW} and Chaikin's} +\label{sec:dp-vw-chaikin} {\DP}\cite{douglas1973algorithms} and {\VW}\cite{visvalingam1993line} are "classical" line simplification computer graphics algorithms. They are @@ -253,11 +236,11 @@ line smoothing algorithm\cite{chaikin1974algorithm} via \href{https://postgis.net/docs/ST_ChaikinSmoothing.html}{PostGIS \texttt{ST\_ChaikinSmoothing}}. -To use in generalization examples, we will use two rivers: Šalčia and Visinčia -(Visinčia flows into Šalčia). These rivers were chosen, because they have both -large and small bends, and thus convenient to analyze for both small and large -scale generalization. Figure~\ref{fig:salvis-25} illustrates the original two -rivers without any simplification. +To use in generalization examples, we will use two rivers: Šalčia and Visinčia. +These rivers were chosen, because they have both large and small bends, and +thus convenient to analyze for both small and large scale generalization. +Figure~\onpage{fig:salvis-25} illustrates the original two rivers without any +simplification. \begin{figure}[h] \centering @@ -433,6 +416,36 @@ wider cartographic society than proprietary ones. \subsection{Problematic with generalization of rivers} +Section~\ref{sec:dp-vw-chaikin} illustrates the current gaps with Line +Simplification algorithms for real rivers. To sum up, we highlight the +following cartographic problems from our examples: + +\begin{description} + + \item[Long bends] should remain as long bends, instead of become fully + straight lines. + + \item[Many small bends] should not be removed. To retain river's character, + the algorithm should retain some small bends, and, when they are too + small to be visible, should be combined or exaggerated. + +\end{description} + +Like discussed in section~\label{sec:from-simplification-to-generalization}, we +limiting the problem to cartographic line generalization. That is, full +cartographic generalization, which takes topology and other feature classes +into account, is out of scope. + +Figure~\onpage{fig:wang125} illustrates {\WM} algorithm from their original +paper. Note how the long bends retain curvy, and how some small bends got +exaggerated. + +\begin{figure}[h] + \includegraphics[width=\textwidth]{wang125} + \caption{Originally Figure 12.5 from \titlecite{wang1998line}} + \label{fig:wang125} +\end{figure} + \section{Methodology} \label{sec:methodology} diff --git a/wang125.png b/wang125.png new file mode 100644 index 0000000000000000000000000000000000000000..07f4b87386785341032d604e750d037e2cc66221 GIT binary patch literal 86831 zcmeFYbyQtXwl2DGcY?dSy9IZL5Fj{gTsJPk-GaNjyF&;NAh<)Y00|IWLa?B3C*7y} z*YBQp?mOe&^Iz{V7-Ln{S6|JVR&&?dM5(LFp&=6?0|0=gATO;60PtG?0Aqp(=>Tr4 ze+UBrxr>jsuA8Q*CxtWE$INV8>+V=I|&h&O@MeiS`Z>HDY-ugct!EC-Wy{LHr7xsSeZ}5Na zAIX=KeY_9rbxh$Y8cF`?Uiibk5clOvL}UDne4AfFKKJg(<6`fO^PgE@o^yIjuj?LN z6JI{(6IXj8vzHODhVA?!(|SOqI52j$xhUy5i{lT!dARqzB|<{EXm`K(5Igorn3``D zAYJ-)diPyH$(?t^cGxC<^OMNa)s^~F@9in;4|Y%0`y;)F$1Cf>t9J)}&)qj}p7n1n z`CUN@N1sc2%Ww03$g(BP-|OyH|ENFjd0*fE+SB5UPUw@9bS8+)^LR{!#up)LwBt$iXF 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