more problematic

mj-msc.tex

@@ -124,28 +124,27 @@ is more tricky with natural features that have many bends, like coastlines,
 rivers or forest boundaries.
 
 To create a small-scale map from a large-scale data source, features need to be
-generalized, i.e. detail should be reduced. While performing the generalization, it
+simplified, i.e., detail should be reduced. While performing the
-is important to retain the "defining" shape of the original feature. Otherwise,
+simplification, it is important to retain the "defining" shape of the original
-if the generalized feature looks too different than the original, the result
+feature. Otherwise, if the simplified feature looks too different than the
-will look unrealistic.
+original, the result will look unrealistic.
 
-For example, if a river is nearly straight, it should be nearly straight after
+For example, if a river is nearly straight, it should remain such after
-generalization. A too straightened river will look like a canal, and the other
+simplification. An overly straightened river will look like a canal, and the
-way around --- too curvy would not reflect the natural shape. Conversely, if
+other way around --- too curvy would not reflect the natural shape. Conversely,
-the river is highly wiggly, the number of bends should be reduced, but not
+if the river originally is highly wiggly, the number of bends should be
-removed altogether.
+reduced, but not removed altogether.
 
-Generalization problem for other objects can often be solved by other
+Simplification problem for other objects can often be solved by other
 non-geometric means:
 
 \begin{itemize}
-    \item Towns and cities can be filtered and generalized by number of
+    \item Towns and cities can be filtered by number of inhabitants.
-        inhabitants.
     \item Roads can be eliminated by the road length, number of lanes, or
         classification of the road (local, regional, international).
 \end{itemize}
 
-To sum up, natural line generalization problem can be viewed as a task of
+To sum up, natural line simplification problem can be viewed as a task of
 finding a delicate balance between two competing goals:
 
 \begin{itemize}
@@ -153,13 +152,71 @@ finding a delicate balance between two competing goals:
     \item Retain enough detail, so the original is still recognize-able.
 \end{itemize}
 
-Given the discussed complexities, a fine line between under-generalization
+Given the discussed complexities, a fine line between under-simplification
-(leaving object as-is) and over-generalization (making a straight line) needs
+(leaving object as-is) and over-simplification (making a straight line) needs
-to be found. Therein lies the complexity of generalization algorithms: all have
+to be found. Therein lies the complexity of simplification algorithms: all have
 different trade-offs.
 
-\section{Literature review and problematic}
+\section{Literature Review and Problematic}
-\label{sec:literature-review}
+\label{sec:literature-review-problematic}
+
+\subsection{Simplification, Cartographic Simplification and Generalization}
+
+It is important to note the distinction between simplification, line
+generalization and cartographic generalization.
+
+Simplification reduces object's detail in isolation, not taking object's
+natural properties or surrounding objects into account. For example, if a
+river is simplified, it may have an approximate shape of the original river,
+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.
+
+  \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.
+
+\end{itemize}
+
+In other words, simplification simplifies the line ignoring its cartographic
+features. It is works well when the features are man-made (e.g., roads,
+administrative boundaries, buildings)
+
+
+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 <TODO:
+Reference needed>. 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
@@ -172,13 +229,15 @@ which only theorize, but do not provide an implementation.
 
 \subsection{Available algorithms}
 
+\subsection{Simplification requirements}
+
 \subsubsection{{\DP}, {\VW} and Chaikin's}
 
 {\DP}\cite{douglas1973algorithms} and {\VW}\cite{visvalingam1993line} are
-"classical" line generalization computer graphics algorithms. They are
+"classical" line simplification computer graphics algorithms. They are
 relatively simple to implement, require few runtime resources. Both of them
-accept only a single parameter, based on desired scale of the map, which makes
+accept a single parameter, based on desired scale of the map, which makes them
-them straightforward to adjust for different scales.
+straightforward to adjust for different scales.
 
 Both algorithms are part of PostGIS, a free-software GIS suite:
 \begin{itemize}
@@ -194,12 +253,11 @@ 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.
+To use in generalization examples, we will use two rivers: Šalčia and Visinčia
-Figure~\ref{fig:salvis-25} illustrates the original two rivers without any
+(Visinčia flows into Šalčia). These rivers were chosen, because they have both
-processing.
+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
-These rivers were chosen, because they have both large and small bends, and
+rivers without any simplification.
-thus convenient to analyze for both small and large scale generalization.
 
 \begin{figure}[h]
     \centering
@@ -224,11 +282,12 @@ thus convenient to analyze for both small and large scale generalization.
     \label{fig:salvis-50-250}
 \end{figure}
 
-Same rivers, unprocessed, but with higher density (scales 1:\numprint{50000}
+Same rivers, unprocessed, but in higher scales (1:\numprint{50000} and
-and 1:\numprint{250000}) are depicted in figure~\onpage{fig:salvis-50-250}.
+1:\numprint{250000}) are depicted in figure~\onpage{fig:salvis-50-250}. Some
-Some river features are so compact that a reasonably thin line depicting the
+river features are so compact that a reasonably thin line depicting the river
-river is touching itself, creating a thicker line. As a result, generalization
+is touching itself, creating a thicker line. We can assume that some
-for this river for a smaller scale is worthy.
+simplification for scale 1:\numprint{50000} and especially for
+1:\numprint{250000} are worthwhile.
 
 \begin{figure}[h]
     \centering
@@ -246,7 +305,7 @@ for this river for a smaller scale is worthy.
 \end{figure}
 
 Figure~\onpage{fig:salvis-generalized-50k} illustrates the same river bend, but
-generalized using {\DP} and {\VW} algorithms. The resulting lines are jagged,
+simplified using {\DP} and {\VW} algorithms. The resulting lines are jagged,
 thus the resulting line looks unlike a real river. To smoothen the jaggedness,
 traditionally, Chaikin's\cite{chaikin1974algorithm} is applied after
 generalization, illustrated in
@@ -284,7 +343,7 @@ 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.
+aesthetically pleasing result, however, it obscures natural river features.
 Given the absence of rocks, the only natural features that influence the river
 direction are topographic:
 
@@ -340,7 +399,7 @@ have emerged. These modern replacements fall into roughly two categories:
         as {\WM}'s algorithm.
 
     \item Mathematical shape transformation which yields a more cartographic
-        result. E.g. \titlecite{jiang2003line},
+        result. E.g., \titlecite{jiang2003line},
         \titlecite{dyken2009simultaneous}, \titlecite{mustafa2006dynamic},
         \titlecite{nollenburg2008morphing}.