add wang125
This commit is contained in:
parent
82b4ac94d3
commit
f63e4ce252
117
mj-msc.tex
117
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 <TODO: Reference needed>.
|
||||
|
||||
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
|
||||
{\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}
|
||||
|
||||
|
|
Binary file not shown.
After Width: | Height: | Size: 85 KiB |
Loading…
Reference in New Issue