diff --git a/IV/mj-msc.tex b/IV/mj-msc.tex index 191f9cf..3a1c84c 100644 --- a/IV/mj-msc.tex +++ b/IV/mj-msc.tex @@ -1312,9 +1312,9 @@ implementation. A single exaggeration increment is done as follows: is linearly interpolated between $[s,1]$, using the same rules as for the first half. - The first version of the algorithm used simple linear interpolation based - on the point's position in the line. The current version applies a few - coefficients, which were derived empirically, by observing the + The first version of the algorithm used simple linear interpolation + based on the point's position in the line. The current version applies + a few coefficients, which were derived empirically, by observing the resulting bend. \item Each point (except the beginning and end vertices of the bend) will @@ -1323,9 +1323,6 @@ implementation. A single exaggeration increment is done as follows: \end{enumerate} -Figure~\ref{fig:isolated-1-exaggerated} illustrates an exaggerated bend with -the algorithm. - \begin{figure}[ht] \centering \includegraphics[width=.5\textwidth]{isolated-1-exaggerated} @@ -1333,6 +1330,24 @@ the algorithm. \label{fig:isolated-1-exaggerated} \end{figure} +The technical implementation of the algorithm contains two implementations +of exaggeration operator: + +\begin{description} + + \item[\normalfont\textsc{wm\_exaggerate\_bend}] is the original one. It + uses simple linear interpolation. It is fast, but simple. It tends to + leave jagged bends. + + \item[\normalfont\textsc{wm\_exaggerate\_bend2}] is a more computationally + expensive function, which leaves better-looking exaggerated bends. + +\end{description} + +Both functions are inter-change-able and can be found in listing~\ref{lst:wm.sql}. +Figure~\ref{fig:isolated-1-exaggerated} illustrates an exaggerated bend using +\textsc{wm\_exaggerate\_bend2}. + \section{Results} \label{sec:results} @@ -1349,8 +1364,7 @@ table~\ref{table:scale-halfcirlce-diameter}: \item 1:\numprint{250000}: 220. \end{itemize} -The original feature is orange. As can be seen, some isolated bends are -exaggerated, and some small bends are removed. +\subsubsection{Medium-scale (1:\numprint{50000})} \begin{figure}[ht] \centering @@ -1368,11 +1382,15 @@ exaggerated, and some small bends are removed. \label{fig:salvis-wm-50k} \end{figure} -As one can see in figure~\ref{fig:salvis-wm-50k}, some of the small bends have -been exaggerated, and some removed. It mostly works as expected, except some of -the jagged lines approximately in the middle of the figure. +As one can see in figure~\ref{fig:salvis-wm-50k}, the illustrations deliver +what was promised by the algorithm, but with a few caveats. West-side of the +river looks reasonably well simplified: long bends remain slightly curved, +small bends are removed or slightly exaggerated. + +Approximately at the middle of the figure some jagged and sharp bends appear. Figure~\ref{fig:salvis-wm-50k-overlaid-zoom} zooms in, overlaying the original -river (in orange). +river (in orange). These will become more pronounced in even larger-scale +simplification in the next section. \begin{figure}[ht] \centering @@ -1381,12 +1399,6 @@ river (in orange). \label{fig:salvis-wm-50k-overlaid-zoom} \end{figure} - -These will become -more pronounced in large-scale simplification in the next section. Other than -some sharp edges, this algorithm works reasonably well for mid-scale -simplification. - \subsubsection{Large-scale (1:\numprint{250000})} As visible in figure~\ref{fig:salvis-wm-250k}, for large-scale map, some of the @@ -1421,8 +1433,8 @@ simplification and overlays the original (in orange). A conglomeration of bends is visible, especially in north-east side of the center. We assume this was caused by two bends significantly exaggerated, leaving no space to exaggerate for those between the two. For the same reason, -the 1:\numprint{50000} figure~\ref{fig:salvis-wm-50k} has many smaller bends -at approximately the same location. +the figure~\ref{fig:salvis-wm-50k} (of scale 1:\numprint{50000}) has many +smaller bends at approximately the same location. \subsection{Comparison of Generalization Result with National Spatial Datasets}