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Motiejus Jakštys 2021-05-07 22:08:20 +03:00
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IV/mj-msc.tex
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@ -285,7 +285,7 @@ simplification for scale 1:\numprint{50000} and especially for
\includegraphics[width=\textwidth]{salvis-visvalingam-64-50k}
\caption{Using {\VW}.}
\end{subfigure}
\caption{Generalized using classical algorithms (1:\numprint{50000}).}
\caption{Simplified using classical algorithms (1:\numprint{50000}).}
\label{fig:salvis-generalized-50k}
\end{figure}
@ -300,14 +300,14 @@ figure~\onpage{fig:salvis-generalized-chaikin-50k}.
\centering
\begin{subfigure}[b]{.49\textwidth}
\includegraphics[width=\textwidth]{salvis-douglas-64-chaikin-50k}
\caption{{\DP} + Chaikin's.}
\caption{{\DP} and Chaikin's.}
\end{subfigure}
\hfill
\begin{subfigure}[b]{.49\textwidth}
\includegraphics[width=\textwidth]{salvis-visvalingam-64-chaikin-50k}
\caption{{\VW} + Chaikin's.}
\caption{{\VW} and Chaikin's.}
\end{subfigure}
\caption{Generalized and smoothened river (1:\numprint{50000}).}
\caption{Simplified and smoothened river (1:\numprint{50000}).}
\label{fig:salvis-generalized-chaikin-50k}
\end{figure}
@ -315,18 +315,18 @@ figure~\onpage{fig:salvis-generalized-chaikin-50k}.
\centering
\begin{subfigure}[b]{.49\textwidth}
\includegraphics[width=\textwidth]{salvis-overlaid-douglas-64-chaikin-50k}
\caption{{\DP} + Chaikin's.}
\caption{{\DP} and Chaikin's.}
\end{subfigure}
\hfill
\begin{subfigure}[b]{.49\textwidth}
\includegraphics[width=\textwidth]{salvis-overlaid-visvalingam-64-chaikin-50k}
\caption{{\VW} + Chaikin's.}
\caption{{\VW} and Chaikin's.}
\end{subfigure}
\caption{Zoomed-in generalized and smoothened river + original.}
\caption{Zoomed-in simplified and smoothened river and original.}
\label{fig:salvis-overlaid-generalized-chaikin-50k}
\end{figure}
The resulting generalized and smoothened example
The resulting simplified and smoothened example
(figure~\onpage{fig:salvis-generalized-chaikin-50k}) yields a more
aesthetically pleasing result, however, it obscures natural river features.
Given the absence of rocks, the only natural features that influence the river
@ -433,7 +433,7 @@ following cartographic problems from our examples:
\end{description}
Like discussed in section~\label{sec:from-simplification-to-generalization}, we
Like discussed in section~\ref{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.
@ -445,7 +445,9 @@ exaggerated.
\begin{figure}[h]
\centering
\includegraphics[width=.8\textwidth]{wang125}
\caption{Originally Figure 12.5 from \cite{wang1998line}.}
\caption{Originally figure 12.5: cartographic line generalization example.}
\label{fig:wang125}
\end{figure}
@ -517,10 +519,9 @@ throughout this paper and the implementation.
quadruples.
$O$ notation was first suggested by
Bachmann\cite{bachmann1894analytische} and
Landau\cite{landau1911} in late XIX'th century, and clarified
and popularized for computing science by Donald
Knuth\cite{knuth1976big} in the 1970s.
Bachmann\cite{bachmann1894analytische} and Landau\cite{landau1911} in
late \textsc{xix} century, and clarified and popularized for
computing science by Donald Knuth\cite{knuth1976big} in the 1970s.
\end{description}
@ -551,12 +552,12 @@ the implementation:
\begin{itemize}
\item Created a function \textsc{wm\_exaggeration}, which exaggerates bends
following the rules. It worked well over simple geometries, but, due to
a subtle bug, created a self-crossing bend in Visinčia. We copied the
offending bend to the automated test suite and fixed the bug. The test
suite has the bend itself (a hook-like bend on the right-hand side of
figure~\ref{fig:test-figures}) and code to verify that it was correctly
exaggerated.
following the rules. It worked well over simple geometries, but, due to a
subtle bug, created a self-crossing bend in Visinčia. We copied the
offending bend to the automated test suite and fixed the bug. The test
suite has the bend itself (a hook-looking bend on the right-hand side of
figure~\ref{fig:test-figures}) and code to verify that it was correctly
exaggerated.
Later, while adding a feature to exaggeration code, I introduced a
different bug, which was automatically captured by the same bend.
@ -672,14 +673,14 @@ of 45cm (1.5 feet) is 1.5mm, as analyzed in \titlecite{mappingunits}.
In our case, our target is line bend, rather than a symbol. Assume 1.5mm is a
diameter of the bend. A semi-circle of 1.5mm diameter is depicted in
figure~\ref{fig:half-circle}. In other words, a bend of this size or larger,
when adjusted to scale, will not be generalized.
when adjusted to scale, will not be simplified.
\begin{figure}[h]
\centering
\begin{tikzpicture}[x=1mm,y=1mm]
\draw[] (-10, 0) -- (-.75,0) arc (225:-45:.75) -- (10, 0);
\end{tikzpicture}
\caption{Smallest feature that will be not generalized (to scale).}
\caption{Smallest feature that will be not simplified (to scale).}
\label{fig:half-circle}
\end{figure}
@ -691,14 +692,13 @@ table~\ref{table:scale-halfcirlce-diameter}.
\begin{table}[h]
\centering
\begin{tabular}{| c | D{.}{.}{1} |}
\hline
Scale & \multicolumn{1}{c|}{$D(m)$} \\ \hline
1:\numprint{10000} & 15 \\ \hline
1:\numprint{15000} & 22.5 \\ \hline
1:\numprint{25000} & 37.5 \\ \hline
1:\numprint{50000} & 75 \\ \hline
1:\numprint{250000} & 375 \\ \hline
\begin{tabular}{ c D{.}{.}{1} }
Scale & \multicolumn{1}{c}{$D(m)$} \\ \hline
1:\numprint{10000} & 15 \\
1:\numprint{15000} & 22.5 \\
1:\numprint{25000} & 37.5 \\
1:\numprint{50000} & 75 \\
1:\numprint{250000} & 375 \\
\end{tabular}
\caption{{\WM} half-circle diameter $D$ for popular scales.}
\label{table:scale-halfcirlce-diameter}
@ -715,7 +715,7 @@ from circle's area formula $A = 2\pi \frac{D}{2}^2$:
In reverse, adjusted size $A_{adj}$ from half-circle's diameter:
\[
A_{adj} = \frac{1}{8} \pi D^2
A_{adj} = \frac{\pi D^2}{8}
\]
\subsection{Definition of a Bend}
@ -806,8 +806,7 @@ vertices to the next bend.
\includegraphics[width=\textwidth]{inflection-1-gentle-inflection-after}
\caption{After applying the inflection rule.}
\end{subfigure}
\caption{Gentle inflection at the end of the bend when multiple vertices
are moved.}
\caption{Gentle inflection at the end of the bend with multiple vertices.}
\label{fig:inflection-1-gentle-inflection}
\end{figure}