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Motiejus Jakštys 2021-05-19 22:57:52 +03:00 committed by Motiejus Jakštys
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@ -261,7 +261,7 @@ simplification.
\end{figure}
Same rivers, unprocessed but in higher scales (1:\numprint{50000} and
1:\numprint{250000}), are depicted in figure~\ref{fig:salvis-50-250}. Some
1:\numprint{250000}), are depicted in Figure~\ref{fig:salvis-50-250}. Some
river features are so compact that a reasonably thin line depicting the river
is touching itself, creating a thicker line. We can assume that some
simplification for scale 1:\numprint{50000} and especially for
@ -286,7 +286,7 @@ Figure~\ref{fig:salvis-generalized-50k} illustrates the same river bend, but
simplified using {\DP} and {\VW} algorithms. The resulting lines are jagged,
and thus the resulting line looks unlike a real river. To smoothen the jaggedness,
traditionally, Chaikin's\cite{chaikin1974algorithm} is applied after
generalization, illustrated in figure~\ref{fig:salvis-generalized-chaikin-50k}.
generalization, illustrated in Figure~\ref{fig:salvis-generalized-chaikin-50k}.
\begin{figure}[ht!]
\centering
@ -334,7 +334,7 @@ generalization, illustrated in figure~\ref{fig:salvis-generalized-chaikin-50k}.
\end{figure}
The resulting simplified and smoothened example
(figure~\onpage{fig:salvis-generalized-chaikin-50k}) yields a more
(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
@ -740,7 +740,7 @@ results have been manually calculated. The test suite executes parts of the
algorithm against a predefined set of geometries, and asserts that the output
matches the resulting hand-calculated geometries.
The full set of test geometries is visualized in figure~\ref{fig:test-figures}.
The full set of test geometries is visualized in Figure~\ref{fig:test-figures}.
\begin{figure}[ht]
\centering
@ -762,7 +762,7 @@ the implementation:
a subtle bug, created a self-crossing bend in Visinčia. The offending
bend was copied to the automated test suite, which helped fix the bug.
Now the test suite contains the same bend (a hook-like bend on the
right-hand side of figure~\ref{fig:test-figures}) and code to verify
right-hand side of Figure~\ref{fig:test-figures}) and code to verify
that it was correctly exaggerated.
\item During algorithm development, automated tests run about once a
@ -883,7 +883,7 @@ purpose of each column in \textsc{wm\_debug} is described below:
sub-stage name, e.g., \textsc{bbends-polygon} creates polygon
geometries after polygons have been detected; this particular example
is used to generate colored polygons in
figure~\ref{fig:fig8-definition-of-a-bend}.
Figure~\ref{fig:fig8-definition-of-a-bend}.
\item[\normalfont\textsc{name}] is the name of the geometry, which comes from
parameter~\textsc{dbgname}.
@ -891,7 +891,7 @@ purpose of each column in \textsc{wm\_debug} is described below:
\item[\normalfont\textsc{gen}] is the top-level iteration number. In other
words, the number of times the execution flow passes through
\textsc{detect bends} phase as depicted in
figure~\onpage{fig:flow-chart}.
Figure~\onpage{fig:flow-chart}.
\item[\normalfont\textsc{nbend}] is the bend's index in its \textsc{line}.
@ -947,7 +947,7 @@ of 45 cm (1.5 feet), is 1.5 mm, as analyzed in \titlecite{mappingunits}.
In our case, our target is line bend, rather than a symbol. Assume 1.5 mm is a
diameter of the bend. A semi-circle of 1.5 mm diameter is depicted in
figure~\ref{fig:half-circle}. A bend of this size or larger, when adjusted to
Figure~\ref{fig:half-circle}. A bend of this size or larger, when adjusted to
scale, will not be simplified.
\begin{figure}[ht]
@ -1056,7 +1056,7 @@ on the number of iterations.
To prove that the algorithm implementation is correct for multiple vertices,
additional example was created and illustrated in
figure~\ref{fig:inflection-1-gentle-inflection}: the rule re-assigns two
Figure~\ref{fig:inflection-1-gentle-inflection}: the rule re-assigns two
vertices to the next bend.
\begin{figure}[ht]
@ -1124,7 +1124,7 @@ Looking at the {\WM} paper alone, it may seem like self-crossing may happen
only with the neighboring bend. This would mean an efficient $O(n)$
implementation\footnote{where $n$ is the number of bends in a line. See
explanation of \textsc{algorithmic complexity} in section~\ref{sec:vocab}.}.
However, as one can see in figure~\ref{fig:selfcrossing-1-non-neighbor}, it may
However, as one can see in Figure~\ref{fig:selfcrossing-1-non-neighbor}, it may
not be the case: any other bend in the line may be crossing it.
If one translates the requirements to code in a straightforward way, it would
@ -1399,30 +1399,30 @@ Our generalized results are viewed from the following angles:
\label{fig:salvis-wm-50k}
\end{figure}
As one can see in figure~\ref{fig:salvis-wm-50k}, the illustrations deliver
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. Left side of the
figure looks reasonably well simplified: long bends remain slightly curved,
small bends are removed or slightly exaggerated.
Figure's~\ref{fig:salvis-wm-50k} left part is clipped to
figure~\ref{fig:salvis-wm-50k-nw}. As one can see, some bends were well
Figure~\ref{fig:salvis-wm-50k-nw}. As one can see, some bends were well
exaggerated, and some bends were eliminated.
\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth]{salvis-wm-50k-nw}
\caption{Left part of figure~\ref{fig:salvis-wm-50k}.}
\caption{Left part of Figure~\ref{fig:salvis-wm-50k}.}
\label{fig:salvis-wm-50k-nw}
\end{figure}
Top--right side (clipped in figure~\ref{fig:salvis-wm-50k-ne}) some jagged
Top--right side (clipped in Figure~\ref{fig:salvis-wm-50k-ne}) some jagged
and sharp bends appear. These will become more pronounced in even larger-scale
simplification in the next section.
\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth]{salvis-wm-50k-ne}
\caption{Top--right part of figure~\ref{fig:salvis-wm-50k}.}
\caption{Top--right part of Figure~\ref{fig:salvis-wm-50k}.}
\label{fig:salvis-wm-50k-ne}
\end{figure}
@ -1432,7 +1432,7 @@ sharp edges for others.
\subsubsection{Large-scale (1:\numprint{250000})}
\label{sec:analyzed-large-scale}
As visible in figure~\ref{fig:salvis-wm-250k-10x}, for large-scale map, some of the
As visible in Figure~\ref{fig:salvis-wm-250k-10x}, for large-scale map, some of the
resulting bends look significantly exaggerated. Why is that?
Figure~\ref{fig:salvis-wm-250k-overlaid-zoom} zooms in the large-scale
simplification and overlays the original.
@ -1527,11 +1527,11 @@ all three shapes: GDR50LT, {\WM}--simplified GDB10LT, and the original GDB10LT.
\begin{figure}[h!]
\centering
\includegraphics[width=\textwidth]{salvis-wm-gdr50-ne}
\caption{Top--right side of figure~\ref{fig:salvis-wm-gdr50}.}
\caption{Top--right side of Figure~\ref{fig:salvis-wm-gdr50}.}
\label{fig:salvis-wm-gdr50-ne}
\end{figure}
Although figures are almost identical, figure~\ref{fig:salvis-wm-gdr50-ne}
Although figures are almost identical, Figure~\ref{fig:salvis-wm-gdr50-ne}
illustrates two small bends that have been removed in GDR50LT, but have been
exaggerated by our implementation.
@ -1688,8 +1688,8 @@ researched and extended.
\section{Acknowledgments}
\label{sec:acknowledgments}
I would like to thank my thesis supervisor, Andrius Balčiūnas, for his help in
formulating the requirements and providing early editorial feedback for the
I would like to thank my thesis supervisor, Dr. Andrius Balčiūnas, for his help
in formulating the requirements and providing early editorial feedback for the
thesis.
I am grateful to Tomas Straupis, who handed me the {\WM}\cite{wang1998line}