diff --git a/IV/mj-msc.tex b/IV/mj-msc.tex index 93c09a3..ad36d4e 100644 --- a/IV/mj-msc.tex +++ b/IV/mj-msc.tex @@ -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}