diff --git a/mj-msc.tex b/mj-msc.tex index 542e36f..812c76b 100644 --- a/mj-msc.tex +++ b/mj-msc.tex @@ -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}