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Motiejus Jakštys 2021-05-19 22:57:47 +03:00 committed by Motiejus Jakštys
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mj-msc.tex
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@ -209,7 +209,8 @@ This section defines vocabulary and terms as defined in the rest of the paper.
\item[Line Segment (or Segment)] joins two vertices by a straight line. A \item[Line Segment (or Segment)] joins two vertices by a straight line. A
segment can be expressed by two coordinate pairs: $(x_1, y_1)$ and segment can be expressed by two coordinate pairs: $(x_1, y_1)$ and
$(x_2, y_2)$. Line Segment and Segment are used interchangeably. $(x_2, y_2)$. Line Segment and Segment are used interchangeably
throughout the paper.
\item[Line] represents a single linear feature in the real world. For \item[Line] represents a single linear feature in the real world. For
example, a river or a coastline. {\tt LINESTRING} in GIS terms. example, a river or a coastline. {\tt LINESTRING} in GIS terms.
@ -272,7 +273,7 @@ purposes) using the following algorithm:
\section{Definition of a Bend} \section{Definition of a Bend}
\label{sec:definition-of-a-bend} \label{sec:definition-of-a-bend}
The original article describes: The original article describes a bend as:
\begin{displayquote}[\cite{wang1998line}][] \begin{displayquote}[\cite{wang1998line}][]
A bend can be defined as that part of a line which contains a number of A bend can be defined as that part of a line which contains a number of
@ -281,21 +282,9 @@ The original article describes:
two end vertices being in opposite signs. two end vertices being in opposite signs.
\end{displayquote} \end{displayquote}
While it gives a good intuitive understanding of what the bend is, some more While it gives a good intuitive understanding of what the bend is, this section
technical details would be appreciated. provides more technical details. Here are some non-obvious characteristics that
are necessary when writing code to detect the bends:
Figure~\ref{fig:fig8-definition-of-a-bend} illustrates article's figure 8,
but with bends colored as polygons: each color is a distinctive bend.
\begin{figure}[h]
\centering
\includegraphics[width=\linewidth]{fig8-definition-of-a-bend}
\caption{Originally figure 8: detected bends are highlighted}
\label{fig:fig8-definition-of-a-bend}
\end{figure}
Once the intuitive definition is established, here are some non-obvious
characteristics that are necessary when writing code to detect the bends:
\begin{itemize} \begin{itemize}
@ -310,6 +299,16 @@ Properties above may be apparent when looking at illustrations at this article
or reading here, but they are nowhere as such when looking at the original or reading here, but they are nowhere as such when looking at the original
article. article.
Figure~\ref{fig:fig8-definition-of-a-bend} illustrates article's Figure 8,
but with bends colored as polygons: each color is a distinctive bend.
\begin{figure}[h]
\centering
\includegraphics[width=\linewidth]{fig8-definition-of-a-bend}
\caption{Originally Figure 8: detected bends are highlighted}
\label{fig:fig8-definition-of-a-bend}
\end{figure}
\section{Gentle Inflection at End of a Bend} \section{Gentle Inflection at End of a Bend}
The gist of the section is in the original article: The gist of the section is in the original article:
@ -333,7 +332,7 @@ when a single vertex is moved outwards the end of the bend.
\includegraphics[width=\textwidth]{fig5-gentle-inflection-after} \includegraphics[width=\textwidth]{fig5-gentle-inflection-after}
\caption{After applying the inflection rule} \caption{After applying the inflection rule}
\end{subfigure} \end{subfigure}
\caption{Originally figure 5: gentle inflections at the ends of the bend} \caption{Originally Figure 5: gentle inflections at the ends of the bend}
\label{fig:fig5-gentle-inflection} \label{fig:fig5-gentle-inflection}
\end{figure} \end{figure}