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Motiejus Jakštys 2021-05-19 22:57:47 +03:00 committed by Motiejus Jakštys
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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
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
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}
\label{sec:definition-of-a-bend}
The original article describes:
The original article describes a bend as:
\begin{displayquote}[\cite{wang1998line}][]
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.
\end{displayquote}
While it gives a good intuitive understanding of what the bend is, some more
technical details would be appreciated.
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:
While it gives a good intuitive understanding of what the bend is, this section
provides more technical details. Here are some non-obvious characteristics that
are necessary when writing code to detect the bends:
\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
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}
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}
\caption{After applying the inflection rule}
\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}
\end{figure}