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mj-msc.tex
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@ -23,6 +23,8 @@
\definecolor{mypurple}{RGB}{117,112,179} \definecolor{mypurple}{RGB}{117,112,179}
\input{version} \input{version}
\newcommand{\onpage}[1]{\ref{#1} on page~\pageref{#1}}
\newcommand{\DP}{Douglas \& Peucker} \newcommand{\DP}{Douglas \& Peucker}
\newcommand{\VW}{Visvalingam--Whyatt} \newcommand{\VW}{Visvalingam--Whyatt}
\newcommand{\WM}{Wang--M{\"u}ller} \newcommand{\WM}{Wang--M{\"u}ller}
@ -187,6 +189,8 @@ In this paper we describe {\WM} in a detail that is more useful for algorithm:
each section will be expanded, with more elaborate and exact illustrations for each section will be expanded, with more elaborate and exact illustrations for
every step of the algorithm. every step of the algorithm.
Algorithms discussed in this paper assume Euclidean geometry.
\section{Automated tests} \section{Automated tests}
As part of the algorithm realization, an automated test suite has been As part of the algorithm realization, an automated test suite has been
@ -195,9 +199,9 @@ results have been manually calculated. The test suite executes parts of the
algorithm against a predefined set of geometries, and asserts that the output algorithm against a predefined set of geometries, and asserts that the output
matches the resulting hand-calculated geometry. matches the resulting hand-calculated geometry.
The full set of test geometries is visualized in figure~\ref{fig:test-figures} The full set of test geometries is visualized in
on page~\pageref{fig:test-figures}. The figure includes arrows depicting figure~\onpage{fig:test-figures}. The figure includes arrows depicting line
line direction. direction.
\begin{figure}[H] \begin{figure}[H]
\centering \centering
@ -210,12 +214,37 @@ The full test suite can be executed with a single command, and completes in a
few seconds. Having an easily accessible test suite boosts confidence that no few seconds. Having an easily accessible test suite boosts confidence that no
unexpected bugs have snug in while modifying the algorithm. unexpected bugs have snug in while modifying the algorithm.
\section{Vocabulary and terminology}
This section defines vocabulary and terms as defined in the rest of the paper.
\begin{description}
\item[Vertex] is a point on a plane, can be expressed unambiguously by a
pair of $(x,y)$ coordinates.
\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.
\item[Line] represents a single linear feature in the real world. For
example, a river or a coastline. {\tt LINESTRING} in GIS terms.
Geometrically, A line is a series of connected line segments, or,
equivalently, a series of connected vertices. Each vertex connects to
two other vertices, except those vertices at either ends of the line:
these two connect to a single other vertex.
\item[Bend] is a subset of a line that humans perceive as "bend". The
geometric definition is complex and is discussed in
section~\onpage{sec:definition-of-a-bend}.
\end{description}
\chapter{Description of the implementation} \chapter{Description of the implementation}
Like alluded in section~\ref{sec:introduction}, \cite{wang1998line} paper skims Like alluded in section~\onpage{sec:introduction}, \cite{wang1998line} paper
over certain details, which are important to implement the algorithm. This skims over certain details, which are important to implement the algorithm.
section goes through each algorithm stage, illustrating the intermediate steps This section goes through each algorithm stage, illustrating the intermediate
and explaining the author's desiderata for a detailed description. steps and explaining the author's desiderata for a detailed description.
Step illustrations of the following sections are extracted from the automated Step illustrations of the following sections are extracted from the automated
test cases. test cases.
@ -224,10 +253,11 @@ Bends are illustrated using the following algorithm:
\begin{itemize} \begin{itemize}
\item Join the first and last vertices of the line, creating a polygon. \item Join the first and last vertices of the line, creating a polygon.
\item Color the polygons using a diverging color scheme. \item Color the polygons.
\end{itemize} \end{itemize}
\section{Definition of a Bend} \section{Definition of a Bend}
\label{sec:definition-of-a-bend}
\begin{figure}[H] \begin{figure}[H]
\centering \centering
@ -236,15 +266,14 @@ Bends are illustrated using the following algorithm:
\label{fig:fig8-definition-of-a-bend} \label{fig:fig8-definition-of-a-bend}
\end{figure} \end{figure}
End vertices of all lines should also be part of the bend. That way, all End line segments of all lines should also be part of the bend. That way, all
vertices belong to 1 or 2 bends. This characteristic is not obvious when line segments belong to 1 or 2 bends. This characteristic is not obvious when
reading the introductory sections, but becomes unavoidable (there could be no reading the introductory sections, but becomes unavoidable (there could be no
other way) when reading the following sections in detail. other way) when reading the following sections in detail.
Last vertex of each bend (except for the two end-line vertices) is also the First and last segments of each bend (except for the two end-line segments) is
first vertex of the next bend. This is apparent when looking at the also the first vertex of the next bend. This is apparent when looking at the
illustration of the detected bends. However, the original {\WM} paper did not illustration of the detected bends.
have such an explanation or illustration.
\section{Gentle Inflection at End of a Bend} \section{Gentle Inflection at End of a Bend}