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\documentclass[a4paper]{report} \documentclass[a4paper]{article}
\usepackage[T1]{fontenc} \usepackage[T1]{fontenc}
%\usepackage[bitstream-charter]{mathdesign} %\usepackage[bitstream-charter]{mathdesign}
@ -78,7 +78,7 @@ Current open-source line generalization solutions have their roots in
\newpage \newpage
\chapter{Introduction} \section{Introduction}
\label{sec:introduction} \label{sec:introduction}
When creating small-scale maps, often the detail of the data source is greater When creating small-scale maps, often the detail of the data source is greater
@ -118,13 +118,13 @@ Given the discussed complexities, a fine line between under-generalization
found. Therein lies the complexity of generalization algorithms: all have found. Therein lies the complexity of generalization algorithms: all have
different trade-offs. different trade-offs.
\chapter{Literature review} \section{Literature review}
\label{sec:literature-review} \label{sec:literature-review}
A number of cartographic line generalization algorithms have been researched. A number of cartographic line generalization algorithms have been researched.
The "classical" ones are {\DP} and {\VW}. The "classical" ones are {\DP} and {\VW}.
\section{{\DP} and {\VW}} \subsection{{\DP} and {\VW}}
\cite{douglas1973algorithms} and \cite{visvalingam1993line} are "classical" \cite{douglas1973algorithms} and \cite{visvalingam1993line} are "classical"
line generalization computer graphics algorithms. They are relatively simple to line generalization computer graphics algorithms. They are relatively simple to
@ -152,7 +152,7 @@ generalization.
<TODO: expand on deficiencies> <TODO: expand on deficiencies>
\section{Modern approaches} \subsection{Modern approaches}
Due to their simplicity and ubiquity, {\DP} and {\VW} have been established as Due to their simplicity and ubiquity, {\DP} and {\VW} have been established as
go-to algorithms for line generalization. During recent years, alternatives go-to algorithms for line generalization. During recent years, alternatives
@ -181,7 +181,7 @@ open-source tools is an important foundation for future cartographic
experimentation and development, thus it it benefits the cartographic society experimentation and development, thus it it benefits the cartographic society
as a whole. as a whole.
\chapter{Methodology} \section{Methodology}
\label{sec:methodology} \label{sec:methodology}
The original \cite{wang1998line} leaves something to be desired for a practical The original \cite{wang1998line} leaves something to be desired for a practical
@ -199,7 +199,7 @@ every step of the algorithm.
Algorithms discussed in this paper assume Euclidean geometry. Algorithms discussed in this paper assume Euclidean geometry.
\section{Vocabulary and terminology} \subsection{Vocabulary and terminology}
This section defines vocabulary and terms as defined in the rest of the paper. This section defines vocabulary and terms as defined in the rest of the paper.
@ -227,7 +227,7 @@ This section defines vocabulary and terms as defined in the rest of the paper.
\end{description} \end{description}
\section{Automated tests} \subsection{Automated tests}
\label{sec:automated-tests} \label{sec: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
@ -251,7 +251,7 @@ 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.
\chapter{Description of the implementation} \section{Description of the implementation}
Like alluded in section~\onpage{sec:introduction}, \cite{wang1998line} paper Like alluded in section~\onpage{sec:introduction}, \cite{wang1998line} paper
skims over certain details, which are important to implement the algorithm. skims over certain details, which are important to implement the algorithm.
@ -271,7 +271,7 @@ purposes) using the following algorithm:
\item Color the polygons using distinct colors. \item Color the polygons using distinct colors.
\end{itemize} \end{itemize}
\section{Definition of a Bend} \subsection{Definition of a Bend}
\label{sec:definition-of-a-bend} \label{sec:definition-of-a-bend}
The original article describes a bend as: The original article describes a bend as:
@ -310,7 +310,7 @@ but with bends colored as polygons: each color is a distinctive bend.
\label{fig:fig8-definition-of-a-bend} \label{fig:fig8-definition-of-a-bend}
\end{figure} \end{figure}
\section{Gentle Inflection at End of a Bend} \subsection{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:
@ -378,41 +378,40 @@ some bends that should be mutated. This implementation does it in the following
The current implementation is the most straightforward, but not optimal: The current implementation is the most straightforward, but not optimal:
reversing of lines and bends could be avoided by walking backwards the lines. reversing of lines and bends could be avoided by walking backwards the lines.
In this case, steps \ref{rev1} and \ref{rev2} could be remove. That would save In this case, steps \ref{rev1} and \ref{rev2} could be spared, thus saving
both memory and computation time. memory and computation time.
The "quite small angle", as mentioned in the article, was arbitrarily chosen to The "quite small angle" was arbitrarily chosen to $\smallAngle$.
$\smallAngle$.
\section{Self-line Crossing When Cutting a Bend} \subsection{Self-line Crossing When Cutting a Bend}
\section{Attributes of a Single Bend} \subsection{Attributes of a Single Bend}
\section{Shape of a Bend} \subsection{Shape of a Bend}
\section{The Context of a Bend: Isolated and Similar Bends} \subsection{The Context of a Bend: Isolated and Similar Bends}
\section{Elimination Operator} \subsection{Elimination Operator}
\section{Combination Operator} \subsection{Combination Operator}
\section{Exaggeration Operator} \subsection{Exaggeration Operator}
\chapter{Program Implementation} \section{Program Implementation}
\chapter{Results of Experiments} \section{Results of Experiments}
\chapter{Conclusions} \section{Conclusions}
\label{sec:conclusions} \label{sec:conclusions}
\chapter{Related Work and future suggestions} \section{Related Work and future suggestions}
\label{sec:related_work} \label{sec:related_work}
\printbibliography \printbibliography
\begin{appendices} \begin{appendices}
\chapter{Code listings} \section{Code listings}
We strongly believe in the ability to reproduce the results is critical for any We strongly believe in the ability to reproduce the results is critical for any
scientific work. To make it possible for this paper, all source files and scientific work. To make it possible for this paper, all source files and