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 \usepackage{csquotes}
 \usepackage[maxbibnames=99,style=authoryear]{biblatex}
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 \usepackage{enumitem}
 \usepackage[toc,page,title]{appendix}
 \addbibresource{bib.bib}
 \usepackage{caption}
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 \usepackage{tikz}
 \usepackage{minted}
 \usetikzlibrary{er,positioning}
 \definecolor{mypurple}{RGB}{117,112,179}
 \input{version}
 
 \newcommand{\DP}{Douglas \& Peucker}
 \newcommand{\VW}{Visvalingam--Whyatt}
 \newcommand{\WM}{Wang--M{\"u}ller}
 
 \newcommand{\MYTITLE}{Cartographic Generalization of Lines using free software (example of rivers)}
 \newcommand{\MYAUTHOR}{Motiejus Jakštys}
 
 \title{\MYTITLE}
 \author{\MYAUTHOR}
 \date{\VCDescribe}
 
 \begin{document}
 
 \begin{titlepage}
     \begin{center}
         \includegraphics[width=0.4\textwidth]{vu}
 
         \huge
         \textbf{\MYTITLE} \\[4ex]
 
         \LARGE
         \textbf{\MYAUTHOR} \\[8ex]
 
         \vfill
 
         A thesis presented for the degree of\\
         Master in Cartography \\[3ex]
 
         \large
         \VCDescribe
     \end{center}
 \end{titlepage}
 
 \begin{abstract}
 \label{sec:abstract}
 Current open-source line generalization solutions have their roots in
     mathematics and geometry, and are not fit for natural objects like rivers
     and coastlines. This paper discusses our implementation of {\WM} algorithm
     under and open-source license, explains things that we would had
     appreciated in the original paper and compares our results to different
     generalization algorithms.
 \end{abstract}
 
 \newpage
 
 \tableofcontents
 \listoffigures
 
 \newpage
 
 \section{Introduction}
 \label{sec:introduction}
 
 When creating small-scale maps, often the detail of the data source is greater
 than desired for the map. This becomes especially acute for natural features
 that have many bends, like coastlines, rivers and forest boundaries.
 
 To create a small-scale map from a large-scale data source, these features need
 to be generalized: detail should be reduced. However, while doing so, it is
 important to preserve the "defining" shape of the original feature, otherwise
 the result will look unrealistic.
 
 For example, if a river is nearly straight, it should be nearly straight after
 generalization, otherwise a too straightened river will look like a canal.
 Conversely, if the river is highly wiggly, the number of bends should be
 reduced, but not removed.
 
 Generalization problem for other objects can often be solved by other
 non-geometric means:
 
 \begin{itemize}
     \item Towns and cities can be filtered and generalized by number of
         inhabitants.
     \item Roads can be eliminated by the road length, number of lanes, or
         classification of the road (local, regional, international).
 \end{itemize}
 
 Natural line generalization problem can be viewed as having two competing
 goals:
 
 \begin{itemize}
     \item Reduce detail by removing or simplifying "less important" features.
     \item Retain enough detail, so the original is still recognize-able.
 \end{itemize}
 
 Given the discussed complexities, a fine line between under-generalization
 (leaving object as-is) and over-generalization (making a straight line) must be
 found. Therein lies the complexity of generalization algorithms: all have
 different trade-offs.
 
 \section{Literature review}
 \label{sec:literature-review}
 
 A number of cartographic line generalization algorithms have been researched.
 The "classical" ones are {\DP} and {\VW}.
 
 \subsection{{\DP} and {\VW}}
 
 \cite{douglas1973algorithms} and \cite{visvalingam1993line} are "classical"
 line generalization computer graphics algorithms. They are relatively simple to
 implement, require few runtime resources. Both of them accept only a single
 parameter, based on desired scale of the map, which makes them very simple to
 adjust for different scales.
 
 Both algorithms are part of PostGIS, a free-software GIS suite:
 \begin{itemize}
     \item \cite{douglas1973algorithms} via
         \href{https://postgis.net/docs/ST_Simplify.html}{PostGIS Simplify}.
 
     \item \cite{visvalingam1993line} via
         \href{https://postgis.net/docs/ST_SimplifyVW.html}{PostGIS SimplifyVW}.
 \end{itemize}
 
 Since both algorithms produce jagged output lines, it is worthwhile to process
 those through a widely available \cite{chaikin1974algorithm} smoothing
 algorithm via \href{https://postgis.net/docs/ST_ChaikinSmoothing.html}{PostGIS
 ChaikinSmoothing}.
 
 Even though {\DP} and {\VW} are simple to understand and computationally
 efficient, they have serious deficiencies for cartographic natural line
 generalization.
 
 <TODO: expand on deficiencies>
 
 \subsection{Modern approaches}
 
 Due to their simplicity and ubiquity, {\DP} and {\VW} have been established as
 go-to algorithms for line generalization. During recent years, more modern
 replacement algorithms have emerged. These fall into roughly two categories:
 
 \begin{itemize}
     \item Cartographic knowledge was encoded to an algorithm (bottom-up
         approach). One among these are \cite{wang1998line}.
     \item Mathematical shape transformation which yields a more cartographic
         result. E.g. \cite{jiang2003line}, \cite{dyken2009simultaneous},
         \cite{mustafa2006dynamic}, \cite{nollenburg2008morphing}.
 \end{itemize}
 
 Authors of most of the aforementioned articles have implemented the
 generalization algorithm, at least to generate the visuals in the articles.
 However, I wasn't able to find code for any of those to evaluate with my
 desired data set, or use as a basis for my own maps. \cite{wang1998line} is
 available in a commercial product.
 
 Lack of robust openly available generalization algorithm implementations poses
 a problem for map creation with free software: there is not a similar
 high-quality simplification algorithm to create down-scaled maps, so any
 cartographic work, which uses line generalization as part of its processing,
 will be of sub-par quality. We believe that availability of high-quality
 open-source tools is an important foundation for future cartographic
 experimentation and development, thus it it benefits the cartographic society
 as a whole.
 
 \section{Methodology}
 \label{sec:methodology}
 
 The original \cite{wang1998line} leaves something to be desired for a practical
 implementation: it is not straightforward to implement the algorithm from the
 paper alone.
 
 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
 every step of the algorithm.
 
 \subsection{Automated tests}
 
 As part of the algorithm realization, an automated test suite has been
 developed. Shapes to test each function have been hand-crafted and expected
 results have been manually calculated. The test suite executes parts of the
 algorithm against a predefined set of geometries, and asserts that the output
 matches the resulting hand-calculated geometry.
 
 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
 unexpected regressions have been added while modifying the algorithm.
 
 <TODO: expand with a screenshot>
 
 \section{Description of the implementation}
 
 \subsection{Definition of a Bend}
 
 \subsection{Gentle Inflection at End of a Bend}
 
 \subsection{Self-line Crossing When Cutting a Bend}
 
 \subsection{Attributes of a Single Bend}
 
 \subsection{Shape of a Bend}
 
 \subsection{The Context of a Bend: Isolated and Similar Bends}
 
 \subsection{Elimination Operator}
 
 \subsection{Combination Operator}
 
 \subsection{Exaggeration Operator}
 
 \section{Program Implementation}
 
 \section{Results of Experiments}
 
 \section{Conclusions}
 \label{sec:conclusions}
 
 \section{Related Work and future suggestions}
 \label{sec:related_work}
 
 \printbibliography
 
 \begin{appendices}
 
 \section{Code listings}
 
 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
     accompanying scripts have been attached to the PDF. To re-generate this
     document and its accompanying graphics, run this script (assuming name of
     this document is {\tt mj-msc-all.pdf}):
 
 \inputminted[fontsize=\small]{bash}{extract-and-generate}
 
 A reasonably up-to-date Linux or OS X system with a working Docker installation
 is required.
 
 \end{appendices}
 \end{document}