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add sine wave example

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Motiejus Jakštys 2020-05-26 11:39:18 +03:00
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II/Referatas/mj-referatas.tex
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@ -1,9 +1,16 @@
\documentclass[a4paper]{article}
\iffalse
\usepackage[L7x,T1]{fontenc}
\usepackage[lithuanian]{babel}
\else
\usepackage[T1]{fontenc}
\usepackage[english]{babel}
\fi
\usepackage[utf8]{inputenc}
\usepackage{a4wide}
\usepackage{csquotes}
\usepackage[english]{babel}
\usepackage[maxbibnames=99,style=authoryear]{biblatex}
\usepackage[pdfusetitle]{hyperref}
\usepackage{enumitem}
@ -58,11 +65,8 @@ what scales and what distances?
\begin{document}
\maketitle
\newpage
\section{Abstract}
\begin{abstract}
\label{sec:abstract}
Current open-source line generalization solutions have their roots in
mathematics and geometry, thus emit poor cartographic output. Therefore, if one
is using open-source technology to create a small-scale map, downscaled lines
@ -70,6 +74,12 @@ is using open-source technology to create a small-scale map, downscaled lines
line generalization algorithms and suggests one for an avid GIS developer to
implement. Once it is usable from within open-source GIS software (e.g. QGIS or
PostGIS), rivers on these small-scale maps will look professionally downscaled.
\end{abstract}
\newpage
\tableofcontents
\listoffigures
\section{Introduction}
\label{sec:introduction}
@ -78,13 +88,20 @@ Cartographic generalization is one of the key processes of creating small-scale
maps: how can one approximate object features, without losing its main
cartographic properties? The problem is universally challenging across many
geographical entities (\cite{muller1991generalization},
\cite{mcmaster1992generalization}). This paper focuses on line generalization,
using natural rivers as examples.
\cite{mcmaster1992generalization}). This paper focuses on line generalization
for natural rivers: which algorithm should be picked when down-scaling a river
map?
Line generalization algorithms are well studied, tested and implemented, but
they expose deficiencies in large-scale reduction (\cite{monmonier1986toward},
\cite{mcmaster1993spatial}). Most of these techniques are based on mathematical
shape representation, rather than cartographic characteristics of the line.
We examine readily available open-source algorithms using a concrete
cartographical example, and make a suggestion on which algorithm could be
implemented next.
\section{What's available}
Line generalization algorithms are well studied, but expose deficiencies in
large-scale reduction (\cite{monmonier1986toward}, \cite{mcmaster1993spatial}).
Most of these techniques are based on mathematical shape representation, rather
than cartographic characteristics of the line.
A number of cartographic line generalization algorithms have been researched,
which claim to better process cartographic objects like lines. These fall into
@ -98,13 +115,12 @@ two rough categories:
\cite{nollenburg2008morphing}.
\end{itemize}
During research, code has been written for all of the algorithms above,
however, it is nowhere to be found completely, or in a usable form. There is
one exception: \cite{wang1998line} is available for general use in a commercial
product, but the author of this paper does not have means to try it.
During research for the mentioned papers, code has been written for all of the
algorithms above, however, is not to be found in a usable form.
\cite{wang1998line} is available in a commercial product, but the author of
this paper does not have means to try it.
Therefore, this paper will be comparing algorithms that readily available for
general public:
To sum up, this paper will be comparing the following algorithms:
\begin{itemize}
\item \cite{douglas1973algorithms} via
\href{https://postgis.net/docs/ST_Simplify.html}{PostGIS Simplify}.
@ -113,10 +129,12 @@ general public:
\href{https://postgis.net/docs/ST_SimplifyVW.html}{PostGIS SimplifyVW}.
\end{itemize}
This article will be using Lakaja and large part of Žeimena (see
figure~\ref{fig:zeimena} on page~\pageref{fig:zeimena}). This location was
chosen because the river exhibits both both straight and curved shape, is a
combination of two curly rivers, and author's familiarity with the location.
\section{Visual comparison}
Lakaja and large part of Žeimena (see figure~\ref{fig:zeimena} on
page~\pageref{fig:zeimena}) will be used, because the river exhibits both both
straight and curved shape, is a combination of two curly rivers, and author's
familiarity with the location.
\begin{figure}[H]
\centering
@ -125,9 +143,7 @@ combination of two curly rivers, and author's familiarity with the location.
\label{fig:zeimena}
\end{figure}
\section{Visually comparing {\DP} and {\VW}}
To visually evaluate the Žeimena sample, a few examples for {\DP} and {\VW}
To visually evaluate the Žeimena sample, examples for {\DP} and {\VW}
were created using the following parameters:
\begin{enumerate}[label=(\Roman*)]
@ -135,13 +151,13 @@ were created using the following parameters:
\item {\VW} tolerance: $vwtolerance = tolerance ^ 2$\label{itm:2}.
\end{enumerate}
Item~\ref{itm:2} requires explanation. Tolerance for {\DP} is specified in
linear units, in this case, meters. Tolerance for {\VW} is specified in areal
units, in this case, $m^2$. As author was not able to locate formal comparisons
between the two (i.e. how to calculate one tolerance value from the other, so
the results are comparable?), {\DP} tolerance was arbitrarily squared and fed
to {\VW}. To author's eye, this provides comparable and reasonable results,
though could be researched.
Parameter~\ref{itm:2} requires explanation. Tolerance for {\DP} is specified in
linear units, in this case, meters. Tolerance for {\VW} is specified in area
units $m^2$. As author was not able to locate formal comparisons between the
two (i.e. how to calculate one tolerance value from the other, so the results
are comparable?), {\DP} tolerance was arbitrarily squared and fed to {\VW}. To
author's eye, this provides comparable and reasonable results, though could be
researched.
As can be observed in table~\ref{tab:dp-vs-vw} on page~\pageref{tab:dp-vs-vw},
both simplication algorithms convert bends to chopped lines. This is especially
@ -180,14 +196,37 @@ retained.
\includegraphics[width=.0625\linewidth]{douglas-4000} &
\includegraphics[width=.0625\linewidth]{visvalingam-4000} \tabularnewline \hline
\end{tabularx}
\caption{{\DP} and {\VW} side-by-side visual comparison.}
\caption{{\DP} and {\VW} side-by-side visual comparison}
\label{tab:dp-vs-vw}
\end{figure}
To sum up, both {\VW} and {\DP} simplify the lines, but their cartographic
output poorly represents lines and bends. Where to look for better output?
\section{Suggested alternative}
\label{sec:suggested_alternative}
TODO:
{\WM} observed how professional cartographers are simplifying rivers and encoded it
to an algorithm which can be implemented by a computer.
Imagine there are two small bends close to each other, similar to
figure~\ref{pic:example-bend} on page~\pageref{pic:example-bend}, and one needs
to generalize it. The bends are too large to ignore replace them with a
straight line, but too small to retain both and retain their complexity.
\begin{figure}[h]
\centering
\begin{tikzpicture}[xscale=.5]
\draw (-4,-1) -- (-1, -1);
\draw (-1,-1) cos (0,0) sin (1,1) cos (2,0) sin (3,-1) cos (4,0) sin (5,1) cos(6,0) sin (7,-1);
\draw (7,-1) -- (10, -1);
\end{tikzpicture}
\caption{Example river bend that should be generalized}
\label{pic:example-bend}
\end{figure}
We would imagine
\begin{itemize}
\item Describe algorithm by {\WM}.
\item Explain how outputs will differ.
@ -203,12 +242,12 @@ and tortuosity for the generalization of linear geographic elements. This
research can provide references to the appropriate settings of the line
generalization parameters for the maps at various scales.
As noted in item~\ref{itm:2} on page~\pageref{itm:2}, it would be useful to
have a formula mapping {\DP} tolerance to {\VW}. That way, visual comparisons
between line simplification algorithms could be more objective.
As noted in parameter~\ref{itm:2} on page~\pageref{itm:2}, it would be useful
to have a formula mapping {\DP} tolerance to {\VW}. That way, visual
comparisons between line simplification algorithms could be more objective.
\section{Conclusions and Further Work}
\label{sec:conclusions_and_further_work}
\section{Conclusions}
\label{sec:conclusions}
We have practically evaluated two readily available line simplification
algorithms with a river sample: {\VW} and {\DP}, and outlined their