commit 17d047bc49435cd2031e163dbf552fadb37e4dab (tree)
parent 068bb3a5463da37adf0df0105a535589f198e299
Author: Motiejus Jakštys <desired.mta@gmail.com>
Date: Tue, 26 May 2020 11:39:18 +0300
add sine wave example
Diffstat:
1 file changed, 77 insertions(+), 38 deletions(-)
diff --git a/II/Referatas/mj-referatas.tex b/II/Referatas/mj-referatas.tex
@@ -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
