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Motiejus Jakštys 2020-06-18 11:05:13 +03:00
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4
II/Referatas/Makefile
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@ -1,8 +1,8 @@
CROSSING = 622916 6109267 626066 6111487 # xmin ymin xmax ymax
ZEIMENA_TOLERANCES = 128 256 512 1024 2048 4096
SINEWAVE_TOLERANCES = 2 16 32
CROSSING_TOLERANCES = 64 128 256
CHAIKIN_CROSSING_TOLERANCES = 128 256
CROSSING_TOLERANCES = 128 256 512
CHAIKIN_CROSSING_TOLERANCES = 128 256 512
SINEWAVE_SIZE = 120x48
GEN1 = $(addsuffix .pdf, \
$(addprefix sinewave2_douglas_,$(SINEWAVE_TOLERANCES)) \

2
II/Referatas/chaikin.sql
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@ -7,7 +7,7 @@ CREATE TABLE :tbl (
INSERT INTO :tbl (geom) (
SELECT
ST_ChaikinSmoothing (geom, 3) AS geoms
ST_ChaikinSmoothing (geom, 5) AS geoms
FROM
:src);

70
II/Referatas/mj-referatas.tex
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@ -33,7 +33,7 @@
\newcommand{\WM}{Wang--M{\"u}ller}
\title{
Cartografic Generalization of Lines using free software \\
Cartographic Generalization of Lines using free software \\
(example of rivers) \\ \vspace{4mm}
}
@ -185,6 +185,9 @@ version will help explain some of the deficiencies in the reviewed algorithms.
\label{fig:crossing}
\end{figure}
\section{Comparison algorithms and parameters}
\label{sec:algs-and-params}
To visually evaluate the Žeimena sample, examples for {\DP} and {\VW}
were created using the following parameters:
@ -193,16 +196,22 @@ were created using the following parameters:
\item {\VW} tolerance: $vwtolerance = tolerance ^ 2$\label{itm:2}.
\end{enumerate}
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.
Tolerance squared, i.e. the 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.
Chaikin's smoothing algorithm was generated using $nIterations = 5$. That
number was chosen for better visual appeal at the expense of computational
power. Smaller number iterations would cause retain visible angles, whereas
larger number of iterations, like 5 (PostGIS supports values from 1 to 5),
causes the resulting lines to be very smooth.
As can be observed in table~\ref{tab:comparison-zeimena} on
page~\pageref{tab:comparison-zeimena}, both simplication algorithms convert
page~\pageref{tab:comparison-zeimena}, both simplification algorithms convert
bends to chopped lines. This is especially visible in tolerances 256 and 512.
In a more robust simplification algorithm, the larger tolerance, the larger the
bends on the original map should be retained.
@ -211,8 +220,8 @@ bends on the original map should be retained.
\renewcommand{\tabularxcolumn}[1]{>{\center\small}m{#1}}
\begin{tabularx}{\textwidth}{ p{2.1cm} | X | X | }
Tolerance DP/VW &
Douglas \& Peucker &
Visvalingam-Whyatt \tabularnewline \hline
{\DP} &
{\VW} \tabularnewline \hline
128/16384 &
\includegraphics[width=\linewidth]{zeimena_douglas_128} &
@ -244,7 +253,7 @@ bends on the original map should be retained.
To ease the discussion on shapes in the resulting output, it is useful to
define what a "blunt bend" is: it is a river bent that looks like a cutout from
a large circle, ilustrated in figure~\ref{fig:blunt-bent}.
a large circle, illustrated in figure~\ref{fig:blunt-bent}.
\begin{figure}[h]
\centering
@ -266,12 +275,8 @@ table~\ref{tab:comparison-crossing} on page~\pageref{tab:comparison-crossing}.
\renewcommand{\tabularxcolumn}[1]{>{\center\small}m{#1}}
\begin{tabularx}{\textwidth}{ p{2.1cm} | X | X | }
Tolerance DP/VW &
Douglas \& Peucker &
Visvalingam-Whyatt \tabularnewline \hline
64/4096 &
\includegraphics[width=\linewidth]{overlaid_zeimena_douglas_64} &
\includegraphics[width=\linewidth]{overlaid_zeimena_visvalingam_64} \tabularnewline \hline
{\DP} &
{\VW} \tabularnewline \hline
128/16384 &
\includegraphics[width=\linewidth]{overlaid_zeimena_douglas_128} &
@ -281,6 +286,10 @@ table~\ref{tab:comparison-crossing} on page~\pageref{tab:comparison-crossing}.
\includegraphics[width=\linewidth]{overlaid_zeimena_douglas_256} &
\includegraphics[width=\linewidth]{overlaid_zeimena_visvalingam_256} \tabularnewline \hline
512/262144 &
\includegraphics[width=\linewidth]{overlaid_zeimena_douglas_512} &
\includegraphics[width=\linewidth]{overlaid_zeimena_visvalingam_512} \tabularnewline \hline
\end{tabularx}
\caption{{\DP} and {\VW} on river crossing area}
\label{tab:comparison-crossing}
@ -288,15 +297,15 @@ table~\ref{tab:comparison-crossing} on page~\pageref{tab:comparison-crossing}.
As the reader may observe, the output lines, especially with higher tolerances,
are jaggy. Higher-tolerance jaggy outputs from {\VW} and {\DP}, passed through
Chaikin with 3 iterations, are displayed in table~\ref{tab:chaikin-crossing} on
Chaikin with 5 iterations, are displayed in table~\ref{tab:chaikin-crossing} on
page~\pageref{tab:chaikin-crossing}.
\begin{figure}[h]
\renewcommand{\tabularxcolumn}[1]{>{\center\small}m{#1}}
\begin{tabularx}{\textwidth}{ p{2.1cm} | X | X | }
Tolerance DP/VW &
Douglas \& Peucker + Chaikin(3) &
Visvalingam-Whyatt + Chaikin(3) \tabularnewline \hline
{\DP} + Chaikin(5) &
{\VW} + Chaikin(5) \tabularnewline \hline
128/16384 &
\includegraphics[width=\linewidth]{overlaid_chaikin_zeimena_douglas_128} &
@ -306,12 +315,16 @@ page~\pageref{tab:chaikin-crossing}.
\includegraphics[width=\linewidth]{overlaid_chaikin_zeimena_douglas_256} &
\includegraphics[width=\linewidth]{overlaid_chaikin_zeimena_visvalingam_256} \tabularnewline \hline
512/262144 &
\includegraphics[width=\linewidth]{overlaid_chaikin_zeimena_douglas_512} &
\includegraphics[width=\linewidth]{overlaid_chaikin_zeimena_visvalingam_512} \tabularnewline \hline
\end{tabularx}
\caption{Chaikin-smoothened {\DP} and {\VW} on river crossing area}
\label{tab:chaikin-crossing}
\end{figure}
There is another issue on the wishlist beyond jaggyness and loss of large bents
There is another issue on the wishlist beyond jaggedness and loss of large bents
-- combining close bends to larger ones.
\subsection{Combining bends}
@ -340,8 +353,8 @@ page~\pageref{tab:comparison-sinewave2}.
\renewcommand{\tabularxcolumn}[1]{>{\center\small}m{#1}}
\begin{tabularx}{\textwidth}{ p{1.5cm} | X | X | }
Tolerance DP/VW &
Douglas \& Peucker &
Visvalingam-Whyatt \tabularnewline \hline
{\DP} &
{\VW} \tabularnewline \hline
2/4 &
\includegraphics[width=\linewidth]{overlaid_sinewave2_douglas_2} &
@ -384,7 +397,7 @@ algorithms {\DP} and {\VW}, and now can enumerate the shortcomings:
\item Resulting generalized lines look jaggy and, when zoomed in,
unpleasant to the eye.
\item Blunt bends are generalized to straight lines, even though sometimes
they should remain blunt bends (or even exhagerated bends).
they should remain blunt bends (or even exaggerated bends).
\item Consecutive small bends should be normalized into a larger bend.
\end{itemize}
@ -453,6 +466,13 @@ Transforms a layer ({\tt :src}) to {\VW} using $tolerance^2$ tolerance into
{\tt :tbl} table.
\inputminted[fontsize=\small]{sql}{visvalingam.sql}
\subsection{chaikin.sql}
Smoothens a layer ({\tt :src}) using Chaikin's algorithm using $nIterations =
5$ into {\tt :tbl} table. The parameters are explained in
section~\ref{sec:algs-and-params} on page~\pageref{sec:algs-and-params}.
\inputminted[fontsize=\small]{sql}{chaikin.sql}
\subsection{fig2layer.py}
Creates figures (square, sine wave) as geopackage files.
\inputminted[fontsize=\small]{python}{fig2layer.py}