\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[maxbibnames=99,style=authoryear]{biblatex} \usepackage[pdfusetitle]{hyperref} \usepackage{enumitem} \usepackage[toc,page,title]{appendix} \addbibresource{bib.bib} \usepackage{caption} \usepackage{subcaption} \usepackage{gensymb} \usepackage{varwidth} \usepackage{tabularx} \usepackage{float} \usepackage{tikz} \usetikzlibrary{er,positioning} \input{version} \newcommand{\DP}{Douglas \& Peucker} \newcommand{\VW}{Visvalingam--Whyatt} \newcommand{\WM}{Wang--M{\"u}ller} \title{ Cartografic Generalization of Lines using free software \\ (example of rivers) \\ \vspace{4mm} } \iffalse https://bost.ocks.org/mike/simplify/ http://bl.ocks.org/msbarry/9152218 small scale: 1:XXXXXX large scale: 1:XXX a4: 210x297mm a5: 148x210mm a6: 105x148xmm a7: 74x105mm a8: 52x74mm Crossing: Xmin: 623306 Ymin: 6109635 Xmax: 625526 Ymax: 6111210 623306 6109635 625526 6111210 Crossing wxh: 2220, 1575 (m) connect rivers first to a single polylines: - some algs can preserve connectivity, some not. ideal hypothesis: mueller algorithm + topology may fully realize cartographic generalization tasks. what scales and what distances? = Intro: Aktualumas FOSS nėra realizuotas tinkamas kartografinio realizavimo algoritmas (2–3 sakiniai). Kad kartografai turėtų įrankį upių generalizavimui. Bazė: imame tai, ką dabar turi kartografai įrankių paletėj. Imti mažus upės vingius. Paimti mažas atkarpėles ir palyginti su originalia. Todėl, kad nėra kilpų. Zeimena extents: [606922,6097557,627230,6126362] 20308 x 28805 (w x h) \fi \author{Motiejus Jakštys} \date{ \vspace{10mm} Version: \VCDescribe \\ \vspace{4mm} Generated At: \GeneratedAt } \begin{document} \maketitle \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 generalize cartographic objects, their downscaled counterparts will be incorrectly scale-adjusted. This paper explores the available down-scaling implementations, highlights some of their deficiencies, and suggests a viable algorithm for an avid GIS developer. Once the new algorithm becomes usable from within open-source GIS software (e.g. QGIS or PostGIS), small-scale maps created by free software will have a chance to be of higher quality. \end{abstract} \newpage \tableofcontents \listoffigures \newpage \section{Introduction} \label{sec:introduction} A number of cartographic line generalization algorithms have been researched, which claim to better process cartographic objects like lines. These fall into two rough 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 cartographically suitable down-scaling. E.g. \cite{jiang2003line}, \cite{dyken2009simultaneous}, \cite{mustafa2006dynamic}, \cite{nollenburg2008morphing}. \end{itemize} During research for the mentioned articles, prototype code has been written for most of the algorithms. However, none of them seem to be available for use except for the two "classical" ones -- {\DP} and {\VW}. \cite{wang1998line} is an algorithm specifically created for cartographic generalization and available for general use, though it is only currently available in a commercial product. This poses a problem for map creation in open source 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. This paper will be reviewing and comparing two widely available algorithms that are often used for line generalization: \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} Review of the available algorithms will be followed by desiderata for a possible open-source addition. In the end, we will issue a recommendation, which algorithm can be picked up and implemented by an avid GIS developer. \section{Visual comparison} Lakaja and large part of Žeimena (see figure~\ref{fig:zeimena} on page~\pageref{fig:zeimena}) will be used as inputs to the generalization algorithms, because the river exhibits both both straight and curved shape, is a combination of two curly rivers, and author's familiarity with the location. Since the map area is large (approx. 20km by 28km, scale $1:150 000$), we will also review a subset of the area of approx 2200m by 1575m. The zoomed-in version will help explain some of the deficiencies in the reviewed algorithms. \begin{figure}[h] \centering \includegraphics[width=67.5mm]{zeimena} \caption{Lakaja and Žeimena, $1:300000$} \label{fig:zeimena} \end{figure} \begin{figure}[h] \centering \includegraphics[width=74mm]{crossing} \caption{River crossing zoomed in, $1:30000$} \label{fig:crossing} \end{figure} To visually evaluate the Žeimena sample, examples for {\DP} and {\VW} were created using the following parameters: \begin{enumerate}[label=(\Roman*)] \item {\DP} tolerance: $tolerance := 125 * 2^n, n = 0,1,...,5$. \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. As can be observed in table~\ref{tab:comparison-zeimena} on page~\pageref{tab:comparison-zeimena}, both simplication algorithms convert bends to chopped lines. This is especially visible in tolerances 250 and 500. In a more robust simplification algorithm, the larger tolerance, the larger the bends on the original map should be retained. \begin{figure}[H] \renewcommand{\tabularxcolumn}[1]{>{\center\small}m{#1}} \begin{tabularx}{\textwidth}{ p{2.1cm} | X | X | } Tolerance DP/VW & Douglas \& Peucker & Visvalingam-Whyatt \tabularnewline \hline 125/15625 & \includegraphics[width=\linewidth]{zeimena-douglas-125} & \includegraphics[width=\linewidth]{zeimena-visvalingam-125} \tabularnewline \hline 250/62500 & \includegraphics[width=.5\linewidth]{zeimena-douglas-250} & \includegraphics[width=.5\linewidth]{zeimena-visvalingam-250} \tabularnewline \hline 500/250000 & \includegraphics[width=.25\linewidth]{zeimena-douglas-500} & \includegraphics[width=.25\linewidth]{zeimena-visvalingam-500} \tabularnewline \hline 1000/1000000 & \includegraphics[width=.125\linewidth]{zeimena-douglas-1000} & \includegraphics[width=.125\linewidth]{zeimena-visvalingam-1000} \tabularnewline \hline 2000/4000000 & \includegraphics[width=.0625\linewidth]{zeimena-douglas-2000} & \includegraphics[width=.0625\linewidth]{zeimena-visvalingam-2000} \tabularnewline \hline 4000/16000000 & \includegraphics[width=.0625\linewidth]{zeimena-douglas-4000} & \includegraphics[width=.0625\linewidth]{zeimena-visvalingam-4000} \tabularnewline \hline \end{tabularx} \caption{{\DP} and {\VW} on Žeimena} \label{tab:comparison-zeimena} \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? \subsection{Combining bends} Consecutive small bends should be combined into larger bends, and that is one of the least developed aspects of automatic line generalization, according to \cite{miuller1995generalization}. {\WM} encoded this process to an algorithm. Imagine there are two small bends close to each other, similar to figure~\ref{pic:sinewave} on page~\pageref{pic:sinewave}, 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 \includegraphics[width=52mm]{sinewave} \caption{Example river bend that should be generalized} \label{pic:sinewave} \end{figure} When one applies {\DP} to figure~\ref{pic:sinewave}, either both bends remain, or become a straight line, see table~\ref{tab:comparison-sinewave} on page~\pageref{tab:comparison-sinewave}. \begin{figure}[h] \renewcommand{\tabularxcolumn}[1]{>{\center\small}m{#1}} \begin{tabularx}{\textwidth}{ p{1.5cm} | X | X | } Tolerance DP/VW & Douglas \& Peucker & Visvalingam-Whyatt \tabularnewline \hline 1/1 & \includegraphics[width=\linewidth]{sinewave-douglas-1} & \includegraphics[width=\linewidth]{sinewave-visvalingam-1} \tabularnewline \hline 20/400 & \includegraphics[width=\linewidth]{sinewave-douglas-20} & \includegraphics[width=\linewidth]{sinewave-visvalingam-20} \tabularnewline \hline 30/900 & \includegraphics[width=\linewidth]{sinewave-douglas-30} & \includegraphics[width=\linewidth]{sinewave-visvalingam-30} \tabularnewline \hline 40/1600 & \includegraphics[width=\linewidth]{sinewave-douglas-40} & \includegraphics[width=\linewidth]{sinewave-visvalingam-40} \tabularnewline \hline \end{tabularx} \caption{{\DP} and {\VW} on example wave} \label{tab:comparison-sinewave} \end{figure} \section{Related Work and future suggestions} \label{sec:related_work} \cite{stanislawski2012automated} studied different types of metric assessments, such as Hausdorff distance, segment length, vector shift, surface displacement, 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 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} \label{sec:conclusions} We have practically evaluated two readily available line simplification algorithms with a river sample: {\VW} and {\DP}, and outlined their deficiencies. We are suggesting to implement {\WM} and compare it to the other two. \printbibliography \begin{appendices} \begin{figure}[H] \centering \includegraphics[width=148mm]{zeimena-pretty} \caption{Lakaja and Žeimena river in context} \end{figure} \end{appendices} \end{document}