\section{Introduction}
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% Fragestellung & Zielsetzung - aim & research objectives
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% Vorgehensweise
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% Why important, who participants, trends, 


Simplification of polygonal data structures is the task of reducing data points while preserving topological characteristics. The simplification often takes the form of removing points that make up the geometry. There are several solutions that tackle the problem in different ways. This thesis aims to compare and classify these solutions by various heuristics. Performance and compression rate are quantitative heuristic used. Positional, length and area errors will also be measured to quantify simplification errors. With the rising trend of moving desktop applications to the web platform also geographic information systems (GIS) have experienced the shift towards web browsers \footnote{\path{https://www.esri.com/about/newsroom/arcnews/implementing-web-gis/}}. Performance is critical in these applications. Since simplification is an important factor to performance the solutions will be tested by constructing a web application using a technology called WebAssembly. 


\subsection{Binary instruction sets on the web platform}

The recent development of WebAssembly allows code written in various programming languages to be run natively in web browsers. So far JavaScript   was the only native programming language on the web. The goals of WebAssembly are to define a binary instruction format as a compilation target to execute code at native speed and taking advantage of common hardware capabilities \footnote{\path{https://webassembly.org/}}. The integration into the web platform brings portability to a wide range of platforms like mobile and internet of things (IoT). The usage of this technology promises performance gains that will be tested by this thesis. The results can give conclusions to whether WebAssembly is worth a consideration for web applications with geographic computational aspects. Web GIS is an example technology that would benefit greatly of such an advancement. Thus far WebAssembly has been shipped to the stable version of the four most used browser engines \footnote{\path{https://lists.w3.org/Archives/Public/public-webassembly/2017Feb/0002.html}]}. The mainly targeted high-level languages for compilation are C and C++. Also a compiler for Rust and a TypeScript subset has been developed. It will be explored how existing implementations could easily be adopted when using a compiler.

\subsection{Performance as important factor for web applications}

There has been a rapid growth of complex applications running in web-browsers. These so called progressive web apps (PWA) combine the fast reachability of web pages with the feature richness of locally installed applications. Even though these applications can grow quire complex, the requirement for fast page loads and instant user interaction still remains. One way to cope this need is the use of compression algorithms to reduce the amount of data transmitted and processed. In a way simplification is a form of data compression. Web servers use lossless compression algorithms like gzip to deflate data before transmission. Browsers that implement these algorithms can then fully restore the requested ressources resulting in lower bandwidth usage. The algorithms presented here however remove information from the data in a way that cannot be restored. This is called lossy compression. The most common usage on the web is the compression of image data. 

\subsection{Topology simplification for rendering performance}

While compression is often used to minimize bandwidth usage the compression of geospatial data can particulary influence rendering performance. The bottleneck for rendering often is the svg transformation used to display topology on the web. Implementing simplification algorithms for use on the web platform can lead to smoother user experience when working with large geodata sets. 

\subsection{Related work}
\todo[inline]{Related Work}

\subsection{Structure of this thesis}

This thesis is structured into a theoretical and a practical component. First the theoretical principles will be reviewed. Topology of polygonal data will be explained as how to describe geodata on the web. A number of algorithms will be introduced in this section. Each algorithm will be dissected by complexity, characteristics and the possible influence to the heuristics mentioned above. An introduction to WebAssembly will be given here.

In the next chapter the practical implementation will be presented. This section is divided in two parts since two web applications are produced in this thesis. The first one is a benchmark comparison of an algorithm implemented in JavaScript and in WebAssembly. It will be used investigate if performance of established implementations can be improved by a new technology. The second part is about several algorithms brought to the web by compiling an existing C++ library. This application can be used for qualitative analysis of the algorithms. It will show live results to see the characteristics and influence of single parameters. 

The results of the above methods will be shown in chapter 4. After discussion of the results a concluion will finish the thesis.

