\subsection{Polyline simplification}

\subsubsection{Heuristics}

\paragraph{Positional errors}

\paragraph{Length errors}

\paragraph{Area Errors}

\subsubsection{Algorithms}
Compression algorithms. 

\paragraph{n-th point algorithm}

\begin{figure}
	\centering
	\includegraphics[width=.7\linewidth]{./images/shi-np.png}
	\caption{Nth point algorithm}
	\label{fig:algo-np}
\end{figure}

\paragraph{Random-point routine}

\paragraph{Radial distance algorithm}

\begin{figure}
	\centering
	\includegraphics[width=.7\linewidth]{../lib/psimpl_v7_src/doc/psimpl_rd.png}
	\caption{Radial distance algorithm}
	\label{fig:algo-rd}
\end{figure}


\paragraph{Perpendicular distance algorithm}

\begin{figure}
	\centering
	\includegraphics[width=.7\linewidth]{../lib/psimpl_v7_src/doc/psimpl_pd.png}
	\caption{Perpendicular distance algorithm}
	\label{fig:algo-pd}
\end{figure}


\paragraph{Reumann-Witkam simplification}

\begin{figure}
	\centering
	\includegraphics[width=.7\linewidth]{../lib/psimpl_v7_src/doc/psimpl_rw.png}
	\caption{Reuman-Witkam algorithm}
	\label{fig:algo-rw}
\end{figure}


\paragraph{Opheim simplification}

\begin{figure}
	\centering
	\includegraphics[width=.7\linewidth]{../lib/psimpl_v7_src/doc/psimpl_op.png}
	\caption{Opheim algorithm}
	\label{fig:algo-op}
\end{figure}


\paragraph{Lang simplification}

\begin{figure}
	\centering
	\includegraphics[width=.7\linewidth]{../lib/psimpl_v7_src/doc/psimpl_la.png}
	\caption{Lang algorithm}
	\label{fig:algo-la}
\end{figure}


\paragraph{Douglas-Peucker simplification}

\begin{figure}
	\centering
	\includegraphics[width=.7\linewidth]{../lib/psimpl_v7_src/doc/psimpl_dp.png}
	\caption{Douglas Peucker algorithm}
	\label{fig:algo-dp}
\end{figure}


\paragraph{with reduction parameter}

\paragraph{Jenks simplification}

\paragraph{Visvalingam-Whyatt simplification}

\paragraph{Zhao-Saalfeld simplification}

\subsubsection{Summary}