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\section{Examples}
\label{sec:kds_examples}
We provide a number of examples of different levels of usage of the
kinetic data structures framework, both for kinetic data structures as
well as sweepline algorithms.
The first example (in Section~\ref{sec:kds_sort_example}) showed
how to used a data structure which maintains a sorted list of points
to compute the arrangement of a set of x-monotone curves in the
plane. Using the other kinetic data structures is substantially
identical. Please see the appropriate files in the
demo/Kinetic\_data\_structures directory.
The next examples cover implementing kinetic data structures. They are
\begin{itemize}
\item Adding a new type of certificate to a kernel in
Section~\ref{sec:kds_add_cert}.
\item A trivial kinetic data structure which has all the parts of a
full kinetic data structure but doesn't do much in
Section~\ref{sec:kds_trivial_example}.
\end{itemize}
In order to see more detail about how to implement a kinetic data
structure, the best place to start is the source code for the kinetic
sorting data structure, \ccc{Kinetic::Sort<Traits, Visitor>}.
\input{Kinetic_framework/adding_certificate.tex}
\input{Kinetic_framework/trivial_kds_example.tex}