\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.

To see how to use existing kinetic data structures, look at the
examples in the previous chapter such as
Section~\ref{sec:kds_sort_example}. 

The here we cover implementing kinetic data structures. The examples
explained are
\begin{itemize}
\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}.
\item Adding a new type of certificate to a kernel in
  Section~\ref{sec:kds_add_cert}.
\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>}. Once you
are familiar with that, \ccc{Kinetic::Delaunay_2<Traits,
Triangulation, Visitor>} is the next step in complexity.


\input{Kinetic_framework/trivial_kds_example.tex}
\input{Kinetic_framework/adding_certificate.tex}