cgal/Kinetic_data_structures/doc_tex/Kinetic_data_structures/main.tex

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\ccUserChapter{Kinetic Data Structures\label{chapter-kds}}
\ccChapterAuthor{Daniel Russel}
%\chapter{Kinetic Data Structures}
\input{Kinetic_data_structures/PkgDescription}
\begingroup
\minitoc
\ccDefGlobalScope{CGAL::}
\def\note#1{$\langle\langle${\bf #1}$\rangle\rangle$}
%\message{Remove note before final version!}
%\def{\th}{^{\rm th}}
% space tweaks
%\addtolength{\parskip}{-1pt}
%\input{Kinetic_data_structures/todo.tex}
Lets say you want to maintain a sorted list of items (each item is
associate with a real number key). You can imagine placing each of the
items on the point on the real line corresponding to its key. Now, let
the key for each item change continuously (i.e. no jumps are allowed).
As long as no two (consecutive) items cross, the sorted order is
intact. When two items cross, they need to be exchanged in the list and then
the sorted order is once again correct. This is a trivial example of a
kinetic data structure. The key observation is that the combinatorial
structure which is maintained changes at discrete times (events) even
though the basic building blocks are changing continuously.
This chapter describes a number of such kinetic data structures
implemented using the Kinetic framework described in
Chapter~\ref{chapter-kinetic}. We first, in
Section~\ref{sec:kds_intro} introduce kinetic data structures and
sweepline algorithms. This section can be skipped if the reader is
already familiar with the area. The next sections,
Section~\ref{sec:kds_terms} and Section~\ref{sec:kds_overview} introduce
the terms and give an overview of the framework. They are recommended
reading for all readers, even if you are just using provided kinetic
data structures. We then present kinetic data structures for Delaunay
triangulations in two and three dimensions in
Section~\ref{sec:kds_provided_kdss}.
If you are already familiar with kinetic data structures and know what
you want to do, you might want to first take a look at the next section
Section~\ref{sec:quick_hints} which covers quick hints.
\input{Kinetic_data_structures/quick_hints.tex}
\input{Kinetic_data_structures/kds_intro.tex}
\input{Kinetic_data_structures/overview.tex}
\input{Kinetic_data_structures/provided_kdss.tex}
% LocalWords: Guibas Menelaos CGAL templated Expr KDSs deschedule
% LocalWords: Karavelas
\endgroup