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fixed: introduction

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Sven Schönherr 1998-03-30 13:38:21 +00:00
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33
Packages/Optimisation_doc/doc_tex/Optimisation/main.tex
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@ -28,32 +28,27 @@
This chapter describes routines for solving geometric optimisation problems. This chapter describes routines for solving geometric optimisation problems.
The first two sections contain algorithms for computing and updating the The first two sections contain algorithms for computing and updating the
smallest enclosing circle (Section~\ref{sec:smallest_enclosing_circles})
resp.\ ellipse (Section~\ref{sec:smallest_enclosing_ellipses}) of a finite
point set. Formally, the `smallest enclosing circle' is the boundary of the
closed disk of minimum area covering the point set. It is known that this
disk is unique. We usually identify the disk with its bounding circle,
allowing us to talk about points being on the boundary of the circle, etc.
The same holds for the smallest enclosing ellipse. These algorithms work in
an incremental manner. They are implemented as semi-dynamic data structures,
thus allowing to insert points while maintaining the smallest enclosing
circle resp.\ ellipse.
The remaining sections describe algorithms for searching in matrices with
specific properties and some applications. In particular, there are
general implementations of
\begin{itemize} \begin{itemize}
\item monotone matrix search (see Section~\ref{secMonotoneMatrixSearch}), \item smallest enclosing circle
(Section~\ref{sec:smallest_enclosing_circles}) and the
\item smallest enclosing ellipse
(Section~\ref{sec:smallest_enclosing_ellipses}), respectively,
\end{itemize}
of a finite point set. The remaining sections describe algorithms for
searching in matrices with specific properties and some applications.
In particular, there are general implementations of
\begin{itemize}
\item monotone matrix search (Section~\ref{secMonotoneMatrixSearch}),
which can be applied to compute which can be applied to compute
\begin{itemize} \begin{itemize}
\item extremal polygons of a convex polygon \item extremal polygons of a convex polygon
(see Section~\ref{secComputingExtremalPolygons}) \textit{or} (Section~\ref{secComputingExtremalPolygons}) \textit{or}
\item all furthest neighbors for the vertices of a convex polygon \item all furthest neighbors for the vertices of a convex polygon
(see Section~\ref{secAllFurthestNeighbors}), (Section~\ref{secAllFurthestNeighbors}),
\end{itemize} \end{itemize}
\item and sorted matrix search (see Section~\ref{secSortedMatrixSearch}), \item and sorted matrix search (Section~\ref{secSortedMatrixSearch}),
which can be used to compute the $p$-centers of a planar point set which can be used to compute the $p$-centers of a planar point set
(see Section~\ref{sec_RectangularPCenters}). (Section~\ref{sec_RectangularPCenters}).
\end{itemize} \end{itemize}
\subsubsection*{Traits Class} \subsubsection*{Traits Class}

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Packages/Optimisation_doc/doc_tex/basic/Optimisation/main.tex
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@ -28,32 +28,27 @@
This chapter describes routines for solving geometric optimisation problems. This chapter describes routines for solving geometric optimisation problems.
The first two sections contain algorithms for computing and updating the The first two sections contain algorithms for computing and updating the
smallest enclosing circle (Section~\ref{sec:smallest_enclosing_circles})
resp.\ ellipse (Section~\ref{sec:smallest_enclosing_ellipses}) of a finite
point set. Formally, the `smallest enclosing circle' is the boundary of the
closed disk of minimum area covering the point set. It is known that this
disk is unique. We usually identify the disk with its bounding circle,
allowing us to talk about points being on the boundary of the circle, etc.
The same holds for the smallest enclosing ellipse. These algorithms work in
an incremental manner. They are implemented as semi-dynamic data structures,
thus allowing to insert points while maintaining the smallest enclosing
circle resp.\ ellipse.
The remaining sections describe algorithms for searching in matrices with
specific properties and some applications. In particular, there are
general implementations of
\begin{itemize} \begin{itemize}
\item monotone matrix search (see Section~\ref{secMonotoneMatrixSearch}), \item smallest enclosing circle
(Section~\ref{sec:smallest_enclosing_circles}) and the
\item smallest enclosing ellipse
(Section~\ref{sec:smallest_enclosing_ellipses}), respectively,
\end{itemize}
of a finite point set. The remaining sections describe algorithms for
searching in matrices with specific properties and some applications.
In particular, there are general implementations of
\begin{itemize}
\item monotone matrix search (Section~\ref{secMonotoneMatrixSearch}),
which can be applied to compute which can be applied to compute
\begin{itemize} \begin{itemize}
\item extremal polygons of a convex polygon \item extremal polygons of a convex polygon
(see Section~\ref{secComputingExtremalPolygons}) \textit{or} (Section~\ref{secComputingExtremalPolygons}) \textit{or}
\item all furthest neighbors for the vertices of a convex polygon \item all furthest neighbors for the vertices of a convex polygon
(see Section~\ref{secAllFurthestNeighbors}), (Section~\ref{secAllFurthestNeighbors}),
\end{itemize} \end{itemize}
\item and sorted matrix search (see Section~\ref{secSortedMatrixSearch}), \item and sorted matrix search (Section~\ref{secSortedMatrixSearch}),
which can be used to compute the $p$-centers of a planar point set which can be used to compute the $p$-centers of a planar point set
(see Section~\ref{sec_RectangularPCenters}). (Section~\ref{sec_RectangularPCenters}).
\end{itemize} \end{itemize}
\subsubsection*{Traits Class} \subsubsection*{Traits Class}