mirror of https://github.com/CGAL/cgal
65 lines
2.5 KiB
TeX
65 lines
2.5 KiB
TeX
% =============================================================================
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% The CGAL User Manual
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% Chapter: Geometric Optimisation
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% -----------------------------------------------------------------------------
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% file : doc_tex/basic/Optimisation/user_part.tex
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% package: Optimisation_doc
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% author : Sven Schönherr <sven@inf.ethz.ch>
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% -----------------------------------------------------------------------------
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% $Revision$
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% $Date$
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% =============================================================================
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%\section{Introduction}
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This chapter describes routines for solving geometric optimisation
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problems.
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There are algorithms for computing and updating the
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\begin{itemize}
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\item smallest enclosing circle (\ccc{Min_circle_2<Traits>}), the
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\item smallest enclosing ellipse (\ccc{Min_ellipse_2<Traits>}), the
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\item smallest enclosing sphere (\ccc{Min_sphere_d<Traits>}), and the
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\item smallest enclosing annulus (\ccc{Min_annulus_d<Traits>}),
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respectively,
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\end{itemize}
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of a finite point set.
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We provide several functions to compute the smallest enclosing region
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$r$ of a planar convex polygon $P$ where $r$ is to be chosen from a
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set $\mathcal{R}$ of candidate regions (\ccc{min_rectangle_2},
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\ccc{min_parallelogram_2}, \ccc{min_strip_2}).
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An algorithm for computing and updating the (squared) distance of two
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convex polytopes is described (\ccc{Polytope_distance_d}).
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The remaining algorithms can be used for searching in matrices with
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specific properties and some applications. In particular, there are
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general implementations of
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\begin{itemize}
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\item monotone matrix search (\ccc{monotone_matrix_search}),
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which can be applied to compute
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\begin{itemize}
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\item extremal polygons of a convex polygon
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(\ccc{maximum_area_inscribed_k_gon_2},
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\ccc{maximum_perimeter_inscribed_k_gon_2},
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\ccc{extremal_polygon_2}) or
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\item all furthest neighbors for the vertices of a convex polygon
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(\ccc{all_furthest_neighbors_2}), and
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\end{itemize}
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\item sorted matrix search (\ccc{sorted_matrix_search}),
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which can be used to compute the $p$-centers of a planar point set
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(\ccc{rectangular_p_center_2}).
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\end{itemize}
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%\subsubsection*{Assertions}
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%The optimisation code uses infix \ccc{OPTIMISATION} in the assertions,
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%e.g.\ defining the compiler flag
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%\ccc{CGAL_OPTIMISATION_NO_PRECONDITIONS} switches precondition
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%checking off, cf.~\cgalReferToAssertions
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% ===== EOF ===================================================================
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