mirror of https://github.com/CGAL/cgal
196 lines
6.3 KiB
TeX
196 lines
6.3 KiB
TeX
%% =============================================================================
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%% The CGAL Reference Manual
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%% Chapter: Geometric Optimisation
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%% -----------------------------------------------------------------------------
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%% file : doc_tex/basic/Optimisation/Optimisation_ref/intro.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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%% $Id$
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%% $Date$
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%% =============================================================================
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\newcommand{\inputOpt}[1]{\input{Optimisation_ref/#1.tex}}
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\newcommand{\linebreakByHand}{\ccTexHtml{\linebreak[4]}{}}
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\newcommand{ \newlineByHand}{\ccTexHtml{\\}{}}
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%% cross references
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\ccIndexSubitemSeeAlso{minimum enclosing}{smallest enclosing}
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\ccIndexSubitemSeeAlso{minimum spanning}{smallest enclosing}
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\ccIndexSubitemSeeAlso{concentric spheres}{annulus}
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%% -----------------------------------------------------------------------------
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\ccRefChapter{Geometric Optimization}
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\ccChapterAuthor{Kaspar Fischer \and Bernd G{\"a}rtner \and Thomas Herrmann \and Michael Hoffmann
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\and Sven Sch{\"o}nherr}
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This chapter describes concepts, classes, and functions for solving
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geometric optimization problems. They are divided into four categories.
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\paragraph{Bounding Areas and Volumes.}
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Smallest enclosing circle and ellipse (2D), smallest enclosing rectangle,
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parallelogram, and strip (2D), rectangular $p$-center (2D), smallest
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enclosing sphere and annulus (dD), approximate
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minimum-volume enclosing ellipsoid with user-specified
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approximation ratio (dD).
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\paragraph{Inscribed Areas.}
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Maximum area and perimeter inscribed $k$-gon (2D), extremal inscribed
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$k$-gon (2D), largest empty isorectangle (2D).
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\paragraph{Optimal Distances.}
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All furthest neigbors (2D), width of point set (3D), polytope distance (dD).
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\paragraph{Advanced Techniques.}
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Monotone and sorted matrix search.
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\section*{Assertions}
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The optimization 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.~Section~\ref{sec:checks}.
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\section{Classified References Pages}
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%% -----------------------------------------------------------------------------
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\subsection*{Bounding Areas and Volumes}
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\ccRefIdfierPage{CGAL::Min_circle_2<Traits>}\\[1ex]
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\ccRefIdfierPage{CGAL::Min_circle_2_traits_2<K>}\\[1ex]
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\ccRefConceptPage{MinCircle2Traits}
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\smallskip
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\ccRefIdfierPage{CGAL::Min_ellipse_2<Traits>}\\[1ex]
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\ccRefIdfierPage{CGAL::Min_ellipse_2_traits_2<K>}\\[1ex]
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\ccRefConceptPage{MinEllipse2Traits}
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\smallskip
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\ccRefIdfierPage{CGAL::Approximate_min_ellipsoid_d<Traits>}\\
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\ccRefConceptPage{ApproximateMinEllipsoid_d_Traits_d}
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\smallskip
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\ccRefIdfierPage{CGAL::min_rectangle_2}\\
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\ccRefIdfierPage{CGAL::min_parallelogram_2}\\
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\ccRefIdfierPage{CGAL::min_strip_2}\\[1ex]
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\ccRefIdfierPage{CGAL::Min_quadrilateral_default_traits_2<R>}\\[1ex]
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\ccRefConceptPage{MinQuadrilateralTraits_2}
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\smallskip
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\ccRefIdfierPage{CGAL::rectangular_p_center_2}\\[1ex]
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\ccRefIdfierPage{CGAL::Rectangular_p_center_default_traits_2<R>}\\[1ex]
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\ccRefConceptPage{RectangularPCenterTraits_2}
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\smallskip
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\ccRefIdfierPage{CGAL::Min_sphere_d<Traits>}\\
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\ccRefIdfierPage{CGAL::Min_annulus_d<Traits>}\\[1ex]
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\ccRefIdfierPage{CGAL::Optimisation_d_traits_2<K,ET,NT>}\\
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\ccRefIdfierPage{CGAL::Optimisation_d_traits_3<K,ET,NT>}\\
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\ccRefIdfierPage{CGAL::Optimisation_d_traits_d<K,ET,NT>}\\[1ex]
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\ccRefConceptPage{OptimisationDTraits}
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\smallskip
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\ccRefIdfierPage{CGAL::Min_sphere_of_spheres_d<Traits>}\\
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\ccRefConceptPage{MinSphereOfSpheresTraits}
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%% -----------------------------------------------------------------------------
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\subsection*{Inscribed Areas}
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\ccRefIdfierPage{CGAL::maximum_area_inscribed_k_gon_2}\\
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\ccRefIdfierPage{CGAL::maximum_perimeter_inscribed_k_gon_2}\\
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\ccRefIdfierPage{CGAL::extremal_polygon_2}\\
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\ccRefIdfierPage{CGAL::Largest_empty_iso_rectangle_2<T>}\\[1ex]
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\ccRefIdfierPage{CGAL::Extremal_polygon_area_traits_2<K>}\\
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\ccRefIdfierPage{CGAL::Extremal_polygon_perimeter_traits_2<K>}\\[1ex]
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\ccRefConceptPage{ExtremalPolygonTraits_2}\\
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\ccRefConceptPage{LargestEmptyIsoRectangleTraits_2}
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%% -----------------------------------------------------------------------------
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\subsection*{Optimal Distances}
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%%\ccRefIdfierPage{CGAL::width_2}%\\[1ex]
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%%\ccRefIdfierPage{CGAL::Min_quadrilateral_default_traits_2<K>}\\[1ex]
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%%\ccRefConceptPage{MinQuadrilateralTraits_2}
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%%\smallskip
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\ccRefIdfierPage{CGAL::all_furthest_neighbors_2}\\[1ex]
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%%\ccRefIdfierPage{CGAL::All_furthest_neighbors_default_traits_2<R>}\\[1ex]
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\ccRefConceptPage{AllFurthestNeighborsTraits_2}
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\smallskip
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\ccRefIdfierPage{CGAL::Width_3<Traits>}\\[1ex]
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\ccRefIdfierPage{CGAL::Width_default_traits_3<K>}\\[1ex]
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\ccRefConceptPage{WidthTraits_3}
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\smallskip
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\ccRefIdfierPage{CGAL::Polytope_distance_d<Traits>}\\[1ex]
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\ccRefIdfierPage{CGAL::Optimisation_d_traits_2<K,ET,NT>}\\
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\ccRefIdfierPage{CGAL::Optimisation_d_traits_3<K,ET,NT>}\\
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\ccRefIdfierPage{CGAL::Optimisation_d_traits_d<K,ET,NT>}\\[1ex]
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\ccRefConceptPage{OptimisationDTraits}
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%% -----------------------------------------------------------------------------
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\subsection*{Advanced Techniques}
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\ccRefIdfierPage{CGAL::monotone_matrix_search}\\[1ex]
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\ccRefIdfierPage{CGAL::Dynamic_matrix<M>}\\[1ex]
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\ccRefConceptPage{MonotoneMatrixSearchTraits}\\
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\ccRefConceptPage{BasicMatrix}
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\smallskip
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\ccRefIdfierPage{CGAL::sorted_matrix_search}\\[1ex]
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\ccRefIdfierPage{CGAL::Sorted_matrix_search_traits_adaptor<F,M>}\\[1ex]
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\ccRefConceptPage{SortedMatrixSearchTraits}
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\smallskip
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%% =============================================================================
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%% Bounding Areas and Volumes
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\inputOpt{main_Min_circle_2}
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\inputOpt{main_Min_ellipse_2}
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\inputOpt{main_Min_quadrilateral_2}
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\inputOpt{main_Rectangular_p_centers}
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\inputOpt{main_Min_sphere_d}
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\inputOpt{main_Min_annulus_d}
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\inputOpt{main_Min_sphere_of_spheres_d}
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\inputOpt{main_Approximate_min_ellipsoid_d}
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\inputOpt{main_Optimisation_d_traits}
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%% Inscribed Areas
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\inputOpt{main_Extremal_polygons}
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\inputOpt{main_Largest_empty_iso_rectangle_2}
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%% Optimal Distances
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\inputOpt{main_All_furthest_neighbors}
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\inputOpt{main_Width_3}
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\inputOpt{main_Polytope_distance_d}
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%% Advanced Techniques
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\inputOpt{main_Matrix_search}
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%% ===== EOF ===================================================================
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