mirror of https://github.com/CGAL/cgal
81 lines
2.6 KiB
TeX
81 lines
2.6 KiB
TeX
% +------------------------------------------------------------------------+
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% | Reference manual page: Euclidean_distance.tex
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% +------------------------------------------------------------------------+
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% | 1.07.2001 Johan W.H. Tangelder
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% | Package: ASPAS
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% |
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\RCSdef{\RCSEuclideandistanceRev}{$Id$}
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\RCSdefDate{\RCSEuclideandistanceDate}{$Date$}
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% |
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%%RefPage: end of header, begin of main body
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% +------------------------------------------------------------------------+
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\begin{ccRefClass}{Euclidean_distance<Traits>} %% add template arg's if necessary
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%% \ccHtmlCrossLink{} %% add further rules for cross referencing links
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%% \ccHtmlIndexC[class]{} %% add further index entries
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\ccDefinition
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The class \ccRefName\ provides an implementation of the concept \ccc{OrthogonalDistance}, with the
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Euclidean distance ($l_2$ metric).
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To optimize distance computations squared distances are used.
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\ccInclude{CGAL/Euclidean_distance.h}
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\ccParameters
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Expects for the first template argument a model of the concept
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\ccc{SearchTraits}, for example \ccc{CGAL::Search_traits_2<CGAL::Cartesian<double> >}.
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\ccIsModel
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\ccc{OrthogonalDistance}
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\ccTypes
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\ccTypedef{Traits::FT FT;}{Number type.}
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\ccTypedef{Traits::Point_d Point_d;}{Point type.}
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\ccTypedef{Point_d Query_item;}{Query item type.}
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\ccCreation
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\ccCreationVariable{ed} %% choose variable name
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\ccConstructor{Euclidean_distance(Traits t=Traits());}{Default constructor.}
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\ccOperations
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\ccMethod{FT transformed_distance(Query_item q, Point_d p) const;}{Returns the squared Euclidean distance between~\ccc{q} and~\ccc{p}.}
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\ccMethod{FT min_distance_to_rectangle(Query_item q, Kd_tree_rectangle<FT> r) const;}
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{Returns the squared Euclidean distance between \ccc{q} and
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the point on the boundary of \ccc{r} closest to \ccc{q}.}
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\ccMethod{FT max_distance_to_rectangle(Query_item q, Kd_tree_rectangle<FT> r;) const;}
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{Returns the squared Euclidean distance, where $d$ denotes the distance between \ccc{q} and
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the point on the boundary of \ccc{r} farthest to \ccc{q}.}
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\ccMethod{FT new_distance(FT dist, FT old_off, FT new_off, int cutting_dimension) const;} {Updates the squared \ccc{dist} incrementally
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and returns the updated squared distance.}
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\ccMethod{FT transformed_distance(FT d) const;} {Returns $d^2$.}
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\ccMethod{FT inverse_of_transformed_distance(FT d) const;} {Returns $d^{1/2}$.}
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\ccSeeAlso
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\ccc{OrthogonalDistance}\\
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\ccc{CGAL::Weighted_Minkowski_distance<Traits>}.
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\end{ccRefClass}
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% +------------------------------------------------------------------------+
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%%RefPage: end of main body, begin of footer
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% EOF
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% +------------------------------------------------------------------------+
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