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% | Reference manual page: Euclidean_distance.tex
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% | 1.07.2001   Johan W.H. Tangelder
% | Package: ASPAS
% | 
\RCSdef{\RCSEuclideandistanceRev}{$Revision$}
\RCSdefDate{\RCSEuclideandistanceDate}{$Date$}
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\begin{ccRefClass}{Euclidean_distance<Traits>}  %% add template arg's if necessary

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\ccDefinition
  
The class \ccRefName\ provides an implementation of the concept \ccc{OrthogonalDistance}, with the
Euclidean distance ($l_2$ metric).
To optimize distance computations squared distances are used.


\ccInclude{CGAL/Euclidean_distance.h}

\ccParameters

Expects for the first template argument a model of the concept
\ccc{SearchTraits}, for example \ccc{CGAL::Search_traits_2<CGAL::Cartesian<double> >}.



\ccIsModel

OrthogonalDistance

\ccTypes

\ccTypedef{Traits::FT FT;}{Number type.}
\ccTypedef{Traits::Point_d Point_d;}{Point type.}
\ccTypedef{Point_d Query_item;}{Query item type.}

\ccCreation
\ccCreationVariable{ed}  %% choose variable name

\ccConstructor{Euclidean_distance();}{Default constructor.}

\ccOperations
 
\ccMethod{FT transformed_distance(Query_item q, Point_d p);}{Returns the squared Euclidean distance between~\ccc{q} and~\ccc{p}.}

\ccMethod{FT min_distance_to_rectangle(Query_item q, Kd_tree_rectangle<FT> r);}
{Returns the squared Euclidean distance between \ccc{q} and
the point on the boundary of \ccc{r} closest to \ccc{q}.}

\ccMethod{FT max_distance_to_rectangle(Query_item q, Kd_tree_rectangle<FT> r;);}
{Returns the squared Euclidean distance, where $d$ denotes the distance between \ccc{q} and
the point on the boundary of \ccc{r} farthest to \ccc{q}.}

\ccMethod{FT new_distance(FT dist, FT old_off, FT new_off, int cutting_dimension);} {Updates the squared \ccc{dist} incrementally
and returns the updated squared distance.}

\ccMethod{FT transformed_distance(FT d);} {Returns $d^2$.}

\ccMethod{FT inverse_of_transformed_distance(FT d);} {Returns $d^{1/2}$.}

\ccSeeAlso

\ccc{OrthogonalDistance}\\
\ccc{CGAL::Weighted_Minkowski_distance<Traits>}.

\end{ccRefClass}

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