mirror of https://github.com/CGAL/cgal
84 lines
2.5 KiB
TeX
Executable File
84 lines
2.5 KiB
TeX
Executable File
% +------------------------------------------------------------------------+
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% | Reference manual page: OrthogonalDistance.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{\RCSOrthogonalDistanceRev}{$Revision$}
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\RCSdefDate{\RCSOrthogonalDistanceDate}{$Date$}
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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{ccRefConcept}{OrthogonalDistance}
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%% \ccHtmlCrossLink{} %% add further rules for cross referencing links
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%% \ccHtmlIndexC[concept]{} %% add further index entries
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\ccDefinition
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Requirements of an orthogonal distance class supporting incremental distance updates.
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To optimize distance computations transformed distances are used.
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E.g., for an Euclidean distance the transformed distance is the squared Euclidean distance.
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\ccRefines
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GeneralDistance
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\ccParameters
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$d$-dimensional query items as well as $d$-dimensional points should be represented
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by a type $Point$.
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\ccTypes
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\ccTypedef{Kernel_traits<Point>::Kernel::FT NT;}{Number type.}
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\ccCreation
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\ccCreationVariable{d} %% choose variable name
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\ccConstructor{OrthogonalDistance(int d);}{Constructor implementing distance for $d$-dimensional points.}
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\ccOperations
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\ccMethod{NT distance(Point q, Point r);}{Returns the transformed distance between \ccc{q} and \ccc{r}.}
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\ccMethod{NT min_distance_to_rectangle(Point q, Kd_tree_rectangle<NT> r;);}
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{Returns the transformed 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{NT max_distance_to_rectangle(Point q, Kd_tree_rectangle<NT> r;);}
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{Returns the transformed 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{NT transformed_distance(NT d);} {Returns the transformed distance.}
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\ccMethod{NT inverse_of_transformed_distance(NT d);} {Returns the inverse of the transformed distance.}
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\ccMethod{NT new_distance(NT dist, NT old_off, NT new_off, int cutting_dimension);} {Updates
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\ccc{dist} incrementally and returns the updated distance.}
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\ccHasModels
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\ccc{CGAL::Euclidean_distance<Point>},
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\ccc{CGAL::Weighted_Minkowski_distance<Point>}.
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\ccSeeAlso
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GeneralDistance,
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\ccc{CGAL::Euclidean_distance<Point>},
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\ccc{CGAL::Weighted_Minkowski_distance<Point>}.
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\end{ccRefConcept}
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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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