\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - Bounding Volumes

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CGAL::Rectangular_p_center_default_traits_2< K > Class Template Reference
Bounding Volumes Reference

`#include <CGAL/rectangular_p_center_2.h>`

## Definition

The class `Rectangular_p_center_default_traits_2` defines types and operations needed to compute rectilinear \( p\)-centers of a planar point set using the function `rectangular_p_center_2()`.

Template Parameters

  K | must be a model for `Kernel`.

Is Model Of:
  `RectangularPCenterTraits_2`

See Also
  `CGAL::rectangular_p_center_2()`

## Types
typedef unspecified_type | FT
| typedef to `K::FT`.
typedef unspecified_type | Point_2
| typedef to `K::Point_2`.
typedef unspecified_type | Iso_rectangle_2
| typedef to `K::Iso_rectangle_2`.
typedef unspecified_type | Less_x_2
| typedef to `K::Less_x_2`.
typedef unspecified_type | Less_y_2
| typedef to `K::Less_y_2`.
typedef unspecified_type | Construct_vertex_2
| typedef to `K::Construct_vertex_2`.
typedef unspecified_type | Construct_iso_rectangle_2
| typedef to `K::Construct_iso_rectangle_2`.
typedef unspecified_type | Signed_x_distance_2
| adaptable binary function class: `Point_2` \( \times\) `Point_2` \( \rightarrow\) `FT` returns the signed distance of two points' \( x\)-coordinates.
typedef unspecified_type | Signed_y_distance_2
| adaptable binary function class: `Point_2` \( \times\) `Point_2` \( \rightarrow\) `FT` returns the signed distance of two points' \( y\)-coordinates.
typedef unspecified_type | Infinity_distance_2
| adaptable binary function class: `Point_2` \( \times\) `Point_2` \( \rightarrow\) `FT` returns the \( ||\cdot||_{\infty}\) distance of two points.
typedef unspecified_type | Signed_infinity_distance_2
| adaptable binary function class: `Point_2` \( \times\) `Point_2` \( \rightarrow\) `FT` returns the signed \( ||\cdot||_{\infty}\) distance of two points.
typedef unspecified_type | Construct_point_2_below_left_implicit_point_2
| 3-argument function class: `Point_2` \( \times\) `Point_2` \( \times\) `FT` \( \rightarrow\) `Point_2`. More...
typedef unspecified_type | Construct_point_2_below_right_implicit_point_2
| 3-argument function class: `Point_2` \( \times\) `Point_2` \( \times\) `FT` \( \rightarrow\) `Point_2`. More...
typedef unspecified_type | Construct_point_2_above_right_implicit_point_2
| 3-argument function class: `Point_2` \( \times\) `Point_2` \( \times\) `FT` \( \rightarrow\) `Point_2`. More...
typedef unspecified_type | Construct_point_2_above_left_implicit_point_2
| 3-argument function class: `Point_2` \( \times\) `Point_2` \( \times\) `FT` \( \rightarrow\) `Point_2`. More...

## Operations
For every function class listed above there is a member function to fetch the corresponding function object.
Inf_distance_2 | inf_distance_2_object () const
Signed_inf_distance_2 | signed_inf_distance_2_object () const
Construct_vertex_2 | construct_vertex_2_object () const
Construct_iso_rectangle_2 | construct_iso_rectangle_2_object () const
Construct_iso_rectangle_2_below_left_point_2 | construct_iso_rectangle_2_below_left_point_2_object () const
Construct_iso_rectangle_2_above_left_point_2 | construct_iso_rectangle_2_above_left_point_2_object () const
Construct_iso_rectangle_2_below_right_point_2 | construct_iso_rectangle_2_below_right_point_2_object () const
Construct_iso_rectangle_2_above_right_point_2 | construct_iso_rectangle_2_above_right_point_2_object () const

## Member Typedef Documentation

template<typename K >

typedef unspecified_type CGAL::Rectangular_p_center_default_traits_2< K >::Construct_point_2_above_left_implicit_point_2

3-argument function class: `Point_2` \( \times\) `Point_2` \( \times\) `FT` \( \rightarrow\) `Point_2`.

For arguments \( (p,\,q,\,r)\) it returns the upper-left corner of the iso-oriented square with sidelength \( r\) and lower-right corner at the intersection of the vertical line through \( p\) and the horizontal line through \( q\).

template<typename K >

typedef unspecified_type CGAL::Rectangular_p_center_default_traits_2< K >::Construct_point_2_above_right_implicit_point_2

3-argument function class: `Point_2` \( \times\) `Point_2` \( \times\) `FT` \( \rightarrow\) `Point_2`.

For arguments \( (p,\,q,\,r)\) it returns the upper-right corner of the iso-oriented square with sidelength \( r\) and lower-left corner at the intersection of the vertical line through \( p\) and the horizontal line through \( q\).

template<typename K >

typedef unspecified_type CGAL::Rectangular_p_center_default_traits_2< K >::Construct_point_2_below_left_implicit_point_2

3-argument function class: `Point_2` \( \times\) `Point_2` \( \times\) `FT` \( \rightarrow\) `Point_2`.

For arguments \( (p,\,q,\,r)\) it returns the lower-left corner of the iso-oriented square with sidelength \( r\) and upper-right corner at the intersection of the vertical line through \( p\) and the horizontal line through \( q\).

template<typename K >

typedef unspecified_type CGAL::Rectangular_p_center_default_traits_2< K >::Construct_point_2_below_right_implicit_point_2

3-argument function class: `Point_2` \( \times\) `Point_2` \( \times\) `FT` \( \rightarrow\) `Point_2`.

For arguments \( (p,\,q,\,r)\) it returns the lower-right corner of the iso-oriented square with sidelength \( r\) and upper-left corner at the intersection of the vertical line through \( p\) and the horizontal line through \( q\).