\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.10.1 - Bounding Volumes
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RectangularPCenterTraits_2 Concept Reference
Concepts

Definition

The concept RectangularPCenterTraits_2 defines types and operations needed to compute rectilinear \( p\)-centers of a planar point set using the function CGAL::rectangular_p_center_2.

Has Models:
CGAL::Rectangular_p_center_default_traits_2<K>
See Also
CGAL::rectangular_p_center_2()

Types

typedef unspecified_type FT
 model for FieldNumberType.
 
typedef unspecified_type Point_2
 model for Kernel::Point_2.
 
typedef unspecified_type Iso_rectangle_2
 model for Kernel::Iso_rectangle_2.
 
typedef unspecified_type Less_x_2
 model for Kernel::Less_x_2.
 
typedef unspecified_type Less_y_2
 model for Kernel::Less_y_2.
 
typedef unspecified_type Construct_vertex_2
 model for Kernel::Construct_vertex_2.
 
typedef unspecified_type Construct_iso_rectangle_2
 model for Kernel::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

typedef unspecified_type RectangularPCenterTraits_2::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 \( q\).

typedef unspecified_type RectangularPCenterTraits_2::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 \( q\).

typedef unspecified_type RectangularPCenterTraits_2::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 \( q\).

typedef unspecified_type RectangularPCenterTraits_2::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 \( q\).