CGAL 5.1.3 - Bounding Volumes
RectangularPCenterTraits_2 Concept Reference

## 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>
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

## ◆ 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 $$q$$.

## ◆ 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 $$q$$.

## ◆ 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 $$q$$.

## ◆ 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 $$q$$.