CGAL::Extremal_polygon_perimeter_traits_2< K > Struct Template Reference

#include <CGAL/Extremal_polygon_traits_2.h>

Definition

template<typename K>
struct CGAL::Extremal_polygon_perimeter_traits_2< K >

This is an advanced class.

Advanced

The class Extremal_polygon_perimeter_traits_2 provides the types and operations needed to compute a maximum perimeter \( k\)-gon \( P_k\) that can be inscribed into a given convex polygon \( P\) using the function extremal_polygon_2().

Template Parameters

K	must be a model of Kernel.

Is model of

ExtremalPolygonTraits_2

See also

CGAL::maximum_area_inscribed_k_gon_2()

CGAL::maximum_perimeter_inscribed_k_gon_2()

CGAL::extremal_polygon_2()

CGAL::Extremal_polygon_area_traits_2<K>

ExtremalPolygonTraits_2

Types
typedef unspecified_type	FT
	typedef to K::FT.
typedef unspecified_type	Point_2
	typedef to K::Point_2.
typedef unspecified_type	Less_xy_2
	typedef to K::Less_xy_2.
typedef unspecified_type	Orientation_2
	typedef to K::Orientation_2.
typedef unspecified_type	Operation
	AdaptableBinaryFunction class op: Point_2 \( \times\) Point_2 \( \rightarrow\) FT.

Operations
int	min_k () const
	returns 2.
FT	init (const Point_2 &p, const Point_2 &q) const
	returns twice the Euclidean distance between p and q.
Operation	operation (const Point_2 &p) const
	returns Operation where p is the fixed \( root\) point.
template<class RandomAccessIterator , class OutputIterator >
OutputIterator	compute_min_k_gon (RandomAccessIterator points_begin, RandomAccessIterator points_end, FT &max_area, OutputIterator o) const
	writes the pair (points_begin[0], p) where p is drawn from [points_begin, points_end) such that the Euclidean distance between both points is maximized (maximum perimeter 2-gon rooted at points_begin[0]) to o and returns the past-the-end iterator for that sequence (== o + 2).
Less_xy_2	less_xy_2_object ()
Orientation_2	orientation_2_object ()

Member Typedef Documentation

FT

template<typename K >

typedef unspecified_type CGAL::Extremal_polygon_perimeter_traits_2< K >::FT

typedef to K::FT.

Less_xy_2

template<typename K >

typedef unspecified_type CGAL::Extremal_polygon_perimeter_traits_2< K >::Less_xy_2

typedef to K::Less_xy_2.

Operation

template<typename K >

typedef unspecified_type CGAL::Extremal_polygon_perimeter_traits_2< K >::Operation

AdaptableBinaryFunction class op: Point_2 \( \times\) Point_2 \( \rightarrow\) FT.

For a fixed Point_2 \( root\), op \( (p,\,q)\) returns \( d(r,\,p) + d(p,\,q) - d(r,\,q)\) where \( d\) denotes the Euclidean distance.

Orientation_2

template<typename K >

typedef unspecified_type CGAL::Extremal_polygon_perimeter_traits_2< K >::Orientation_2

typedef to K::Orientation_2.

Point_2

template<typename K >

typedef unspecified_type CGAL::Extremal_polygon_perimeter_traits_2< K >::Point_2

typedef to K::Point_2.

Member Function Documentation

compute_min_k_gon()

template<typename K >

template<class RandomAccessIterator , class OutputIterator >

OutputIterator CGAL::Extremal_polygon_perimeter_traits_2< K >::compute_min_k_gon	(	RandomAccessIterator	points_begin,
		RandomAccessIterator	points_end,
		FT &	max_area,
		OutputIterator	o
	)		const

writes the pair (points_begin[0], p) where p is drawn from [points_begin, points_end) such that the Euclidean distance between both points is maximized (maximum perimeter 2-gon rooted at points_begin[0]) to o and returns the past-the-end iterator for that sequence (== o + 2).

init()

template<typename K >

FT CGAL::Extremal_polygon_perimeter_traits_2< K >::init	(	const Point_2 &	p,
		const Point_2 &	q
	)		const

returns twice the Euclidean distance between p and q.

less_xy_2_object()

template<typename K >

Less_xy_2 CGAL::Extremal_polygon_perimeter_traits_2< K >::less_xy_2_object

(

)

min_k()

template<typename K >

int CGAL::Extremal_polygon_perimeter_traits_2< K >::min_k

(

)

const

returns 2.

operation()

template<typename K >

Operation CGAL::Extremal_polygon_perimeter_traits_2< K >::operation

(

const Point_2 &

p

)

const

returns Operation where p is the fixed \( root\) point.

orientation_2_object()

template<typename K >

Orientation_2 CGAL::Extremal_polygon_perimeter_traits_2< K >::orientation_2_object

(

)