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Definition

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.

Requirements

The template parameter K is a model for Kernel.

Is Model for the Concept

ExtremalPolygonTraits_2

Types

Extremal_polygon_perimeter_traits_2<K>::FT
	typedef to K::FT.
Extremal_polygon_perimeter_traits_2<K>::Point_2
	typedef to K::Point_2.
Extremal_polygon_perimeter_traits_2<K>::Less_xy_2
	typedef to K::Less_xy_2.
Extremal_polygon_perimeter_traits_2<K>::Orientation_2
	typedef to K::Orientation_2.
Extremal_polygon_perimeter_traits_2<K>::Operation
	AdaptableBinaryFunction class op: Point_2 $$ × Point_2 $$ 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.

Operations

int	t.min_k () const	returns 2.
FT	t.init ( const Point_2& p, const Point_2& q) const
		returns twice the Euclidean distance between p and q.
Operation	t.operation ( const Point_2& p) const
		returns Operation where p is the fixed $$root point.
template < class RandomAccessIterator, class OutputIterator >
OutputIterator	t.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	t.less_xy_2_object ()
Orientation_2	t.orientation_2_object ()

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

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