CGAL::Extremal_polygon_perimeter_traits_2<K>

Definition

The class Extremal_polygon_perimeter_traits_2 provides the types and operations needed to compute a maximum perimeter k-gon Pk 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 Concepts

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