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CGAL 4.8 - Inscribed Areas

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CGAL::Extremal_polygon_area_traits_2< K > Class Template Reference
Inscribed Areas Reference

`#include <CGAL/Extremal_polygon_traits_2.h>`

## Definition

This is an advanced class.

Advanced

The class `Extremal_polygon_area_traits_2` provides the types and operations needed to compute a maximum area \( k\)-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_perimeter_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`. More...

## Operations
int | min_k () const
| returns 3.
FT | init (const Point_2 &p, const Point_2 &q) const
| returns `FT(0)`.
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 vertices of [`points_begin`, `points_end`) forming a maximum area triangle rooted at `points_begin[0]` to o and returns the past-the-end iterator for that sequence (== `o + 3`).
Less_xy_2 | less_xy_2_object ()
Orientation_2 | orientation_2_object ()

## Member Typedef Documentation

template<typename K >

typedef unspecified_type CGAL::Extremal_polygon_area_traits_2< K >::Operation

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

For a fixed `Point_2` \( root\), `op` \( (p,\,q)\) returns twice the area of the triangle \( (root,\, q,\, p)\).