CGAL 6.1 - 2D Polygons

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PolygonTraits_2 Concept Reference
Reference Manual » Concepts

## Definition

The `CGAL::Polygon_2` class and the functions that implement the functionality found in that class each are parameterized by a traits class that defines the primitives used in the algorithms. The concept `PolygonTraits_2` defines this common set of requirements.

The requirements of `PolygonTraits_2` are a subset of the kernel requirements. We only list the types and methods which are required and refer to the description of the kernel concept for details.

Refines
  `DefaultConstructible`
  `CopyConstructable`

Has models
  The kernels supplied by CGAL are models of `PolygonTraits_2`
  `CGAL::Projection_traits_xy_3<K>`
  `CGAL::Projection_traits_yz_3<K>`
  `CGAL::Projection_traits_xz_3<K>`

See also
  `CGAL::Polygon_2<PolygonTraits_2, Container>`

## Types
typedef unspecified_type | FT
| number type
typedef unspecified_type | Point_2
| The point type.
typedef unspecified_type | Segment_2
| The segment type.
typedef unspecified_type | Construct_segment_2
| functor providing `Segment_2 operator()(Point_2, Point_2)` to construct a segment from two points.
typedef unspecified_type | Equal_2
| functor providing `bool operator()(Point_2, Point_2)` to test equality of two points.
typedef unspecified_type | Less_xy_2
| functor providing `bool operator()(Point_2, Point_2)` to compare lexicographically of two points.
typedef unspecified_type | Less_yx_2
| functor providing `bool operator()(Point_2, Point_2)` to compare inverse-lexicographically of two points.
typedef unspecified_type | Compare_x_2
| functor providing `bool operator()(Point_2, Point_2)` to compare the x-coordinate of two points.
typedef unspecified_type | Compare_y_2
| functor providing `bool operator()(Point_2, Point_2)` to compare the y-coordinate of two points.
typedef unspecified_type | Orientation_2
| functor providing `Oriention operator()(Point_2 p, Point_2 q, Point_2 r)` that returns CGAL::LEFT_TURN, if r lies to the left of the oriented line l defined by p and q, CGAL::RIGHT_TURN if r lies to the right of l, and CGAL::COLLINEAR if r lies on l.
typedef unspecified_type | Compute_area_2
| Computes the signed area of the oriented triangle defined by 3 `Point_2` passed as arguments.

## Operations
The following functions that create instances of the above predicate object types must exist.
Equal_2 | equal_2_object ()
| returns the corresponding function object
Less_xy_2 | less_xy_2_object ()
| returns the corresponding function object
Less_yx_2 | less_yx_2_object ()
| returns the corresponding function object
Compare_y_2 | compare_y_2_object ()
| returns the corresponding function object
Compare_x_2 | compare_x_2_object ()
| returns the corresponding function object
Orientation_2 | orientation_2_object ()
| returns the corresponding function object
Compute_area_2 | compute_area_2_object ()
| returns the corresponding function object
Construct_segment_2 | construct_segment_2_object ()
| returns the corresponding function object