\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - 2D Polygons

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PolygonTraits_2 Concept Reference
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.

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>`

## Creation
| PolygonTraits_2 ()
| PolygonTraits_2 (const PolygonTraits_2 &)

## Types
typedef unspecified_type | FT
typedef unspecified_type | Point_2
| The point type.
typedef unspecified_type | Segment_2
| The segment type.
typedef unspecified_type | Construct_segment_2
typedef unspecified_type | Equal_2
typedef unspecified_type | Less_xy_2
typedef unspecified_type | Less_yx_2
typedef unspecified_type | Compare_x_2
typedef unspecified_type | Compare_y_2
typedef unspecified_type | Orientation_2
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 ()
Less_xy_2 | less_xy_2_object ()
Less_yx_2 | less_yx_2_object ()
Compare_y_2 | compare_y_2_object ()
Compare_x_2 | compare_x_2_object ()
Orientation_2 | orientation_2_object ()
Compute_area_2 | compute_area_2_object ()
Construct_segment_2 | construct_segment_2_object ()