CGAL 6.1.1 - Weights

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AnalyticWeightTraits_2 Concept Reference
Reference Manual » Concepts

## Definition

A concept that describes the set of requirements of classes used in the computation of analytic weights in 2D.

Has models
  All models of the CGAL concept `Kernel`
  `sCGAL:Projection_traits_xy_3<K>`
  `CGAL::Projection_traits_yz_3<K>`
  `CGAL::Projection_traits_xz_3<K>`

## Types
typedef unspecified_type | FT
| A model of `FieldNumberType`.
typedef unspecified_type | Comparison_result
| `CGAL::Comparison_result` or `Uncertain<CGAL::Comparison_result>`.
typedef unspecified_type | Orientation
| `CGAL::Orientation` or `Uncertain<CGAL::Orientation>`.

## Geometric Objects
typedef unspecified_type | Point_2
| 2D point type.
typedef unspecified_type | Vector_2
| 2D vector type.

## Constructions
typedef unspecified_type | Compute_area_2
| A construction object that must provide the function operator:
typedef unspecified_type | Compute_squared_distance_2
| A construction object that must provide the function operator:
typedef unspecified_type | Compute_squared_length_2
| A construction object that must provide the function operator:
typedef unspecified_type | Compute_scalar_product_2
| A construction object that must provide the function operator:
typedef unspecified_type | Compute_determinant_2
| A construction object that must provide the function operator:
typedef unspecified_type | Construct_circumcenter_2
| A construction object that must provide the function operator:
typedef unspecified_type | Construct_vector_2
| A construction object that must provide the function operator:
typedef unspecified_type | Construct_midpoint_2
| A construction object that must provide the function operator:
typedef unspecified_type | Construct_centroid_2
| A construction object that must provide the function operator:

## Predicates
typedef unspecified_type | Equal_2
| A predicate object that must provide the function operator:
typedef unspecified_type | Collinear_2
| A predicate object that must provide the function operator:
typedef unspecified_type | Less_xy_2
| A predicate object that must provide the function operator:
typedef unspecified_type | Compare_x_2
| A predicate object that must provide the function operator:
typedef unspecified_type | Compare_y_2
| A predicate object that must provide the function operator:
typedef unspecified_type | Orientation_2
| A predicate object that must provide the function operator:

## Member Typedef Documentation

## ◆ Collinear_2

typedef unspecified_type AnalyticWeightTraits_2::Collinear_2

A predicate object that must provide the function operator:

`bool operator()(const Point_2& p, const Point_2& q, const Point_2& r)`

that returns `true` if the points `p`, `q`, and `r` are collinear and `false` otherwise.

## ◆ Compare_x_2

typedef unspecified_type AnalyticWeightTraits_2::Compare_x_2

A predicate object that must provide the function operator:

`Comparison_result operator()(const Point_2& p, const Point_2& q)`

that compares the Cartesian x-coordinates of the points `p` and `q`.

## ◆ Compare_y_2

typedef unspecified_type AnalyticWeightTraits_2::Compare_y_2

A predicate object that must provide the function operator:

`Comparison_result operator()(const Point_2& p, const Point_2& q)`

that compares the Cartesian y-coordinates of the points `p` and `q`.

## ◆ Compute_area_2

typedef unspecified_type AnalyticWeightTraits_2::Compute_area_2

A construction object that must provide the function operator:

`FT operator()(const Point_2& p, const Point_2& q, const Point_2& r)`

that returns the signed area of the triangle defined by the points `p`, `q`, and `r`.

## ◆ Compute_determinant_2

typedef unspecified_type AnalyticWeightTraits_2::Compute_determinant_2

A construction object that must provide the function operator:

`FT operator()(const Vector_2& v, const Vector_2& w)`

that returns the determinant of the vectors `v` and `w`.

## ◆ Compute_scalar_product_2

typedef unspecified_type AnalyticWeightTraits_2::Compute_scalar_product_2

A construction object that must provide the function operator:

`FT operator()(const Vector_2& v, const Vector_2& w)`

that returns the scalar product of the vectors `v` and `w`.

## ◆ Compute_squared_distance_2

typedef unspecified_type AnalyticWeightTraits_2::Compute_squared_distance_2

A construction object that must provide the function operator:

`FT operator()(const Point_2& p, const Point_2& q)`

that returns the squared Euclidean distance between the points `p` and `q`.

## ◆ Compute_squared_length_2

typedef unspecified_type AnalyticWeightTraits_2::Compute_squared_length_2

A construction object that must provide the function operator:

`FT operator()(const Vector_2& v)`

that returns the squared length of the vector `v`.

## ◆ Construct_centroid_2

typedef unspecified_type AnalyticWeightTraits_2::Construct_centroid_2

A construction object that must provide the function operator:

`Point_2 operator()(const Point_2& p, const Point_2& q, const Point_2& r)`

that returns the centroid of the points `p`, `q`, and `r`.

## ◆ Construct_circumcenter_2

typedef unspecified_type AnalyticWeightTraits_2::Construct_circumcenter_2

A construction object that must provide the function operator:

`Point_2 operator()(const Point_2& p, const Point_2& q, const Point_2& r)`

that returns the center of the circle passing through the points `p`, `q`, and `r`.

Precondition
  The points `p`, `q`, and `r` are not collinear.

## ◆ Construct_midpoint_2

typedef unspecified_type AnalyticWeightTraits_2::Construct_midpoint_2

A construction object that must provide the function operator:

`Point_2 operator()(const Point_2& p, const Point_2& q)`

that returns the midpoint between the points `p` and `q`.

## ◆ Construct_vector_2

typedef unspecified_type AnalyticWeightTraits_2::Construct_vector_2

A construction object that must provide the function operator:

`Vector_2 operator()(const Point_2& p, const Point_2& q)`

that returns the vector through the points `p` and `q`.

## ◆ Equal_2

typedef unspecified_type AnalyticWeightTraits_2::Equal_2

A predicate object that must provide the function operator:

`bool operator()(const Point_2& p, const Point_2& q)`

that returns `true` if `p = q` and `false` otherwise.

## ◆ Less_xy_2

typedef unspecified_type AnalyticWeightTraits_2::Less_xy_2

A predicate object that must provide the function operator:

`bool operator()(const Point_2& p, const Point_2& q)`

that returns `true` iff the x-coordinate of `p` is smaller than the x-coordinate of `q` or if they are the same and the y-coordinate of `p` is smaller than the y-coordinate of `q`.

## ◆ Orientation_2

typedef unspecified_type AnalyticWeightTraits_2::Orientation_2

A predicate object that must provide the function operator:

`Orientation operator()(const Point_2& p, const Point_2& q, const Point_2& r)`

that returns `CGAL::LEFT_TURN` if `r` lies to the left of the oriented line `l` defined by `p` and `q`, returns `CGAL::RIGHT_TURN` if `r` lies to the right of `l`, and returns `CGAL::COLLINEAR` if `r` lies on `l`.