CGAL 5.6.3 - Weights

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AnalyticWeightTraits_3 Concept Reference
Weight Interface Reference » Concepts

## Definition

A concept that describes the set of requirements of classes used in the computation of analytic weights in 3D.

Has Models:
  - All models of `Kernel`

## Types
typedef unspecified_type | FT
| A model of `FieldNumberType`.

## Geometric Objects
typedef unspecified_type | Point_3
| 3D point type.
typedef unspecified_type | Vector_3
| 3D vector type.

## Constructions
typedef unspecified_type | Compute_squared_distance_3
| A construction object that must provide the function operator:
typedef unspecified_type | Compute_squared_length_3
| A construction object that must provide the function operator:
typedef unspecified_type | Compute_scalar_product_3
| A construction object that must provide the function operator:
typedef unspecified_type | Construct_cross_product_vector_3
| A construction object that must provide the function operator:
typedef unspecified_type | Construct_circumcenter_3
| A construction object that must provide the function operator:
typedef unspecified_type | Construct_vector_3
| A construction object that must provide the function operator:
typedef unspecified_type | Construct_midpoint_3
| A construction object that must provide the function operator:
typedef unspecified_type | Construct_centroid_3
| A construction object that must provide two function operators:

## Member Typedef Documentation

## ◆ Compute_scalar_product_3

typedef unspecified_type AnalyticWeightTraits_3::Compute_scalar_product_3

A construction object that must provide the function operator:

`FT operator()(const Vector_3& v, const Vector_3& w)`

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

## ◆ Compute_squared_distance_3

typedef unspecified_type AnalyticWeightTraits_3::Compute_squared_distance_3

A construction object that must provide the function operator:

`FT operator()(const Point_3& p, const Point_3& q)`

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

## ◆ Compute_squared_length_3

typedef unspecified_type AnalyticWeightTraits_3::Compute_squared_length_3

A construction object that must provide the function operator:

`FT operator()(const Vector_3& v)`

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

## ◆ Construct_centroid_3

typedef unspecified_type AnalyticWeightTraits_3::Construct_centroid_3

A construction object that must provide two function operators:

`Point_3 operator()(const Point_3& p, const Point_3& q, const Point_3& r)`

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

`Point_3 operator()(const Point_3& p, const Point_3& q, const Point_3& r, const Point_3& s)`

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

## ◆ Construct_circumcenter_3

typedef unspecified_type AnalyticWeightTraits_3::Construct_circumcenter_3

A construction object that must provide the function operator:

`Point_3 operator()(const Point_3& p, const Point_3& q, const Point_3& 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_cross_product_vector_3

typedef unspecified_type AnalyticWeightTraits_3::Construct_cross_product_vector_3

A construction object that must provide the function operator:

`Vector_3 operator()(const Vector_3& v, const Vector_3& w)`

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

## ◆ Construct_midpoint_3

typedef unspecified_type AnalyticWeightTraits_3::Construct_midpoint_3

A construction object that must provide the function operator:

`Point_3 operator()(const Point_3& p, const Point_3& q)`

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

## ◆ Construct_vector_3

typedef unspecified_type AnalyticWeightTraits_3::Construct_vector_3

A construction object that must provide the function operator:

`Vector_3 operator()(const Point_3& p, const Point_3& q)`

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