CGAL 5.4 - Weights
AnalyticWeightTraits_3 Concept Reference

## 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: More...

typedef unspecified_type Compute_squared_length_3
A construction object that must provide the function operator: More...

typedef unspecified_type Compute_scalar_product_3
A construction object that must provide the function operator: More...

typedef unspecified_type Construct_cross_product_vector_3
A construction object that must provide the function operator: More...

typedef unspecified_type Construct_circumcenter_3
A construction object that must provide the function operator: More...

typedef unspecified_type Construct_vector_3
A construction object that must provide the function operator: More...

typedef unspecified_type Construct_midpoint_3
A construction object that must provide the function operator: More...

typedef unspecified_type Construct_centroid_3
A construction object that must provide two function operators: More...

## ◆ 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

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

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

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

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

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

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

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.