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 the CGAL concept 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. PreconditionThe 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. AnalyticWeightTraits_3 Generated by 1.17.0

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 the CGAL concept 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.