AnalyticWeightTraits_2 Concept Reference

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 Kernel
• CGAL::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.