CGAL::Barycentric_coordinates::BarycentricTraits_2 Concept Reference

Definition

A concept that describes the set of requirements of the template parameter GeomTraits used to parameterize all classes and functions with 2D barycentric coordinates from the namespace CGAL::Barycentric_coordinates.

Has Models:

• All models of Kernel
• CGAL::Projection_traits_3<K>
• 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>.

2D Geometric Objects
typedef unspecified_type	Point_2
	A model of Kernel::Point_2.
typedef unspecified_type	Vector_2
	A model of Kernel::Vector_2.

2D Generalized 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_vector_2
	A construction object that must provide the function operator:

2D Generalized 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	Collinear_are_ordered_along_line_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 CGAL::Barycentric_coordinates::BarycentricTraits_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.

Collinear_are_ordered_along_line_2

typedef unspecified_type CGAL::Barycentric_coordinates::BarycentricTraits_2::Collinear_are_ordered_along_line_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 point q lies between the points p and r and all three points are collinear.

Compare_x_2

typedef unspecified_type CGAL::Barycentric_coordinates::BarycentricTraits_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 CGAL::Barycentric_coordinates::BarycentricTraits_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 CGAL::Barycentric_coordinates::BarycentricTraits_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 CGAL::Barycentric_coordinates::BarycentricTraits_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 CGAL::Barycentric_coordinates::BarycentricTraits_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 CGAL::Barycentric_coordinates::BarycentricTraits_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 CGAL::Barycentric_coordinates::BarycentricTraits_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_vector_2

typedef unspecified_type CGAL::Barycentric_coordinates::BarycentricTraits_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 CGAL::Barycentric_coordinates::BarycentricTraits_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 CGAL::Barycentric_coordinates::BarycentricTraits_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 CGAL::Barycentric_coordinates::BarycentricTraits_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.