BarycentricTraits_3 Concept Reference

Definition

A concept that describes the set of requirements of the template parameter GeomTraits used to parameterize all classes and functions with 3D barycentric coordinates from the namespace CGAL::Barycentric_coordinates. The concept BarycentricTraits_3 extends the concept BarycentricTraits_2 and adds the requirements for 3D objects.

Generalizes:

BarycentricTraits_2

Has models

All models of the CGAL concept Kernel

Types
typedef unspecified_type	FT
	A model of FieldNumberType.

3D Geometric Objects
typedef unspecified_type	Point_3
	A model of Kernel::Point_3.
typedef unspecified_type	Vector_3
	A model of Kernel::Vector_3.
typedef unspecified_type	Plane_3
	A model of Kernel::Plane_3.

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.
typedef unspecified_type	Triangle_2
	A model of Kernel::Triangle_2.
typedef unspecified_type	Iso_rectangle_2
	A model of Kernel::Iso_rectangle_2.

3D Generalized Constructions
typedef unspecified_type	Compute_approximate_angle_3
	A construction object that must provide the function operator:
typedef unspecified_type	Compute_determinant_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	Compute_squared_length_3
	A construction object that must provide the function operator:
typedef unspecified_type	Compute_volume_3
	A construction object that must provide the function operator:
typedef unspecified_type	Cartesian_const_iterator_3
	A model of CartesianConstIterator_3.
typedef unspecified_type	Construct_cartesian_const_iterator_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_projected_xy_point_2
	A construction object that must provide the function operator:
typedef unspecified_type	Construct_plane_3
	A construction object that must provide the function operator:
typedef unspecified_type	Construct_divided_vector_3
	A construction object that must provide the function operator:
typedef unspecified_type	Construct_point_3
	A construction object that must provide the function operator:
typedef unspecified_type	Construct_scaled_vector_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:

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_scalar_product_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	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	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	Equal_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	Orientation_2
	A predicate object that must provide the function operator:
Collinear_2	collinear_2_object ()
	The following functions give access to the predicate and constructor objects.

Member Typedef Documentation

Collinear_2

typedef unspecified_type BarycentricTraits_3::Collinear_2

A predicate object that must provide the function operator:

bool operator()(Point_2 p, Point_2 q, 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 BarycentricTraits_3::Collinear_are_ordered_along_line_2

A predicate object that must provide the function operator:

bool operator()(Point_2 p, Point_2 q, Point_2 r)

that returns true, iff q lies between p and r and p, q, and r satisfy the precondition that they are collinear.

Compare_x_2

typedef unspecified_type BarycentricTraits_3::Compare_x_2

A predicate object that must provide the function operator:

Comparison_result operator()(Point_2 p, Point_2 q)

that returns SMALLER, EQUAL or LARGER according to the \( x\)-ordering of points p and q.

Compare_y_2

typedef unspecified_type BarycentricTraits_3::Compare_y_2

A predicate object that must provide the function operator:

Comparison_result operator()(Point_2 p, Point_2 q)

that returns SMALLER, EQUAL or LARGER according to the \( y\)-ordering of points p and q.

Compute_approximate_angle_3

typedef unspecified_type BarycentricTraits_3::Compute_approximate_angle_3

A construction object that must provide the function operator:

FT operator(Vector_3 u, Vector_3 v)

that returns an approximation of the angle between u and v. The angle is given in degrees.

Compute_area_2

typedef unspecified_type BarycentricTraits_3::Compute_area_2

A construction object that must provide the function operator:

FT operator(Point_2 p0, Point_2 p1, Point_3 p2)

that returns the signed area of the triangle defined by the three points p0, p1, and p2.

Compute_determinant_3

typedef unspecified_type BarycentricTraits_3::Compute_determinant_3

A construction object that must provide the function operator:

FT operator(Vector_3 u, Vector_3 v, Vector_3 w)

that returns the determinant of the three vectors u, v and w.

Compute_scalar_product_2

typedef unspecified_type BarycentricTraits_3::Compute_scalar_product_2

A construction object that must provide the function operator:

FT operator()(Vector_2 v, Vector_2 w)

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

Compute_scalar_product_3

typedef unspecified_type BarycentricTraits_3::Compute_scalar_product_3

A construction object that must provide the function operator:

FT operator(Vector_3 v, Vector_3 w)

that returns the scalar (inner) product of the two vectors v and w.

Compute_squared_distance_2

typedef unspecified_type BarycentricTraits_3::Compute_squared_distance_2

A construction object that must provide the function operator:

FT operator()(Point_2 p, Point_2 q),

which returns the squared distance between p and q.

Compute_squared_length_3

typedef unspecified_type BarycentricTraits_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.

Compute_volume_3

typedef unspecified_type BarycentricTraits_3::Compute_volume_3

A construction object that must provide the function operator:

FT operator(Point_3 p0, Point_3 p1, Point_3 p2, Point_3 p3)

that returns the signed volume of the tetrahedron defined by the four points p0, p1, p2, and p3.

Construct_cartesian_const_iterator_3

typedef unspecified_type BarycentricTraits_3::Construct_cartesian_const_iterator_3

A construction object that must provide the function operator:

Cartesian_const_iterator_3 operator() (Point_3 p)

returns an iterator on the zeroth Cartesian coordinate of p.

Construct_cross_product_vector_3

typedef unspecified_type BarycentricTraits_3::Construct_cross_product_vector_3

A construction object that must provide the function operator:

Vector_3 operator(Vector_3 u, Vector_3 v)

that returns the cross product between u and v.

Construct_divided_vector_3

typedef unspecified_type BarycentricTraits_3::Construct_divided_vector_3

A construction object that must provide the function operator:

Vector_3 operator()(Vector_3 v, FT t)

returning the vector v / t.

Construct_plane_3

typedef unspecified_type BarycentricTraits_3::Construct_plane_3

A construction object that must provide the function operator:

Plane_3 operator()(Point_3 p, Point_3 q, Point_3 r),

which constructs a plane passing through p, q, and r and oriented in a positive sense when seen from the positive side of the plane.

Construct_point_3

typedef unspecified_type BarycentricTraits_3::Construct_point_3

A construction object that must provide the function operator:

Point_3 operator(FT x, FT y, FT z)

that returns the point with coordinates x, y and z.

Construct_projected_xy_point_2

typedef unspecified_type BarycentricTraits_3::Construct_projected_xy_point_2

A construction object that must provide the function operator:

Point_2 operator()(Plane_3 h, Point_3 p),

which returns image point of the projection of p under an affine transformation, which maps h onto the xy-plane, with the z-coordinate removed.

Construct_scaled_vector_3

typedef unspecified_type BarycentricTraits_3::Construct_scaled_vector_3

A construction object that must provide the function operator:

Vector_3 operator()(Vector_3 v, FT t)

returning the vector v * t.

Construct_vector_2

typedef unspecified_type BarycentricTraits_3::Construct_vector_2

A construction object that must provide the function operator:

Vector_2 operator()(Point_2 a, Point_2 b)

that computes the vector b-a.

Construct_vector_3

typedef unspecified_type BarycentricTraits_3::Construct_vector_3

A construction object that must provide the function operator:

Vector_3 operator(Point_3 p, Point_3 q)

that returns the vector q - p.

Equal_2

typedef unspecified_type BarycentricTraits_3::Equal_2

A predicate object that must provide the function operator:

bool operator()(Point_2 p, Point_2 q),

which returns true iff p is equal to q.

Less_xy_2

typedef unspecified_type BarycentricTraits_3::Less_xy_2

A predicate object that must provide the function operator:

bool operator()(Point_2 p, Point_2 q)

where true is returned iff \( p <_{xy} q\). We have \( p<_{xy}q\), iff \( p_x < q_x\) or \( p_x = q_x\) and \( p_y < q_y\), where \( p_x\) and \( p_y\) denote \( x\) and \( y\) coordinate of point \( p\), respectively.

Orientation_2

typedef unspecified_type BarycentricTraits_3::Orientation_2

A predicate object that must provide the function operator:

Orientation operator()(Point_2 p, Point_2 q, 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.