Definition

The concept ImplicitSurfaceTraits_3 describes the requirements of the traits class to be plugged as Traits in CGAL::Implicit_surface_3<Traits, Function>.

When make_surface_mesh is called with a surface of type CGAL::Implicit_surface_3<Traits,Function>, the surface mesher traits generator generates automatically a traits class that is a model of SurfaceMeshTraits_3. Actually, the concept ImplicitSurfaceTraits_3 provides the types, predicates and constructors that are passed to the generated model of SurfaceMeshTraits_3.

Has models
: All models of the CGAL concept Kernel

See also: CGAL::Implicit_surface_3<Traits, Function>; CGAL::make_surface_mesh()

Types
typedef unspecified_type	FT
	The numerical type.

typedef unspecified_type	Point_3
	The point type.

typedef unspecified_type	Line_3
	The line type.

typedef unspecified_type	Ray_3
	The ray type.

typedef unspecified_type	Segment_3
	The segment type.

typedef unspecified_type	Vector_3
	The vector type.

typedef unspecified_type	Sphere_3
	The sphere type.

typedef unspecified_type	Compute_scalar_product_3
	A function object providing the operator.

typedef unspecified_type	Compute_squared_distance_3
	A function object providing the operator.

typedef unspecified_type	Compute_squared_radius_3
	A function object providing the operator.

typedef unspecified_type	Construct_center_3
	A function object providing the operator.

typedef unspecified_type	Construct_midpoint_3
	A function object providing the operator.

typedef unspecified_type	Construct_point_on_3
	A function object providing the following operators:

typedef unspecified_type	Construct_segment_3
	A function object providing the operator.

typedef unspecified_type	Construct_scaled_vector_3
	A function object providing the operator.

typedef unspecified_type	Construct_translated_point_3
	A function object providing the operator.

typedef unspecified_type	Construct_vector_3
	A function object providing the operator.

typedef unspecified_type	Has_on_bounded_side_3
	A function object providing the operator.

Operations
The following functions give access to the predicate and construction objects:
Compute_scalar_product_3	compute_scalar_product_3_object ()

Compute_squared_distance_3	compute_squared_distance_3_object ()

Compute_squared_radius_3	compute_squared_radius_3_object ()

Construct_center_3	construct_center_3_object ()

Construct_midpoint_3	construct_midpoint_3_object ()

Construct_point_on_3	construct_point_on_3_object ()

Construct_scaled_vector_3	construct_scaled_vector_3_object ()

Construct_segment_3	construct_segment_3_object ()

Construct_translated_point_3	construct_translated_point_3_object ()

Construct_vector_3	construct_vector_3_object ()

Has_on_bounded_side_3	has_on_bounded_side_3_object ()

Member Typedef Documentation

◆ Compute_scalar_product_3

typedef unspecified_type ImplicitSurfaceTraits_3::Compute_scalar_product_3

A function object providing the operator.

FT operator()(Vector_3 v, Vector_3 w) which returns the scalar (inner) product of the two vectors v and w.

◆ Compute_squared_distance_3

typedef unspecified_type ImplicitSurfaceTraits_3::Compute_squared_distance_3

A function object providing the operator.

FT operator()(Point_3, Point_3) which returns the squared distance between two points.

◆ Compute_squared_radius_3

typedef unspecified_type ImplicitSurfaceTraits_3::Compute_squared_radius_3

A function object providing the operator.

FT operator()(const Sphere_3& s) which returns the squared radius of s.

◆ Construct_center_3

typedef unspecified_type ImplicitSurfaceTraits_3::Construct_center_3

A function object providing the operator.

Point_3 operator()(const Sphere_3& s) which computes the center of the sphere s.

◆ Construct_midpoint_3

typedef unspecified_type ImplicitSurfaceTraits_3::Construct_midpoint_3

A function object providing the operator.

Point_3 operator()(const Point_3& p, const Point_3& q) which computes the midpoint of the segment pq.

◆ Construct_point_on_3

typedef unspecified_type ImplicitSurfaceTraits_3::Construct_point_on_3

A function object providing the following operators:

Point_3 operator()(const Line_3& l,int i) which returns an arbitrary point on l. It holds point(i) == point(j), iff i==j. Furthermore, is directed from point(i) to point(j), for all i \( <\) j.

Point_3 operator()(const Ray_3& r,int i) which returns a point on r. point(0) is the source, point(i), with \( i>0\), is different from the source.

Precondition: \( i \geq0\).

Point_3 operator()(const Segment_3& s,int i) which returns source or target of s: point(0) returns the source of s, point(1) returns the target of s. The parameter i is taken modulo 2, which gives easy access to the other end point.

◆ Construct_scaled_vector_3

typedef unspecified_type ImplicitSurfaceTraits_3::Construct_scaled_vector_3

A function object providing the operator.

Vector_3 operator()(const Vector_3 &v, const FT& scale) which returns the vector v scaled by a factor scale.

◆ Construct_segment_3

typedef unspecified_type ImplicitSurfaceTraits_3::Construct_segment_3

A function object providing the operator.

Segment_3 operator()(const Point_3 &p, const Point_3 &q) which returns a segment with source p and target q. It is directed from the source towards the target.