ImplicitSurfaceTraits_3

Definition

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

When make_surface_mesh is called with a surface of type 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.

Types

ImplicitSurfaceTraits_3::FT
	The numerical type. It must be model of SqrtFieldNumberType and constructible from a double.
ImplicitSurfaceTraits_3::Point_3
	The point type. This point type must have a constructor Point_3(FT, FT, FT).
ImplicitSurfaceTraits_3::Line_3
	The line type.
ImplicitSurfaceTraits_3::Ray_3
	The ray type.
ImplicitSurfaceTraits_3::Segment_3
	The segment type.
ImplicitSurfaceTraits_3::Vector_3
	The vector type.
ImplicitSurfaceTraits_3::Sphere_3
	The sphere type.
ImplicitSurfaceTraits_3::Compute_scalar_product_3
	A function object that provides the operator FT operator()(Vector_3 v, Vector_3 w) which returns the scalar (inner) product of the two vectors v and w.
ImplicitSurfaceTraits_3::Compute_squared_distance_3
	A function object that provides the operator FT operator()(Point_3, Point_3) which returns the squared distance between two points.
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.
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.
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.
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: $$i 0. Point_3 operator()(const Segment_3& s,int i); which returns source or target of s: point(0) returns the source of s, point(1) returns the target of s. The parameter i is taken modulo 2, which gives easy access to the other end point.
ImplicitSurfaceTraits_3::Construct_segment_3
	A function object providing the operators Segment_3 operator()(const Point_3 &p, const Point_3 &q); which returns a segment with source $$p and target $$q. It is directed from the source towards the target.
ImplicitSurfaceTraits_3::Construct_scaled_vector_3
	A function object providing the operator Vector_3 operator()(const Vector_3 &v, const FT& scale) which returns the vector v scaled by a factor scale.
ImplicitSurfaceTraits_3::Construct_translated_point_3
	A function object providing the operator Point_3 operator()(const Point_3& p, const Vector_3& v) which returns the point obtained by translating p by the vector v.
ImplicitSurfaceTraits_3::Construct_vector_3
	A function object providing the operator Vector_3 operator()(const Point_3 &a, const Point_3 &b) which returns the vector b-a.
ImplicitSurfaceTraits_3::Has_on_bounded_side_3
	A function object providing the operator bool operator()(const Sphere_3&s, const Point_3&p); which returns true iff $$p lies on the bounded side of $$s.

Operations

The following functions give access to the predicate and construction objects:

Compute_scalar_product_3
	traits.compute_scalar_product_3_object ()
Compute_squared_distance_3
	traits.compute_squared_distance_3_object ()
Compute_squared_radius_3
	traits.compute_squared_radius_3_object ()
Construct_center_3	traits.construct_center_3_object ()
Construct_midpoint_3
	traits.construct_midpoint_3_object ()
Construct_point_on_3
	traits.construct_point_on_3_object ()
Construct_scaled_vector_3
	traits.construct_scaled_vector_3_object ()
Construct_segment_3
	traits.construct_segment_3_object ()
Construct_translated_point_3
	traits.construct_translated_point_3_object ()
Construct_vector_3	traits.construct_vector_3_object ()
Has_on_bounded_side_3
	traits.has_on_bounded_side_3_object ()

Has Models

Any CGAL Kernel.

See Also

Implicit_surface_3<Traits, Function>,
make_surface_mesh