Definition

The concept PMPDistanceTraits is a refinement of the concepts AABBGeomTraits_3 and SpatialSortingTraits_3. In addition to the types required by those concepts, it also requires types and functors needed by the functions approximate_max_distance_to_point_set(), sample_triangle_mesh(), approximate_Hausdorff_distance() and max_distance_to_triangle_mesh().

Refines: AABBGeomTraits_3
: SpatialSortingTraits_3

Has models
: Any 3D Kernel is a model of this concept

Public Types
typedef unspecified_type	FT
	A number type model of Field and RealEmbeddable.
typedef unspecified_type	Point_3
	3D point type It must be default constructible, and can be constructed from 3 objects of type FT.
typedef unspecified_type	Vector_3
	3D vector type

Functors
typedef unspecified_type	Compute_squared_area_3
	Functor for computing squared area of a triangle.
typedef unspecified_type	Compute_squared_length_3
	Functor for computing squared length of a segment.
typedef unspecified_type	Construct_translated_point_3
	Functor for constructing translated points.
typedef unspecified_type	Construct_vector_3
	Functor for constructing vectors.
typedef unspecified_type	Construct_scaled_vector_3
	Functor for constructing scaled vectors.

Functions
Compute_squared_area_3	compute_squared_area_3_object ()
Compute_squared_length_3	compute_squared_length_3_object ()
Construct_translated_point_3	construct_translated_point_3_object ()
Construct_vector_3	construct_vector_3_object ()
Construct_scaled_vector_3	construct_scaled_vector_3_object ()

Member Typedef Documentation

◆ Compute_squared_area_3

typedef unspecified_type PMPDistanceTraits::Compute_squared_area_3

Functor for computing squared area of a triangle.

It provides FT operator()(const Point_3&, const Point_3&, const Point_3&) const and FT operator()(const Triangle_3&) const and has FT as result_type.

◆ Compute_squared_length_3

typedef unspecified_type PMPDistanceTraits::Compute_squared_length_3

Functor for computing squared length of a segment.

and FT operator()(const Segment_3&) const and has FT as result_type.

◆ Construct_scaled_vector_3

typedef unspecified_type PMPDistanceTraits::Construct_scaled_vector_3

Functor for constructing scaled vectors.

It provides Vector_3 operator()(const Vector_3 &, const FT &)

◆ Construct_translated_point_3

typedef unspecified_type PMPDistanceTraits::Construct_translated_point_3

Functor for constructing translated points.

It provides Point_3 operator()(const Point_3 &, const Vector_3 &)

◆ Construct_vector_3

typedef unspecified_type PMPDistanceTraits::Construct_vector_3

Functor for constructing vectors.

It provides Vector_3 operator()(const Point_3 &, const Point_3 &)

◆ Point_3

typedef unspecified_type PMPDistanceTraits::Point_3

3D point type It must be default constructible, and can be constructed from 3 objects of type FT.

bool operator<(Point_3, Point_3) to lexicographically compare two points must be available. Access to Cartesian coordinates must be possible using Point_3::x(), Point_3::y(), Point_3::z() and FT operator[](int i) with 0 <= i < 3.

There must be a specialization of CGAL::Kernel_traits such that CGAL::Kernel_traits<Point_3>::Kernel is a model implementing this concept.