AABBGeomTraits Concept Reference

Definition

The concept AABBGeomTraits defines the requirements for the first template parameter of the class CGAL::AABB_traits<AABBGeomTraits, AABBPrimitive>. It provides predicates and constructors to detect and compute intersections between query objects and the primitives stored in the AABB tree. In addition, it contains predicates and constructors to compute distances between a point query and the primitives stored in the AABB tree.

Has Models:

Any Kernel is a model of this traits concept.

See Also

CGAL::AABB_traits<AABBGeomTraits,AABBPrimitive>

Types
typedef unspecified_type	Sphere_3
	Sphere type, that should be consistent with the distance function chosen for the distance queries, namely the Squared_distance_3 functor.
typedef unspecified_type	Point_3
	Point type.
typedef unspecified_type	Do_intersect_3
	A functor object to detect intersections between two geometric objects. More...
typedef unspecified_type	Intersect_3
	A functor object to construct the intersection between two geometric objects. More...
typedef unspecified_type	Construct_sphere_3
	A functor object to construct the sphere centered at one point and passing through another one. More...
typedef unspecified_type	Compute_closest_point_3
	A functor object to compute the point on a geometric primitive which is closest from a query. More...
typedef unspecified_type	Has_on_bounded_side_3
	A functor object to detect if a point lies inside a sphere or not. More...
typedef unspecified_type	Compute_squared_radius_3
	A functor object to compute the squared radius of a sphere. More...
typedef unspecified_type	Compute_squared_distance_3
	A functor object to compute the squared distance between two points. More...

Operations
Do_intersect_3	do_intersect_3_object ()
	Returns the intersection detection functor.
Intersect_3	intersect_3_object ()
	Returns the intersection constructor.
Construct_sphere_3	construct_sphere_3_object ()
	Returns the distance comparison functor.
Compute_closest_point_3	compute_closest_point_3_object ()
	Returns the closest point constructor.
Has_on_bounded_side_3	has_on_bounded_side_3_object ()
	Returns the closest point constructor.
Compute_squared_radius_3	compute_squared_radius_3_object ()
	Returns the squared radius functor.
Compute_squared_distance_3	compute_squared_distance_3_object ()
	Returns the squared distance functor.

Member Typedef Documentation

typedef unspecified_type AABBGeomTraits::Compute_closest_point_3

A functor object to compute the point on a geometric primitive which is closest from a query.

Provides the operator: Point_3 operator()(const Point_3& p, const Type_2& type_2); where Type_2 is any type among Segment_3 and Triangle_3. The operator returns the point on type_2 which is closest to p.

typedef unspecified_type AABBGeomTraits::Compute_squared_distance_3

A functor object to compute the squared distance between two points.

Provides the operator: FT operator()(const Point_3& p, const Point_3& q);} which returns the squared distance between p and q.

typedef unspecified_type AABBGeomTraits::Compute_squared_radius_3

A functor object to compute the squared radius of a sphere.

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

typedef unspecified_type AABBGeomTraits::Construct_sphere_3

A functor object to construct the sphere centered at one point and passing through another one.

Provides the operator: Sphere_3 operator()(const Point_3& p, const Point_3 & q); which returns the sphere centered at p and passing through q.

typedef unspecified_type AABBGeomTraits::Do_intersect_3

A functor object to detect intersections between two geometric objects.

Provides the operators: bool operator()(const Type_1& type_1, const Type_2& type_2); where Type_1 and Type_2 are relevant types among Ray_3, Segment_3, Line_3, Triangle_3, Plane_3 and Bbox_3. Relevant herein means that a line primitive (ray, segment, line) is tested against a planar or solid primitive (plane, triangle, box), and a solid primitive is tested against another solid primitive (box against box). The operator returns true iff type_1 and type_2 have a non empty intersection.

typedef unspecified_type AABBGeomTraits::Has_on_bounded_side_3

A functor object to detect if a point lies inside a sphere or not.

Provides the operator: bool operator()(const Sphere_3& s, const Point_3& p); which returns true iff the closed volume bounded by s contains p.

typedef unspecified_type AABBGeomTraits::Intersect_3

A functor object to construct the intersection between two geometric objects.

This functor must support the result_of protocol, that is the return type of the operator()(A, B) is CGAL::cpp11::result<Intersect_3(A,B)>.

Provides the operators: CGAL::cpp11::result<Intersect_3(A,B)> operator()(const A& a, const B& b); where A and B are any relevant types among Ray_3, Segment_3, Line_3, Triangle_3, Plane_3 and Bbox_3. Relevant herein means that a line primitive (ray, segment, line) is tested against a planar or solid primitive (plane, triangle, box). A model of Kernel::Intersect_3 fulfills those requirements.