AABBGeomTraits_3 Concept Reference

Definition

The concept AABBGeomTraits_3 defines the requirements for the first template parameter of the class CGAL::AABB_traits_3<AABBGeomTraits_3, 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.

Refines

SearchGeomTraits_3

Has models

All models of the concept Kernel

See also

CGAL::AABB_traits_3<AABBGeomTraits_3,AABBPrimitive>

CGAL::AABB_tree<AABBTraits>

AABBPrimitive

Types
typedef unspecified_type	Do_intersect_3
	A functor object to detect intersections between two geometric objects.
typedef unspecified_type	Intersect_3
	A functor object to construct the intersection between two geometric objects.
typedef unspecified_type	Construct_sphere_3
	A functor object to construct the sphere specified by its center and squared radius.
typedef unspecified_type	Construct_projected_point_3
	A functor object to compute the point on a geometric primitive which is closest from a query point.
typedef unspecified_type	Compare_distance_3
	A functor object to compare the distance of two points wrt a third one.
typedef unspecified_type	Compute_squared_distance_3
	A functor object to compute the squared distance between two points.
typedef unspecified_type	Less_x_3
	A functor object to compare the x-coordinates of two points.
typedef unspecified_type	Less_y_3
	A functor object to compare the y-coordinates of two points.
typedef unspecified_type	Less_z_3
	A functor object to compare the z-coordinates of two points.
typedef unspecified_type	Equal_3
	A functor object to compare two points.

Operations
Do_intersect_3	do_intersect_3_object ()
	returns the intersection detection predicate.
Intersect_3	intersect_3_object ()
	returns the intersection constructor.
Construct_sphere_3	construct_sphere_3_object ()
	returns the sphere constructor.
Construct_projected_point_3	construct_projected_point_3_object ()
	returns the closest point constructor.
Compare_distance_3	compare_distance_3_object ()
	returns the compare distance predicate.
Compute_squared_distance_3	compute_squared_distance_3_object ()
	returns the squared distance functor.
Less_x_3	less_x_3_object ()
	returns the Less_x_3 predicate.
Less_y_3	less_y_3_object ()
	returns the Less_y_3 predicate.
Less_z_3	less_z_3_object ()
	returns the Less_z_3 predicate.
Equal_3	equal_3_object ()
	returns the equal predicate.

Member Typedef Documentation

Compare_distance_3

typedef unspecified_type AABBGeomTraits_3::Compare_distance_3

A functor object to compare the distance of two points wrt a third one.

Provides the operator:

CGAL::Comparison_result operator()(const Point_3& p1, const Point_3& p2, const Point_3& p3),

which compares the distance between p1 and p2, to the distance between p1 and p3.

Compute_squared_distance_3

typedef unspecified_type AABBGeomTraits_3::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.

Construct_projected_point_3

typedef unspecified_type AABBGeomTraits_3::Construct_projected_point_3

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

Provides the operator:

Point_3 operator()(const Primitive::Datum& d, const Point_3& p),

which returns the point on d that is closest to p.

Construct_sphere_3

typedef unspecified_type AABBGeomTraits_3::Construct_sphere_3

A functor object to construct the sphere specified by its center and squared radius.

Provides the operator:

Sphere_3 operator()(const Point_3& p, const FT & sr),

which returns the sphere centered at p with sr as squared radius.

Do_intersect_3

typedef unspecified_type AABBGeomTraits_3::Do_intersect_3

A functor object to detect intersections between two geometric objects.

Provides the following operators:

bool operator()(const Query& q, const Bbox_3& b),

bool operator()(const Query& q, const Primitive::Datum& d),

bool operator()(const Sphere_3& s, const Bbox_3& b).

The operator returns true iff there is an intersection.

Equal_3

typedef unspecified_type AABBGeomTraits_3::Equal_3

A functor object to compare two points.

Provides the operator:

bool operator()(const Point_3& p, const Point_3& q),

which returns true iff p is equal to q.

Intersect_3

typedef unspecified_type AABBGeomTraits_3::Intersect_3

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

Provides the operator:

return_type operator()(const Query& q, const Primitive::Datum& d),

which computes the intersection between q and d. The type of the returned object must be a std::optional of a std::variant of the possible intersection types.

Less_x_3

typedef unspecified_type AABBGeomTraits_3::Less_x_3

A functor object to compare the x-coordinates of two points.

Provides the operator:

bool operator()(const Point_3& p, const Point_3& q),

which returns true iff the x-coordinate of p is smaller than the x-coordinate of q.

Less_y_3

typedef unspecified_type AABBGeomTraits_3::Less_y_3

A functor object to compare the y-coordinates of two points.

Provides the operator:

bool operator()(const Point_3& p, const Point_3& q),

which returns true iff the y-coordinate of p is smaller than the y-coordinate of q.

Less_z_3

typedef unspecified_type AABBGeomTraits_3::Less_z_3

A functor object to compare the z-coordinates of two points.

Provides the operator:

bool operator()(const Point_3& p, const Point_3& q),

which returns true iff the z-coordinate of p is smaller than the z-coordinate of q.