AABBGeomTraits_2 Concept Reference

Definition

The concept AABBGeomTraits_2 defines the requirements for the first template parameter of the class CGAL::AABB_traits_2<AABBGeomTraits_2, 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_2

Has models

All models of the concept Kernel

See also

CGAL::AABB_traits_2<AABBGeomTraits_2,AABBPrimitive>

CGAL::AABB_tree<AABBTraits>

AABBPrimitive

Types
typedef unspecified_type	Do_intersect_2
	A functor object to detect intersections between two geometric objects.
typedef unspecified_type	Intersect_2
	A functor object to construct the intersection between two geometric objects.
typedef unspecified_type	Construct_circle_2
	A functor object to construct the circle specified by its center and squared radius.
typedef unspecified_type	Construct_projected_point_2
	A functor object to compute the point on a geometric primitive which is closest from a query point.
typedef unspecified_type	Compare_distance_2
	A functor object to compare the distance of two points wrt a third one.
typedef unspecified_type	Compute_squared_distance_2
	A functor object to compute the squared distance between two points.
typedef unspecified_type	Less_x_2
	A functor object to compare the x-coordinates of two points.
typedef unspecified_type	Less_y_2
	A functor object to compare the y-coordinates of two points.
typedef unspecified_type	Equal_2
	A functor object to compare two points.

Operations
Do_intersect_2	do_intersect_2_object ()
	returns the intersection detection predicate.
Intersect_2	intersect_2_object ()
	returns the intersection constructor.
Construct_circle_2	construct_circle_2_object ()
	returns the circle constructor.
Construct_projected_point_2	construct_projected_point_2_object ()
	returns the closest point constructor.
Compare_distance_2	compare_distance_2_object ()
	returns the compare distance predicate.
Compute_squared_distance_2	compute_squared_distance_2_object ()
	returns the squared distance functor.
Less_x_2	less_x_2_object ()
	returns the Less_x_2 predicate.
Less_y_2	less_y_2_object ()
	returns the Less_y_2 predicate.
Equal_2	equal_2_object ()
	returns the equal predicate.

Member Typedef Documentation

Compare_distance_2

typedef unspecified_type AABBGeomTraits_2::Compare_distance_2

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

Provides the operator:

CGAL::Comparison_result operator()(const Point_2& p1, const Point_2& p2, const Point_2& p3),

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

Compute_squared_distance_2

typedef unspecified_type AABBGeomTraits_2::Compute_squared_distance_2

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

Provides the operator:

FT operator()(const Point_2& p, const Point_2& q),

which returns the squared distance between p and q.

Construct_circle_2

typedef unspecified_type AABBGeomTraits_2::Construct_circle_2

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

Provides the operator:

Circle_2 operator()(const Point_2& p, const FT & sr),

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

Construct_projected_point_2

typedef unspecified_type AABBGeomTraits_2::Construct_projected_point_2

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

Provides the operator:

Point_2 operator()(const Primitive::Datum& d, const Point_2& p),

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

Do_intersect_2

typedef unspecified_type AABBGeomTraits_2::Do_intersect_2

A functor object to detect intersections between two geometric objects.

Provides the following operators:

bool operator()(const Query& q, const Bbox_2& b),

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

bool operator()(const Circle_2& c, const Bbox_2& b).

The operator returns true iff there is an intersection.

Equal_2

typedef unspecified_type AABBGeomTraits_2::Equal_2

A functor object to compare two points.

Provides the operator:

bool operator()(const Point_2& p, const Point_2& q),

which returns true iff p is equal to q.

Intersect_2

typedef unspecified_type AABBGeomTraits_2::Intersect_2

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_2

typedef unspecified_type AABBGeomTraits_2::Less_x_2

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

Provides the operator:

bool operator()(const Point_2& p, const Point_2& q),

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

Less_y_2

typedef unspecified_type AABBGeomTraits_2::Less_y_2

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

Provides the operator:

bool operator()(const Point_2& p, const Point_2& q),

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