CGAL 6.1.2 - Fast Intersection and Distance Computation (AABB Tree): AABBGeomTraits_2 Concept Reference

CGAL 6.1.2 - Fast Intersection and Distance Computation (AABB Tree)

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AABBGeomTraits_2 Concept Reference
Reference Manual » Concepts

## 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`.