Add AABBGeomTraits_2

AABB_tree/doc/AABB_tree/Concepts/AABBGeomTraits_2.h

@@ -0,0 +1,202 @@
+
+/*!
+\ingroup PkgAABBTreeConcepts
+\cgalConcept
+
+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.
+
+\cgalRefines{SearchGeomTraits_2}
+
+\cgalHasModelsBegin
+\cgalHasModelsBare{All models of the concept `Kernel`}
+\cgalHasModelsEnd
+
+\sa `CGAL::AABB_traits<AABBGeomTraits_2,AABBPrimitive>`
+\sa `CGAL::AABB_tree<AABBTraits>`
+\sa `AABBPrimitive`
+
+*/
+
+class AABBGeomTraits_2 {
+public:
+
+/// \name Types
+/// @{
+
+/*!
+A functor object to detect intersections between two geometric objects.
+Provides the following operators:
+
+`bool operator()(Query, Bbox_2)`,
+
+`bool operator()(Query, Primitive::Datum)`,
+
+`bool operator()(Circle_2, Bbox_2)`.
+
+The operator returns `true` iff there exists a non-empty intersection.
+*/
+typedef unspecified_type Do_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.
+*/
+typedef unspecified_type Intersect_2;
+
+/*!
+A functor object to construct the circle centered at one point and passing through another one.
+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.
+*/
+typedef unspecified_type Construct_circle_2;
+
+/*!
+A functor object to compute the point on a geometric primitive which is closest from a query.
+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`.
+*/
+typedef unspecified_type Construct_projected_point_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`, and between `p2` and `p3`.
+*/
+typedef unspecified_type Compare_distance_2;
+
+/*!
+A functor object to compute the squared radius of a circle.
+Provides the operator:
+
+`FT operator()(const Circle_2& s),`
+
+which returns the squared radius of `s`.
+*/
+typedef unspecified_type Compute_squared_radius_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`.
+*/
+typedef unspecified_type Compute_squared_distance_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`.
+*/
+typedef unspecified_type Less_x_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`.
+*/
+typedef unspecified_type Less_y_2;
+
+/*!
+A functor object to compare the z-coordinates of two points. Provides the operator:
+
+`bool operator()(const Point_2& p, const Point_2& q)`,
+
+which returns `true` iff the z-coordinate of `p` is smaller than the z-coordinate of `q`.
+*/
+typedef unspecified_type Less_z_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`.
+*/
+typedef unspecified_type Equal_2;
+
+/// @}
+
+/// \name Operations
+/// @{
+
+/*!
+returns the intersection detection predicate.
+*/
+Do_intersect_2 do_intersect_2_object();
+
+/*!
+returns the intersection constructor.
+*/
+Intersect_2 intersect_2_object();
+
+/*!
+returns the circle constructor.
+*/
+Construct_circle_2 construct_circle_2_object();
+
+/*!
+returns the closest point constructor.
+*/
+Construct_projected_point_2 construct_projected_point_2_object();
+
+/*!
+returns the compare distance predicate.
+*/
+Compare_distance_2 compare_distance_2_object();
+
+/*!
+returns the squared radius functor.
+*/
+Compute_squared_radius_2 compute_squared_radius_2_object();
+
+/*!
+returns the squared distance functor.
+*/
+Compute_squared_distance_2 compute_squared_distance_2_object();
+
+/*!
+returns the `Less_x_2` predicate.
+*/
+Less_x_2 less_x_2_object();
+
+/*!
+returns the `Less_y_2` predicate.
+*/
+Less_y_2 less_y_2_object();
+
+/*!
+returns the `Less_z_2` predicate.
+*/
+Less_z_2 less_z_2_object();
+
+/*!
+returns the equal predicate.
+*/
+Equal_2 equal_2_object();
+
+/// @}
+
+}; /* end AABBGeomTraits_2 */