CGAL 5.1.3  3D Fast Intersection and Distance Computation (AABB Tree)

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.
CGAL::AABB_traits<AABBGeomTraits,AABBPrimitive>
Types  
typedef unspecified_type  FT 
A number type model of Field .  
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  Construct_projected_point_3 
A functor object to compute the point on a geometric primitive which is closest from a query. More...  
typedef unspecified_type  Compare_distance_3 
A functor object to compare the distance of two points wrt a third one. 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...  
typedef unspecified_type  Less_x_3 
A functor object to compare the xcoordinates of two points. More...  
typedef unspecified_type  Less_y_3 
A functor object to compare the ycoordinates of two points. More...  
typedef unspecified_type  Less_z_3 
A functor object to compare the zcoordinates of two points. More...  
typedef unspecified_type  Equal_3 
A functor object to compare 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 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 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.  
Less_x_3  less_x_3_object () 
returns the Less_x_3 functor.  
Less_y_3  less_y_3_object () 
returns the Less_y_3 functor.  
Less_z_3  less_z_3_object () 
returns the Less_z_3 functor.  
Equal_3  equal_3_object () 
returns the equal functor.  
A functor object to compare the distance of two points wrt a third one.
Provides the operator: CGAL::Comparision_result operator()(const Point_3& p1, const Point_3& p2, const Point_3& p3)
. The operator compare the distance between p1 and
p2, and between
p2and
p3`.
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
.
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
.
A functor object to compute the point on a geometric primitive which is closest from a query.
Provides the operator: Point_3 operator()(const Type_2& type_2, const Point_3& p);
where Type_2
can be any of the following types : Segment_3
, Ray_3
, or Triangle_3
. The operator returns the point on type_2
which is closest to p
.
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 FT & sr)
which returns the sphere centered at p
with sr
as squared radius. 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.
A functor object to compare two points.
Provides the operator: bool operator()(const Point_3& p, const Point_3& q);}
which returns true
if p
is equal to q
.
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
.
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.
A functor object to compare the xcoordinates of two points.
Provides the operator: bool operator()(const Point_3& p, const Point_3& q);}
which returns true
if the xcoordinate of p
is smaller than the xcoordinate of q
.
A functor object to compare the ycoordinates of two points.
Provides the operator: bool operator()(const Point_3& p, const Point_3& q);}
which returns true
if the ycoordinate of p
is smaller than the ycoordinate of q
.
A functor object to compare the zcoordinates of two points.
Provides the operator: bool operator()(const Point_3& p, const Point_3& q);}
which returns true
if the zcoordinate of p
is smaller than the zcoordinate of q
.