CGAL 6.0  Fast Intersection and Distance Computation (AABB Tree)

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.
SearchGeomTraits_3
Kernel
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 xcoordinates of two points.  
typedef unspecified_type  Less_y_3 
A functor object to compare the ycoordinates of two points.  
typedef unspecified_type  Less_z_3 
A functor object to compare the zcoordinates 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.  
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
.
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 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
.
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.
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.
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
.
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.
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
iff 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
iff 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
iff the zcoordinate of p
is smaller than the zcoordinate of q
.