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CGAL 4.13.2 - 3D Fast Intersection and Distance Computation (AABB Tree)
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CGAL 4.13.2 - 3D Fast Intersection and Distance Computation (AABB Tree)
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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 x-coordinates of two points. More... | |
| typedef unspecified_type | Less_y_3 |
| A functor object to compare the y-coordinates of two points. More... | |
| typedef unspecified_type | Less_z_3 |
| A functor object to compare the z-coordinates 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 andp2, and betweenp2andp3`.
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 x-coordinates of two points.
Provides the operator: bool operator()(const Point_3& p, const Point_3& q);} which returns true if the x-coordinate of p is smaller than the x-coordinate of q.
A functor object to compare the y-coordinates of two points.
Provides the operator: bool operator()(const Point_3& p, const Point_3& q);} which returns true if the y-coordinate of p is smaller than the y-coordinate of q.
A functor object to compare the z-coordinates of two points.
Provides the operator: bool operator()(const Point_3& p, const Point_3& q);} which returns true if the z-coordinate of p is smaller than the z-coordinate of q.
1.8.13