The function box_intersection_all_pairs_d computes the pairwise intersecting boxes between two sequences of isooriented boxes in arbitrary dimension. It does so by comparing all possible pairs of boxes and is thus inferior to the fast CGAL::box_intersection_d algorithm on page \icon.
The sequences of boxes are given with two forward iterator ranges. The sequences are not modified. For each intersecting pair of boxes a callback function object is called with the two intersecting boxes as argument; the first argument is a box from the first sequence, the second argument a box from the second sequence.
The algorithm is interface compatible with the CGAL::box_intersection_d function. Similarly, we call the value_type of the iterators the box handle, which is either our box type or a pointer type to our box type.
A $$ddimensional isooriented box is defined as the Cartesian product of $$d intervals. We call the box halfopen if the $$d intervals $${ [lo_{i},hi_{i})  0 i < d} are halfopen intervals, and we call the box closed if the $$d intervals $${ [lo_{i},hi_{i}]  0 i < d} are closed intervals. Note that closed boxes support zerowidth boxes and they can intersect at their boundaries, while nonempty halfopen boxes always have a positive volume and they only intersect iff their interiors overlap. The distinction between closed or halfopen boxes does not require a different representation of boxes, just a different interpretation when comparing boxes, which is selected with the topology parameter and its two values, CGAL::Box_intersection_d::HALF_OPEN and CGAL::Box_intersection_d::CLOSED.
In addition, a box has an unique idnumber. Boxes with equal idnumber are not reported since they obviously intersect trivially.
The algorithm uses a traits class of the BoxIntersectionTraits_d concept to access the boxes. A default traits class is provided that assumes that the box type is a model of the BoxIntersectionBox_d concept and that the box handle, i.e., the iterators value type, is identical to the box type or a pointer to the box type.
An important special application of this algorithm is the test for selfintersections where the second box sequence is an identical copy of the first sequence including the preserved idnumber. We offer a specialized implementation CGAL::box_self_intersection_all_pairs for this application.
#include <CGAL/box_intersection_d.h>
 

 
Invocation of box intersection with default box traits CGAL::Box_intersection_d::Box_traits_d<Box_handle>, where Box_handle corresponds to the iterator value type of ForwardIterator1.  
 

 
Invocation with custom box traits. 
CGAL::box_intersection_d
CGAL::box_self_intersection_d
CGAL::box_self_intersection_all_pairs_d
CGAL::Box_intersection_d::Box_traits_d<BoxHandle>
BoxIntersectionBox_d
BoxIntersectionTraits_d
The algorithm is trivially testing all pairs and runs therefore in time $$O(nm) where $$n is the size of the first sequence and $$m is the size of the second sequence.