The function box_self_intersection_all_pairs_d computes the pairwise intersecting boxes in a sequence 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_self_intersection_d algorithm on page \icon.
The sequence of boxes is given with a forward iterator range. 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 algorithm is interface compatible with the CGAL::box_self_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.
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.
#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 ForwardIterator.  
 

 
Invocation with custom box traits. 
CGAL::box_intersection_d
CGAL::box_self_intersection_d
CGAL::box_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 $$O(n^{2}) where $$n is the size of the input sequence. This algorithm does not use the idnumber of the boxes.