The function box_intersection_all_pairs_d computes the pairwise intersecting boxes between two sequences of iso-oriented 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 -dimensional iso-oriented box is defined as the Cartesian product of intervals. We call the box half-open if the intervals are half-open intervals, and we call the box closed if the intervals are closed intervals. Note that closed boxes support zero-width boxes and they can intersect at their boundaries, while non-empty half-open boxes always have a positive volume and they only intersect iff their interiors overlap. The distinction between closed or half-open 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 id-number. Boxes with equal id-number 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 self-intersections where the second box sequence is an identical copy of the first sequence including the preserved id-number. We offer a specialized implementation CGAL::box_self_intersection_all_pairs for this application.
|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.|
The algorithm is trivially testing all pairs and runs therefore in time where is the size of the first sequence and is the size of the second sequence.