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CGAL 5.5.1 - Intersecting Sequences of dD Iso-oriented Boxes
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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 box_intersection_d() algorithm.

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 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 d-dimensional iso-oriented box is defined as the Cartesian product of d intervals. We call the box half-open if the d intervals \{ [lo_i,hi_i) \,|\, 0 \leq i < d\} are half-open intervals, and we call the box closed if the d intervals \{ [lo_i,hi_i] \,|\, 0 \leq i < d\} 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, Box_intersection_d::HALF_OPEN and Box_intersection_d::CLOSED.

In addition, a box has a 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 box_self_intersection_all_pairs_d() for this application.

Requirements

See also
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

Implementation

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.

Functions

template<class ForwardIterator1 , class ForwardIterator2 , class Callback >
void CGAL::box_intersection_all_pairs_d (ForwardIterator1 begin1, ForwardIterator1 end1, ForwardIterator2 begin2, ForwardIterator2 end2, Callback callback, CGAL::Box_intersection_d::Topology topology=CGAL::Box_intersection_d::CLOSED)
 Invocation of box intersection with default box traits Box_intersection_d::Box_traits_d<Box_handle>, where Box_handle corresponds to the iterator value type of ForwardIterator1.
 
template<class ForwardIterator1 , class ForwardIterator2 , class Callback , class BoxTraits >
void CGAL::box_intersection_all_pairs_d (ForwardIterator1 begin1, ForwardIterator1 end1, ForwardIterator2 begin2, ForwardIterator2 end2, Callback callback, BoxTraits box_traits, CGAL::Box_intersection_d::Topology topology=CGAL::Box_intersection_d::CLOSED)
 Invocation with custom box traits.