CGAL 5.3 - Intersecting Sequences of dD Iso-oriented Boxes
CGAL::box_self_intersection_all_pairs_d()

The function box_self_intersection_all_pairs_d() computes the pairwise intersecting boxes in a sequence 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_self_intersection_d() algorithm.

The sequence of boxes is given with a forward iterator range. The sequence is 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 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 $$d$$-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.

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.

Requirements

• ForwardIter must meet the requirements of ForwardIterator. We call its value type Box_handle in the following.
• Callback must be of the BinaryFunction concept. The Box_handle must be convertible to both argument types. The return type is not used and can be void.
• The Box_handle must be a model of the Assignable concept.
• In addition, if the default box traits is used the Box_handle must be a class type T or a pointer to a class type T, where T must be a model of the BoxIntersectionBox_d concept. In both cases, the default box traits specializes to a suitable implementation.
• BoxTraits must be of the BoxIntersectionTraits_d concept.
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

Implementation

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 id-number of the boxes.

## Functions

template<class ForwardIter , class Callback >
void CGAL::box_self_intersection_all_pairs_d (ForwardIter begin, ForwardIter end, 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 ForwardIter.

template<class ForwardIter , class Callback , class BoxTraits >
void CGAL::box_self_intersection_all_pairs_d (ForwardIter begin, ForwardIter end, Callback callback, BoxTraits box_traits, CGAL::Box_intersection_d::Topology topology=CGAL::Box_intersection_d::CLOSED)
Invocation with custom box traits.