\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - Intersecting Sequences of dD Iso-oriented Boxes

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Box_intersection_d/custom_box_grid.cpp
#include <CGAL/box_intersection_d.h>
#include <vector>
#include <algorithm>
#include <iterator>
#include <cassert>
struct Box {
typedef int NT;
typedef std::ptrdiff_t ID;
int lo[2], hi[2];
Box( int lo0, int lo1, int hi0, int hi1) { lo[0]=lo0; lo[1]=lo1; hi[0]=hi0; hi[1]=hi1;}
static int dimension() { return 2; }
int min_coord(int dim) const { return lo[dim]; }
int max_coord(int dim) const { return hi[dim]; }
// id-function using address of current box,
// requires to work with pointers to boxes later
std::ptrdiff_t id() const { return (std::ptrdiff_t)(this); }
};
// 9 boxes of a grid
Box boxes[9] = { Box( 0,0,1,1), Box( 1,0,2,1), Box( 2,0,3,1), // low
Box( 0,1,1,2), Box( 1,1,2,2), Box( 2,1,3,2), // middle
Box( 0,2,1,3), Box( 1,2,2,3), Box( 2,2,3,3)};// upper
// 2 selected boxes as query; center and upper right
Box query[2] = { Box( 1,1,2,2), Box( 2,2,3,3)};
// With the special id-function we need to work on box pointers
Box* b_ptr[9] = { boxes, boxes+1, boxes+2, boxes+3, boxes+4, boxes+5,
boxes+6, boxes+7, boxes+8};
Box* q_ptr[2] = { query, query+1};
// callback function object writing results to an output iterator
template <class OutputIterator>
struct Report {
OutputIterator it;
Report( OutputIterator i) : it(i) {} // store iterator in object
// We write the position with respect to 'boxes' to the output iterator
// assuming that box b (the query box) is not interesting in the result.
void operator()( const Box* a, const Box*) {
*it++ = ( reinterpret_cast<Box*>(a->id()) - boxes);
}
};
template <class Iter> // helper function to create the function object
Report<Iter> report( Iter it) { return Report<Iter>(it); }
int main() {
// run the intersection algorithm and store results in a vector
std::vector<std::size_t> result;
CGAL::box_intersection_d( b_ptr, b_ptr+9, q_ptr, q_ptr+2,
report( std::back_inserter( result)),
std::ptrdiff_t(0));
// sort and check result
std::sort( result.begin(), result.end());
std::size_t chk[13] = {0,1,2,3,4,4,5,5,6,7,7,8,8};
assert( result.size()==13 && std::equal(chk,chk+13,result.begin()));
return 0;
}