Box_intersection_d/proximity_custom_box_traits.cpp

#include <CGAL/Simple_cartesian.h>
#include <CGAL/box_intersection_d.h>
#include <CGAL/point_generators_3.h>
#include <CGAL/algorithm.h>
#include <vector>
#include <algorithm>
#include <iterator>
#include <cmath>

typedef CGAL::Simple_cartesian<float>             Kernel;
typedef Kernel::Point_3                           Point_3;
typedef CGAL::Random_points_on_sphere_3<Point_3>  Points_on_sphere;

std::vector<Point_3>  points;
std::vector<Point_3*> boxes;     // boxes are just pointers to points
const float           eps = 0.1f; // finds point pairs of distance < 2*eps

// Boxes are just pointers to 3d points. The traits class adds the
// +- eps size to each interval around the point, effectively building
// on the fly a box of size 2*eps centered at the point.
struct Traits {
    typedef float          NT;
    typedef Point_3*       Box_parameter;
    typedef std::ptrdiff_t ID;

    static int   dimension() { return 3; }
    static float coord( Box_parameter b, int d) {
        return (d == 0) ? b->x() : ((d == 1) ? b->y() : b->z());
    }
    static float min_coord( Box_parameter b, int d) { return coord(b,d)-eps;}
    static float max_coord( Box_parameter b, int d) { return coord(b,d)+eps;}
    // id-function using address of current box,
    // requires to work with pointers to boxes later
    static std::ptrdiff_t id(Box_parameter b) { return (std::ptrdiff_t)(b); }
};

// callback function reports pairs in close proximity
void report( const Point_3* a, const Point_3* b) {
    float dist = std::sqrt( CGAL::squared_distance( *a, *b));
    if ( dist < 2*eps) {
        std::cout << "Point " << (a - &(points.front())) << " and Point "
                  << (b - &(points.front())) << " have distance " << dist
                  << "." << std::endl;
    }
}

int main() {
    // create some random points on the sphere of radius 1.0
    Points_on_sphere generator( 1.0);
    points.reserve( 50);
    for ( int i = 0; i != 50; ++i) {
        points.push_back( *generator++);
        boxes.push_back( & points.back());
    }

    // run the intersection algorithm and report proximity pairs
    CGAL::box_self_intersection_d( boxes.begin(), boxes.end(),
                                   report, Traits());
    return 0;
}