struct Distance {
  typedef Point Query_item;

  double transformed_distance(const Point& p1, const Point& p2) const {
    double distx= p1.x()-p2.x();
    double disty= p1.y()-p2.y();
    double distz= p1.z()-p2.z();
    return distx*distx+disty*disty+distz*distz;
  }

  template <class TreeTraits>
  double min_distance_to_rectangle(const Point& p,
				   const CGAL::Kd_tree_rectangle<TreeTraits>& b) const {   
    double distance(0.0), h = p.x();
    if (h < b.min_coord(0)) distance += (b.min_coord(0)-h)*(b.min_coord(0)-h);
    if (h > b.max_coord(0)) distance += (h-b.max_coord(0))*(h-b.max_coord(0));
    h=p.y();
    if (h < b.min_coord(1)) distance += (b.min_coord(1)-h)*(b.min_coord(1)-h);
    if (h > b.max_coord(1)) distance += (h-b.max_coord(1))*(h-b.min_coord(1));
    h=p.z();
    if (h < b.min_coord(2)) distance += (b.min_coord(2)-h)*(b.min_coord(2)-h);
    if (h > b.max_coord(2)) distance += (h-b.max_coord(2))*(h-b.max_coord(2));
    return distance;
  }
  
  template <class TreeTraits>
  double max_distance_to_rectangle(const Point& p,
				   const CGAL::Kd_tree_rectangle<TreeTraits>& b) const {   
    double h = p.x();

    double d0 = (h >= (b.min_coord(0)+b.max_coord(0))/2.0) ?
                (h-b.min_coord(0))*(h-b.min_coord(0)) : (b.max_coord(0)-h)*(b.max_coord(0)-h);
    
    h=p.y();
    double d1 = (h >= (b.min_coord(1)+b.max_coord(1))/2.0) ?
                (h-b.min_coord(1))*(h-b.min_coord(1)) : (b.max_coord(1)-h)*(b.max_coord(1)-h);
    h=p.z();
    double d2 = (h >= (b.min_coord(2)+b.max_coord(2))/2.0) ?
                (h-b.min_coord(2))*(h-b.min_coord(2)) : (b.max_coord(2)-h)*(b.max_coord(2)-h);
    return d0 + d1 + d2;
  }
  
  double new_distance(double& dist, double old_off, double new_off,
		      int cutting_dimension)  const {
    return dist + new_off*new_off - old_off*old_off;
  }
  
  double transformed_distance(double d) const { return d*d; }
  
  double inverse_of_transformed_distance(double d) { return sqrt(d); }
  
}; // end of struct Distance