// Copyright (c) 1997-2004 Utrecht University (The Netherlands),
// ETH Zurich (Switzerland), Freie Universitaet Berlin (Germany),
// INRIA Sophia-Antipolis (France), Martin-Luther-University Halle-Wittenberg
// (Germany), Max-Planck-Institute Saarbruecken (Germany), RISC Linz (Austria),
// and Tel-Aviv University (Israel). All rights reserved.
//
// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public License as
// published by the Free Software Foundation; version 2.1 of the License.
// See the file LICENSE.LGPL distributed with CGAL.
//
// Licensees holding a valid commercial license may use this file in
// accordance with the commercial license agreement provided with the software.
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// $Source: /CVSROOT/CGAL/Packages/Intersections_3/include/CGAL/intersection_3_1.C,v $
// $Revision: 1.12 $ $Date: 2004/06/23 03:20:14 $
// $Name: $
//
// Author(s) : Geert-Jan Giezeman <geert@cs.uu.nl>
#include <CGAL/wmult.h>
CGAL_BEGIN_NAMESPACE
namespace CGALi {
template <class K>
Object
intersection(const typename CGAL_WRAP(K)::Plane_3 &plane,
const typename CGAL_WRAP(K)::Line_3 &line,
const K&)
{
typedef typename K::Point_3 Point_3;
typedef typename K::Direction_3 Direction_3;
typedef typename K::RT RT;
const Point_3 &line_pt = line.point();
const Direction_3 &line_dir = line.direction();
RT num, den;
num = plane.a()*line_pt.hx() + plane.b()*line_pt.hy()
+ plane.c()*line_pt.hz() + wmult((K*)0, plane.d(), line_pt.hw());
den = plane.a()*line_dir.dx() + plane.b()*line_dir.dy()
+ plane.c()*line_dir.dz();
if (den == RT(0)) {
if (num == RT(0)) {
// all line
return make_object(line);
} else {
// no intersection
return Object();
}
}
return make_object(Point_3(
den*line_pt.hx()-num*line_dir.dx(),
den*line_pt.hy()-num*line_dir.dy(),
den*line_pt.hz()-num*line_dir.dz(),
wmult((K*)0, den, line_pt.hw())));
}
template <class K>
inline
Object
intersection(const typename CGAL_WRAP(K)::Line_3 &line,
const typename CGAL_WRAP(K)::Plane_3 &plane,
const K& k)
{
return intersection(plane, line, k);
}
template <class K>
Object
intersection(const typename CGAL_WRAP(K)::Plane_3 &plane1,
const typename CGAL_WRAP(K)::Plane_3 &plane2,
const K&)
{
typedef typename K::Point_3 Point_3;
typedef typename K::Direction_3 Direction_3;
typedef typename K::Line_3 Line_3;
typedef typename K::RT RT;
const RT &a = plane1.a();
const RT &b = plane1.b();
const RT &c = plane1.c();
const RT &d = plane1.d();
const RT &p = plane2.a();
const RT &q = plane2.b();
const RT &r = plane2.c();
const RT &s = plane2.d();
const RT zero = RT(0);
RT det;
Point_3 is_pt;
Direction_3 is_dir;
det = a*q-p*b;
if (det != zero) {
is_pt = Point_3(b*s-d*q, p*d-a*s, zero, det);
is_dir = Direction_3(b*r-c*q, p*c-a*r, det);
return make_object(Line_3(is_pt, is_dir));
}
det = a*r-p*c;
if (det != zero) {
is_pt = Point_3(c*s-d*r, zero, p*d-a*s, det);
is_dir = Direction_3(c*q-b*r, det, p*b-a*q);
return make_object(Line_3(is_pt, is_dir));
}
det = b*r-c*q;
if (det != zero) {
is_pt = Point_3(zero, c*s-d*r, d*q-b*s, det);
is_dir = Direction_3(det, c*p-a*r, a*q-b*p);
return make_object(Line_3(is_pt, is_dir));
}
// degenerate case
if (a!=zero || p!=zero) {
if (a*s == p*d)
return make_object(plane1);
else
return Object();
}
if (b!=zero || q!=zero) {
if (b*s == q*d)
return make_object(plane1);
else
return Object();
}
if (c!=zero || r!=zero) {
if (c*s == r*d)
return make_object(plane1);
else
return Object();
}
return make_object(plane1);
}
template <class K>
Object
intersection(const typename CGAL_WRAP(K)::Plane_3 &plane1,
const typename CGAL_WRAP(K)::Plane_3 &plane2,
const typename CGAL_WRAP(K)::Plane_3 &plane3,
const K& k)
{
typedef typename K::Line_3 Line_3;
typedef typename K::Plane_3 Plane_3;
// Intersection between plane1 and plane2 can either be
// a line, a plane, or empty.
Object o12 = CGALi::intersection(plane1, plane2, k);
Line_3 l;
if (assign(l, o12))
return CGALi::intersection(plane3, l, k);
Plane_3 pl;
if (assign(pl, o12))
return CGALi::intersection(plane3, pl, k);
return Object();
}
template <class K>
bool
do_intersect(const typename CGAL_WRAP(K)::Plane_3 &plane,
const typename CGAL_WRAP(K)::Line_3 &line,
const K&)
{
typedef typename K::Point_3 Point_3;
typedef typename K::Direction_3 Direction_3;
typedef typename K::RT RT;
const Point_3 &line_pt = line.point();
const Direction_3 &line_dir = line.direction();
RT num, den;
den = plane.a()*line_dir.dx() + plane.b()*line_dir.dy()
+ plane.c()*line_dir.dz();
if (den != RT(0))
return true;
num = plane.a()*line_pt.hx() + plane.b()*line_pt.hy()
+ plane.c()*line_pt.hz() + wmult((K*)0, plane.d(), line_pt.hw());
if (num == RT(0)) {
// all line
return true;
} else {
// no intersection
return false;
}
}
template <class K>
inline
bool
do_intersect(const typename CGAL_WRAP(K)::Line_3 &line,
const typename CGAL_WRAP(K)::Plane_3 &plane,
const K& k)
{
return do_intersect(plane, line, k);
}
template <class K>
Object
intersection(const typename CGAL_WRAP(K)::Plane_3 &plane,
const typename CGAL_WRAP(K)::Ray_3 &ray,
const K& k)
{
typedef typename K::Point_3 Point_3;
const Object line_intersection =
intersection(plane, ray.supporting_line(), k);
Point_3 isp;
if (assign(isp, line_intersection)) {
if (ray.collinear_has_on(isp))
return line_intersection;
else
return Object();
}
if (line_intersection.is_empty())
return line_intersection;
return make_object(ray);
}
template <class K>
inline
Object
intersection(const typename CGAL_WRAP(K)::Ray_3 &ray,
const typename CGAL_WRAP(K)::Plane_3 &plane,
const K& k)
{
return intersection(plane, ray, k);
}
template <class K>
bool
do_intersect(const typename CGAL_WRAP(K)::Plane_3 &plane,
const typename CGAL_WRAP(K)::Ray_3 &ray,
const K& k)
{
typedef typename K::Point_3 Point_3;
const Object line_intersection =
intersection(plane, ray.supporting_line(), k);
if (line_intersection.is_empty())
return false;
Point_3 isp;
if (assign(isp, line_intersection)) {
if (ray.collinear_has_on(isp))
return true;
else
return false;
}
return true;
}
template <class K>
inline
bool
do_intersect(const typename CGAL_WRAP(K)::Ray_3 &ray,
const typename CGAL_WRAP(K)::Plane_3 &plane,
const K& k)
{
return do_intersect(plane, ray, k);
}
template <class K>
Object
intersection(const typename CGAL_WRAP(K)::Plane_3 &plane,
const typename CGAL_WRAP(K)::Segment_3 &seg,
const K& k)
{
typedef typename K::Point_3 Point_3;
const Point_3 &source = seg.source();
const Point_3 &target = seg.target();
Oriented_side source_side,target_side;
source_side = plane.oriented_side(source);
target_side = plane.oriented_side(target);
switch (source_side) {
case ON_ORIENTED_BOUNDARY:
if (target_side == ON_ORIENTED_BOUNDARY)
return make_object(seg);
else
return make_object(source);
case ON_POSITIVE_SIDE:
switch (target_side) {
case ON_ORIENTED_BOUNDARY:
return make_object(target);
case ON_POSITIVE_SIDE:
return Object();
case ON_NEGATIVE_SIDE:
return intersection(plane, seg.supporting_line(), k);
}
case ON_NEGATIVE_SIDE:
switch (target_side) {
case ON_ORIENTED_BOUNDARY:
return make_object(target);
case ON_POSITIVE_SIDE:
return intersection(plane, seg.supporting_line(), k);
case ON_NEGATIVE_SIDE:
return Object();
}
}
CGAL_kernel_assertion_msg(false, "Supposedly unreachable code.");
return Object();
}
template <class K>
inline
Object
intersection(const typename CGAL_WRAP(K)::Segment_3 &seg,
const typename CGAL_WRAP(K)::Plane_3 &plane,
const K& k)
{
return intersection(plane, seg, k);
}
template <class K>
bool
do_intersect(const typename CGAL_WRAP(K)::Plane_3 &plane,
const typename CGAL_WRAP(K)::Segment_3 &seg,
const K&)
{
typedef typename K::Point_3 Point_3;
const Point_3 &source = seg.source();
const Point_3 &target = seg.target();
Oriented_side source_side,target_side;
source_side = plane.oriented_side(source);
target_side = plane.oriented_side(target);
if ( source_side == target_side
&& target_side != ON_ORIENTED_BOUNDARY) {
return false;
}
return true;
}
template <class K>
inline
bool
do_intersect(const typename CGAL_WRAP(K)::Segment_3 &seg,
const typename CGAL_WRAP(K)::Plane_3 &plane,
const K& k)
{
return do_intersect(plane, seg, k);
}
template <class K>
Object
intersection(const typename CGAL_WRAP(K)::Line_3 &line,
const Bbox_3 &box,
const K&)
{
typedef typename K::Point_3 Point_3;
typedef typename K::Direction_3 Direction_3;
const Point_3 &linepoint = line.point();
const Direction_3 &linedir = line.direction();
return intersection_bl(box,
CGAL::to_double(linepoint.x()),
CGAL::to_double(linepoint.y()),
CGAL::to_double(linepoint.z()),
CGAL::to_double(linedir.dx()),
CGAL::to_double(linedir.dy()),
CGAL::to_double(linedir.dz()),
true, true
);
}
template <class K>
inline
Object
intersection(const Bbox_3 &box,
const typename CGAL_WRAP(K)::Line_3 &line,
const K& k)
{
return intersection(line, box, k);
}
template <class K>
Object
intersection(const typename CGAL_WRAP(K)::Ray_3 &ray,
const Bbox_3 &box,
const K&)
{
typedef typename K::Point_3 Point_3;
typedef typename K::Direction_3 Direction_3;
const Point_3 &linepoint = ray.source();
const Direction_3 &linedir = ray.direction();
return intersection_bl(box,
CGAL::to_double(linepoint.x()),
CGAL::to_double(linepoint.y()),
CGAL::to_double(linepoint.z()),
CGAL::to_double(linedir.dx()),
CGAL::to_double(linedir.dy()),
CGAL::to_double(linedir.dz()),
false, true
);
}
template <class K>
inline
Object
intersection(const Bbox_3 &box,
const typename CGAL_WRAP(K)::Ray_3 &ray,
const K& k)
{
return intersection(ray, box, k);
}
template <class K>
Object
intersection(const typename CGAL_WRAP(K)::Segment_3 &seg,
const Bbox_3 &box,
const K&)
{
typedef typename K::Point_3 Point_3;
typedef typename K::Vector_3 Vector_3;
const Point_3 &linepoint = seg.source();
const Vector_3 &diffvec = seg.target()-linepoint;
return intersection_bl(box,
CGAL::to_double(linepoint.x()),
CGAL::to_double(linepoint.y()),
CGAL::to_double(linepoint.z()),
CGAL::to_double(diffvec.x()),
CGAL::to_double(diffvec.y()),
CGAL::to_double(diffvec.z()),
false, false
);
}
template <class K>
inline
Object
intersection(const Bbox_3 &box,
const typename CGAL_WRAP(K)::Segment_3 &seg,
const K& k)
{
return intersection(seg, box, k);
}
template <class K>
Object
intersection(const typename CGAL_WRAP(K)::Line_3 &line,
const typename CGAL_WRAP(K)::Iso_cuboid_3 &box,
const K&)
{
typedef typename K::Point_3 Point_3;
typedef typename K::Vector_3 Vector_3;
typedef typename K::Segment_3 Segment_3;
typedef typename K::RT RT;
typedef typename K::FT FT;
bool all_values = true;
FT _min, _max;
Point_3 const & _ref_point=line.point();
Vector_3 const & _dir=line.direction().vector();
Point_3 const & _iso_min=box.min();
Point_3 const & _iso_max=box.max();
int i;
for (i=0; i< _ref_point.dimension(); i++) {
if (_dir.homogeneous(i) == RT(0)) {
if (_ref_point.cartesian(i) < _iso_min.cartesian(i)) {
return Object();
}
if (_ref_point.cartesian(i) > _iso_max.cartesian(i)) {
return Object();
}
} else {
FT newmin, newmax;
if (_dir.homogeneous(i) > RT(0)) {
newmin = (_iso_min.cartesian(i) - _ref_point.cartesian(i)) /
_dir.cartesian(i);
newmax = (_iso_max.cartesian(i) - _ref_point.cartesian(i)) /
_dir.cartesian(i);
} else {
newmin = (_iso_max.cartesian(i) - _ref_point.cartesian(i)) /
_dir.cartesian(i);
newmax = (_iso_min.cartesian(i) - _ref_point.cartesian(i)) /
_dir.cartesian(i);
}
if (all_values) {
_min = newmin;
_max = newmax;
} else {
if (newmin > _min)
_min = newmin;
if (newmax < _max)
_max = newmax;
if (_max < _min) {
return Object();
}
}
all_values = false;
}
}
CGAL_kernel_assertion(!all_values);
if (_max == _min) {
return make_object(Point_3(_ref_point + _dir * _min ));
}
return make_object(
Segment_3(_ref_point + _dir*_min, _ref_point + _dir*_max));
}
template <class K>
inline
Object
intersection(const typename CGAL_WRAP(K)::Iso_cuboid_3 &box,
const typename CGAL_WRAP(K)::Line_3 &line,
const K& k)
{
return intersection(line, box, k);
}
template <class K>
Object
intersection(const typename CGAL_WRAP(K)::Ray_3 &ray,
const typename CGAL_WRAP(K)::Iso_cuboid_3 &box,
const K&)
{
typedef typename K::Point_3 Point_3;
typedef typename K::Vector_3 Vector_3;
typedef typename K::Segment_3 Segment_3;
typedef typename K::RT RT;
typedef typename K::FT FT;
bool all_values = true;
FT _min= FT(0), _max;
Point_3 const & _ref_point=ray.source();
Vector_3 const & _dir=ray.direction().vector();
Point_3 const & _iso_min=box.min();
Point_3 const & _iso_max=box.max();
int i;
for (i=0; i< _ref_point.dimension(); i++) {
if (_dir.homogeneous(i) == RT(0)) {
if (_ref_point.cartesian(i) < _iso_min.cartesian(i)) {
return Object();
}
if (_ref_point.cartesian(i) > _iso_max.cartesian(i)) {
return Object();
}
} else {
FT newmin, newmax;
if (_dir.homogeneous(i) > RT(0)) {
newmin = (_iso_min.cartesian(i) - _ref_point.cartesian(i)) /
_dir.cartesian(i);
newmax = (_iso_max.cartesian(i) - _ref_point.cartesian(i)) /
_dir.cartesian(i);
} else {
newmin = (_iso_max.cartesian(i) - _ref_point.cartesian(i)) /
_dir.cartesian(i);
newmax = (_iso_min.cartesian(i) - _ref_point.cartesian(i)) /
_dir.cartesian(i);
}
if (all_values) {
_max = newmax;
} else {
if (newmax < _max)
_max = newmax;
}
if (newmin > _min)
_min = newmin;
if (_max < _min)
return Object();
all_values = false;
}
}
CGAL_kernel_assertion(!all_values);
if (_max == _min) {
return make_object(Point_3(_ref_point + _dir * _min ));
}
return make_object(
Segment_3(_ref_point + _dir*_min, _ref_point + _dir*_max));
}
template <class K>
inline
Object
intersection(const typename CGAL_WRAP(K)::Iso_cuboid_3 &box,
const typename CGAL_WRAP(K)::Ray_3 &ray,
const K& k)
{
return intersection(ray, box, k);
}
template <class K>
Object
intersection(const typename CGAL_WRAP(K)::Segment_3 &seg,
const typename CGAL_WRAP(K)::Iso_cuboid_3 &box,
const K&)
{
typedef typename K::Point_3 Point_3;
typedef typename K::Vector_3 Vector_3;
typedef typename K::Segment_3 Segment_3;
typedef typename K::RT RT;
typedef typename K::FT FT;
FT _min= FT(0), _max;
Point_3 const & _ref_point=seg.source();
Vector_3 const & _dir=seg.direction().vector();
Point_3 const & _iso_min=box.min();
Point_3 const & _iso_max=box.max();
int main_dir =
(CGAL_NTS abs(_dir.x()) > CGAL_NTS abs(_dir.y()) )
? (CGAL_NTS abs(_dir.x()) > CGAL_NTS abs(_dir.z()) ? 0 : 2)
: (CGAL_NTS abs(_dir.y()) > CGAL_NTS abs(_dir.z()) ? 1 : 2);
_max = (seg.target().cartesian(main_dir)-_ref_point.cartesian(main_dir)) /
_dir.cartesian(main_dir);
int i;
for (i=0; i< _ref_point.dimension(); i++) {
if (_dir.homogeneous(i) == RT(0)) {
if (_ref_point.cartesian(i) < _iso_min.cartesian(i)) {
return Object();
}
if (_ref_point.cartesian(i) > _iso_max.cartesian(i)) {
return Object();
}
} else {
FT newmin, newmax;
if (_dir.homogeneous(i) > RT(0)) {
newmin = (_iso_min.cartesian(i) - _ref_point.cartesian(i)) /
_dir.cartesian(i);
newmax = (_iso_max.cartesian(i) - _ref_point.cartesian(i)) /
_dir.cartesian(i);
} else {
newmin = (_iso_max.cartesian(i) - _ref_point.cartesian(i)) /
_dir.cartesian(i);
newmax = (_iso_min.cartesian(i) - _ref_point.cartesian(i)) /
_dir.cartesian(i);
}
if (newmax < _max)
_max = newmax;
if (newmin > _min)
_min = newmin;
if (_max < _min)
return Object();
}
}
if (_max == _min) {
return make_object(Point_3(_ref_point + _dir * _min ));
}
return make_object(
Segment_3(_ref_point + _dir*_min, _ref_point + _dir*_max));
}
template <class K>
inline
Object
intersection(const typename CGAL_WRAP(K)::Iso_cuboid_3 &box,
const typename CGAL_WRAP(K)::Segment_3 &seg,
const K& k)
{
return intersection(seg, box, k);
}
template <class K>
Object
intersection(
const typename CGAL_WRAP(K)::Iso_cuboid_3 &icub1,
const typename CGAL_WRAP(K)::Iso_cuboid_3 &icub2,
const K&)
{
typedef typename K::Point_3 Point_3;
typedef typename K::Iso_cuboid_3 Iso_cuboid_3;
Point_3 min_points[2];
Point_3 max_points[2];
min_points[0] = icub1.min();
min_points[1] = icub2.min();
max_points[0] = icub1.max();
max_points[1] = icub2.max();
typedef typename K::FT FT;
const int DIM = 3;
int min_idx[DIM];
int max_idx[DIM];
Point_3 newmin;
Point_3 newmax;
for (int dim = 0; dim < DIM; ++dim) {
min_idx[dim] =
min_points[0].cartesian(dim) >= min_points[1].cartesian(dim) ? 0 : 1;
max_idx[dim] =
max_points[0].cartesian(dim) <= max_points[1].cartesian(dim) ? 0 : 1;
if (min_idx[dim] != max_idx[dim]
&& max_points[max_idx[dim]].cartesian(dim)
< min_points[min_idx[dim]].cartesian(dim))
return Object();
}
if (min_idx[0] == min_idx[1] && min_idx[0] == min_idx[2]) {
newmin = min_points[min_idx[0]];
} else {
newmin = Point_3(
min_idx[0] == 0
? wmult((K*)0, min_points[0].hx(), min_points[1].hw())
: wmult((K*)0, min_points[1].hx(), min_points[0].hw())
,
min_idx[1] == 0
? wmult((K*)0, min_points[0].hy(), min_points[1].hw())
: wmult((K*)0, min_points[1].hy(), min_points[0].hw())
,
min_idx[2] == 0
? wmult((K*)0, min_points[0].hz(), min_points[1].hw())
: wmult((K*)0, min_points[1].hz(), min_points[0].hw())
,
wmult((K*)0, min_points[0].hw(), min_points[1].hw()) );
}
if (max_idx[0] == max_idx[1] && max_idx[0] == max_idx[2]) {
newmax = max_points[max_idx[0]];
} else {
newmax = Point_3(
max_idx[0] == 0
? wmult((K*)0, max_points[0].hx(), max_points[1].hw())
: wmult((K*)0, max_points[1].hx(), max_points[0].hw())
,
max_idx[1] == 0
? wmult((K*)0, max_points[0].hy(), max_points[1].hw())
: wmult((K*)0, max_points[1].hy(), max_points[0].hw())
,
max_idx[2] == 0
? wmult((K*)0, max_points[0].hz(), max_points[1].hw())
: wmult((K*)0, max_points[1].hz(), max_points[0].hw())
,
wmult((K*)0, max_points[0].hw(), max_points[1].hw()) );
}
Object result = make_object(Iso_cuboid_3(newmin, newmax));
return result;
}
} // namespace CGALi
template <class K>
inline
Object
intersection(const Plane_3<K> &plane1, const Plane_3<K> &plane2)
{
return typename K::Intersect_3()(plane1, plane2);
}
template <class K>
inline
Object
intersection(const Plane_3<K> &plane1, const Plane_3<K> &plane2,
const Plane_3<K> &plane3)
{
return typename K::Intersect_3()(plane1, plane2, plane3);
}
template <class K>
inline
Object
intersection(const Plane_3<K> &plane, const Line_3<K> &line)
{
return typename K::Intersect_3()(plane, line);
}
template <class K>
inline
bool
do_intersect(const Plane_3<K> &plane, const Line_3<K> &line)
{
return typename K::Do_intersect_3()(plane, line);
}
template <class K>
inline
Object
intersection(const Plane_3<K> &plane, const Ray_3<K> &ray)
{
return typename K::Intersect_3()(plane, ray);
}
template <class K>
inline
bool
do_intersect(const Plane_3<K> &plane, const Ray_3<K> &ray)
{
return typename K::Do_intersect_3()(plane, ray);
}
template <class K>
inline
Object
intersection(const Plane_3<K> &plane, const Segment_3<K> &seg)
{
return typename K::Intersect_3()(plane, seg);
}
template <class K>
inline
bool
do_intersect(const Plane_3<K> &plane, const Segment_3<K> &seg)
{
return typename K::Do_intersect_3()(plane, seg);
}
template <class K>
inline
Object
intersection(const Line_3<K> &line,
const Bbox_3 &box)
{
return typename K::Intersect_3()(line, box);
}
template <class K>
inline
Object
intersection(const Ray_3<K> &ray,
const Bbox_3 &box)
{
return typename K::Intersect_3()(ray, box);
}
template <class K>
inline
Object
intersection(const Segment_3<K> &seg,
const Bbox_3 &box)
{
return typename K::Intersect_3()(seg, box);
}
template <class K>
inline
Object
intersection(const Line_3<K> &line,
const Iso_cuboid_3<K> &box)
{
return typename K::Intersect_3()(line, box);
}
template <class K>
inline
Object
intersection(const Ray_3<K> &ray,
const Iso_cuboid_3<K> &box)
{
return typename K::Intersect_3()(ray, box);
}
template <class K>
inline
Object
intersection(const Segment_3<K> &seg,
const Iso_cuboid_3<K> &box)
{
return typename K::Intersect_3()(seg, box);
}
template <class K>
inline
Object
intersection(const Iso_cuboid_3<K> &icub1,
const Iso_cuboid_3<K> &icub2)
{
return typename K::Intersect_3()(icub1, icub2);
}
CGAL_END_NAMESPACE
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