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// Copyright (c) 2008 INRIA Sophia-Antipolis (France), ETH Zurich (Switzerland).
// Copyright (c) 2010, 2014 GeometryFactory Sarl (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org)
//
// $URL: https://github.com/CGAL/cgal/blob/v6.1/Intersections_3/include/CGAL/Intersections_3/internal/Line_3_Line_3_intersection.h $
// $Id: include/CGAL/Intersections_3/internal/Line_3_Line_3_intersection.h b26b07a1242 $
// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s) : Camille Wormser, Jane Tournois, Pierre Alliez
#ifndef CGAL_INTERNAL_INTERSECTIONS_3_LINE_3_LINE_3_INTERSECTION_H
#define CGAL_INTERNAL_INTERSECTIONS_3_LINE_3_LINE_3_INTERSECTION_H
#include <CGAL/Intersection_traits_3.h>
#include <CGAL/number_utils.h>
#include <CGAL/Uncertain.h>
namespace CGAL {
namespace Intersections {
namespace internal {
template <class K>
typename Intersection_traits<K, typename K::Line_3, typename K::Line_3>::result_type
intersection(const typename K::Line_3& l1,
const typename K::Line_3& l2,
const K& k)
{
typedef typename K::FT FT;
typedef typename K::Point_3 Point_3;
typedef typename K::Vector_3 Vector_3;
if(k.has_on_3_object()(l1, l2.point()))
{
const Vector_3& v1 = l1.to_vector();
const Vector_3& v2 = l2.to_vector();
if((v1.x() * v2.y() == v1.y() * v2.x()) &&
(v1.x() * v2.z() == v1.z() * v2.x()) &&
(v1.y() * v2.z() == v1.z() * v2.y()))
return intersection_return<typename K::Intersect_3, typename K::Line_3, typename K::Line_3>(l1);
}
if(k.are_parallel_3_object()(l1,l2))
return intersection_return<typename K::Intersect_3, typename K::Line_3, typename K::Line_3>();
const Point_3& p1 = l1.point();
const Point_3& p3 = l2.point();
const Vector_3& v1 = l1.to_vector();
const Vector_3& v2 = l2.to_vector();
const Point_3 p2 = p1 + v1;
const Point_3 p4 = p2 + v2;
if(!k.coplanar_3_object()(p1,p2,p3,p4))
return intersection_return<typename K::Intersect_3, typename K::Line_3, typename K::Line_3>();
const Vector_3 v3 = p3 - p1;
const Vector_3 v3v2 = cross_product(v3,v2);
const Vector_3 v1v2 = cross_product(v1,v2);
const FT sl = v1v2.squared_length();
if(certainly(is_zero(sl)))
return intersection_return<typename K::Intersect_3, typename K::Line_3, typename K::Line_3>();
const FT t = ((v3v2.x()*v1v2.x()) + (v3v2.y()*v1v2.y()) + (v3v2.z()*v1v2.z())) / sl;
return intersection_return<typename K::Intersect_3, typename K::Line_3, typename K::Line_3>(p1 + (v1 * t));
}
} // namespace internal
} // namespace Intersections
} // namespace CGAL
#endif // CGAL_INTERNAL_INTERSECTIONS_3_LINE_3_LINE_3_INTERSECTION_H
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