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// Copyright (c) 1999
// Utrecht University (The Netherlands),
// ETH Zurich (Switzerland),
// INRIA Sophia-Antipolis (France),
// Max-Planck-Institute Saarbruecken (Germany),
// and Tel-Aviv University (Israel). All rights reserved.
//
// This file is part of CGAL (www.cgal.org)
//
// $URL: https://github.com/CGAL/cgal/blob/v6.0.1/Homogeneous_kernel/include/CGAL/Homogeneous/basic_constructionsH3.h $
// $Id: include/CGAL/Homogeneous/basic_constructionsH3.h 50cfbde3b84 $
// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s) : Stefan Schirra
#ifndef CGAL_BASIC_CONSTRUCTIONSH3_H
#define CGAL_BASIC_CONSTRUCTIONSH3_H
#include <CGAL/Cartesian/Point_3.h>
#include <CGAL/Cartesian/Plane_3.h>
namespace CGAL {
template <class R>
typename R::Point_3
_projection(const typename R::Point_3& p, const PlaneH3<R>& pl)
{
typedef typename R::RT RT;
if ( pl.has_on(p) ) return p;
RT A = pl.a();
RT B = pl.b();
RT C = pl.c();
RT D = pl.d();
RT phx = p.hx();
RT phy = p.hy();
RT phz = p.hz();
RT phw = p.hw();
RT num = A * phx + B * phy + C * phz + D * phw;
RT den = A * A + B * B + C * C;
return typename R::Point_3( num * A - den * phx,
num * B - den * phy,
num * C - den * phz,
-den );
}
template <class R>
typename R::Point_3
gp_linear_intersection(const PlaneH3<R> &f,
const PlaneH3<R> &g,
const PlaneH3<R> &h)
{
typedef typename R::RT RT;
return typename R::Point_3(
determinant<RT>(-f.d(), f.b(), f.c(),
-g.d(), g.b(), g.c(),
-h.d(), h.b(), h.c()),
determinant<RT>( f.a(),-f.d(), f.c(),
g.a(),-g.d(), g.c(),
h.a(),-h.d(), h.c()),
determinant<RT>( f.a(), f.b(),-f.d(),
g.a(), g.b(),-g.d(),
h.a(), h.b(),-h.d()),
determinant<RT>( f.a(), f.b(), f.c(),
g.a(), g.b(), g.c(),
h.a(), h.b(), h.c()));
}
template <class R>
CGAL_KERNEL_INLINE
typename R::FT
squared_distance( PointH3<R> const& p, PointH3<R> const& q)
{ return (p-q)*(p-q); }
} //namespace CGAL
#endif // CGAL_BASIC_CONSTRUCTIONSH3_H
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