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// Copyright (c) 1999 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.
//
// $URL: svn+ssh://scm.gforge.inria.fr/svn/cgal/branches/CGAL-3.5-branch/Homogeneous_kernel/include/CGAL/Homogeneous/basic_constructionsH3.h $
// $Id: basic_constructionsH3.h 42811 2008-04-09 13:35:34Z spion $
//
//
// Author(s) : Stefan Schirra
#ifndef CGAL_BASIC_CONSTRUCTIONSH3_H
#define CGAL_BASIC_CONSTRUCTIONSH3_H
CGAL_BEGIN_NAMESPACE
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); }
CGAL_END_NAMESPACE
#endif // CGAL_BASIC_CONSTRUCTIONSH3_H
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