// 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.
//
// $Source: /CVSROOT/CGAL/Packages/H2/include/CGAL/Homogeneous/basic_constructionsH2.h,v $
// $Revision: 1.13 $ $Date: 2004/03/13 14:15:01 $
// $Name:  $
//
// Author(s)     : Sven Schoenherr
//                 Stefan Schirra
 

#ifndef CGAL_BASIC_CONSTRUCTIONSH2_H
#define CGAL_BASIC_CONSTRUCTIONSH2_H

#include <CGAL/Homogeneous/PointH2.h>
#include <CGAL/Homogeneous/LineH2.h>

CGAL_BEGIN_NAMESPACE

template <class R>
CGAL_KERNEL_MEDIUM_INLINE
typename R::Point_2
gp_linear_intersection(const LineH2<R>& l1, const LineH2<R>& l2)
{
  return typename R::Point_2( l1.b()*l2.c() - l2.b()*l1.c(),
                              l2.a()*l1.c() - l1.a()*l2.c(),
                              l1.a()*l2.b() - l2.a()*l1.b() );
}

template <class R>
CGAL_KERNEL_MEDIUM_INLINE
typename R::FT
squared_distance( const PointH2<R>& p, const PointH2<R>& q )
{
  typedef typename R::RT RT;
  typedef typename R::FT FT;

  const RT & phx = p.hx();
  const RT & phy = p.hy();
  const RT & phw = p.hw();
  const RT & qhx = q.hx();
  const RT & qhy = q.hy();
  const RT & qhw = q.hw();

  RT sq_dist_numerator =
          phx * phx * qhw * qhw
    - RT(2) * phx * qhx * phw * qhw
    +     qhx * qhx * phw * phw

    +     phy * phy * qhw * qhw
    - RT(2) * phy * qhy * phw * qhw
    +     qhy * qhy * phw * phw ;

  RT sq_dist_denominator = qhw * qhw * phw * phw ;

  return FT( sq_dist_numerator ) / FT( sq_dist_denominator );
}

CGAL_END_NAMESPACE

#endif // CGAL_BASIC_CONSTRUCTIONSH2_H