// 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.
//
// $URL$
// $Id$
// 
//
// Author(s)     : Stefan Schirra
 

#ifndef CGAL_HOMOGENEOUS_VECTOR_2_h
#define CGAL_HOMOGENEOUS_VECTOR_2_h

#include <CGAL/Origin.h>
#include <CGAL/Threetuple.h>

CGAL_BEGIN_NAMESPACE

template < class R_ >
class VectorH2
{
  typedef VectorH2<R_>                      Self;
  typedef typename R_::FT                   FT;
  typedef typename R_::RT                   RT;
  typedef typename R_::Point_2              Point_2;
  typedef typename R_::Segment_2            Segment_2;
  typedef typename R_::Ray_2                Ray_2;
  typedef typename R_::Line_2               Line_2;
  typedef typename R_::Direction_2          Direction_2;
  typedef typename R_::Vector_2             Vector_2;

  typedef Threetuple<RT>                           Rep;
  typedef typename R_::template Handle<Rep>::type  Base;

  typedef Rational_traits<FT>               Rat_traits;

  Base base;

public:
  typedef const FT Cartesian_coordinate_type;
  typedef const RT& Homogeneous_coordinate_type;
  typedef R_                                    R;

   VectorH2() {}

   VectorH2(int x, int y)
      : base(x, y, RT(1)) {}
  
   VectorH2(const RT& x, const RT& y)
      : base (x, y, RT(1)) {}

   VectorH2(const FT& x, const FT& y)
      : base(Rat_traits().numerator(x) * Rat_traits().denominator(y),
             Rat_traits().numerator(y) * Rat_traits().denominator(x),
             Rat_traits().denominator(x) * Rat_traits().denominator(y))
   {
     CGAL_kernel_assertion(hw() > 0);
   }

   VectorH2(const RT& x, const RT& y, const RT& w )
   {
     if ( w >= RT(0)   )
       base = Rep( x,  y,  w);
     else
       base = Rep(-x, -y, -w);
   }

  const Self&
  rep() const
  {
    return static_cast<const Self& >(*this);
  }
  
   bool    operator==( const VectorH2<R>& v) const;
   bool    operator!=( const VectorH2<R>& v) const;
   bool    operator==( const Null_vector&) const;
   bool    operator!=( const Null_vector& v) const;

   const RT & hx() const { return get(base).e0; };
   const RT & hy() const { return get(base).e1; };
   const RT & hw() const { return get(base).e2; };

   FT      x()  const { return FT(hx()) / FT(hw()); };
   FT      y()  const { return FT(hy()) / FT(hw()); };

   FT      cartesian(int i)   const;
   const RT & homogeneous(int i) const;
   FT      operator[](int i)  const;

   int     dimension() const;
   Direction_2 direction() const;
   Vector_2 perpendicular(const Orientation& o ) const;

  //   Vector_2 operator+(const VectorH2 &v) const;
   Vector_2 operator-(const VectorH2 &v) const;
   Vector_2 operator-() const;
   Vector_2 opposite() const;
   FT squared_length() const;
  //   Vector_2 operator/(const RT &f) const;
  //Vector_2 operator/(const FT &f) const;

// undocumented:
   VectorH2(const Direction_2 & dir)
      : base ( dir) {}

  VectorH2(const Point_2 & p)
     : base ( p) {}
};

template < class R >
inline
bool
VectorH2<R>::operator==( const Null_vector&) const
{ return (hx() == RT(0)) && (hy() == RT(0)); }

template < class R >
inline
bool
VectorH2<R>::operator!=( const Null_vector& v) const
{ return !(*this == v); }

template < class R >
CGAL_KERNEL_INLINE
bool
VectorH2<R>::operator==( const VectorH2<R>& v) const
{
  return (  (hx() * v.hw() == v.hx() * hw() )
          &&(hy() * v.hw() == v.hy() * hw() ) );
}

template < class R >
inline
bool
VectorH2<R>::operator!=( const VectorH2<R>& v) const
{ return !(*this == v); }  /* XXX */

template < class R >
CGAL_KERNEL_INLINE
typename VectorH2<R>::FT
VectorH2<R>::cartesian(int i) const
{
  CGAL_kernel_precondition( (i==0 || i==1) );
  if (i==0)
      return x();
  return y();
}

template < class R >
CGAL_KERNEL_INLINE
const typename VectorH2<R>::RT &
VectorH2<R>::homogeneous(int i) const
{
  CGAL_kernel_precondition( (i>=0) && (i<=2) );
  if (i==0)
      return hx();
  if (i==1)
      return hy();
  return hw();
}

template < class R >
inline
typename VectorH2<R>::FT
VectorH2<R>::operator[](int i) const
{ return cartesian(i); }

template < class R >
inline
int
VectorH2<R>::dimension() const
{ return 2; }

template < class R >
CGAL_KERNEL_INLINE
typename VectorH2<R>::Direction_2
VectorH2<R>::direction() const
{ return Direction_2(hx(), hy()); }

template < class R >
inline
typename VectorH2<R>::Vector_2
VectorH2<R>::operator-() const
{ return VectorH2<R>(- hx(), - hy(), hw() ); }

template < class R >
inline
typename VectorH2<R>::Vector_2
VectorH2<R>::opposite() const
{ return VectorH2<R>(- hx(), - hy(), hw() ); }


template <class R>
CGAL_KERNEL_INLINE
typename VectorH2<R>::Vector_2
VectorH2<R>::operator-(const VectorH2<R>& v) const
{
  return VectorH2<R>( hx()*v.hw() - v.hx()*hw(),
                      hy()*v.hw() - v.hy()*hw(),
                      hw()*v.hw() );
}

template <class R>
CGAL_KERNEL_INLINE
typename VectorH2<R>::FT
VectorH2<R>::squared_length() const
{
  typedef typename R::FT FT;
  return 
    FT( CGAL_NTS square(hx()) + CGAL_NTS square(hy()) ) / 
    FT( CGAL_NTS square(hw()) );
}


template < class R >
CGAL_KERNEL_INLINE
typename R::Vector_2
VectorH2<R>::perpendicular(const Orientation& o) const
{
  CGAL_kernel_precondition(o != COLLINEAR);
  if (o == COUNTERCLOCKWISE)
      return typename R::Vector_2(-hy(), hx(), hw());
  else
      return typename R::Vector_2(hy(), -hx(), hw());
}

CGAL_END_NAMESPACE

#endif // CGAL_HOMOGENEOUS_VECTOR_2_h