// ======================================================================
//
// Copyright (c) 1999 The CGAL Consortium
//
// This software and related documentation is part of an INTERNAL release
// of the Computational Geometry Algorithms Library (CGAL). It is not
// intended for general use.
//
// ----------------------------------------------------------------------
// 
// release       : 
// release_date  : 
// 
// file          : include/CGAL/Homogeneous/predicates_on_rtH2.h
// revision      : $Revision$
// revision_date : $Date$
// author(s)     : Stefan Schirra
//
// coordinator   : MPI, Saarbruecken
// ======================================================================
 

#ifndef CGAL_PREDICATES_ON_RTH2_H
#define CGAL_PREDICATES_ON_RTH2_H

CGAL_BEGIN_NAMESPACE

template <class RT>
CGAL_KERNEL_INLINE
Orientation
orientationH2( const RT& phx, const RT& phy, const RT& phw,
               const RT& qhx, const RT& qhy, const RT& qhw,
               const RT& rhx, const RT& rhy, const RT& rhw )
{
  const RT  RT0 = RT(0);
  
  // | A B |
  // | C D |
  
  RT  A = phx*rhw - phw*rhx;
  RT  B = phy*rhw - phw*rhy;
  RT  C = qhx*rhw - qhw*rhx;
  RT  D = qhy*rhw - qhw*rhy;
  
  RT  det =  A*D - B*C;
  
  
  if (det < RT0  )
  {
      return CLOCKWISE;
  }
  else
  {
      return (RT0 < det) ? COUNTERCLOCKWISE : COLLINEAR;
  }
}

template <class RT>
CGAL_KERNEL_INLINE
bool
left_turnH2( const RT& phx, const RT& phy, const RT& phw,
             const RT& qhx, const RT& qhy, const RT& qhw,
             const RT& rhx, const RT& rhy, const RT& rhw )
{
  const RT  RT0 = RT(0);
  
  // | A B |
  // | C D |
  
  RT  A = phx*rhw - phw*rhx;
  RT  B = phy*rhw - phw*rhy;
  RT  C = qhx*rhw - qhw*rhx;
  RT  D = qhy*rhw - qhw*rhy;
  
  RT  det =  A*D - B*C;
  
  
  return ( RT0 < det );
}

#ifndef CGAL_NO_DEPRECATED_CODE
template <class RT>
inline
bool
leftturnH2( const RT& phx, const RT& phy, const RT& phw,
            const RT& qhx, const RT& qhy, const RT& qhw,
            const RT& rhx, const RT& rhy, const RT& rhw )
{
   return left_turnH2(phx, phy, phw, qhx, qhy, qhw, rhx, rhy, rhw);
}
#endif

template <class RT>
CGAL_KERNEL_INLINE
bool
right_turnH2(const RT& phx, const RT& phy, const RT& phw,
             const RT& qhx, const RT& qhy, const RT& qhw,
             const RT& rhx, const RT& rhy, const RT& rhw )
{
  const RT  RT0 = RT(0);
  
  // | A B |
  // | C D |
  
  RT  A = phx*rhw - phw*rhx;
  RT  B = phy*rhw - phw*rhy;
  RT  C = qhx*rhw - qhw*rhx;
  RT  D = qhy*rhw - qhw*rhy;
  
  RT  det =  A*D - B*C;
  
  
  return ( det < RT0 );
}

#ifndef CGAL_NO_DEPRECATED_CODE
template <class RT>
CGAL_KERNEL_INLINE
bool
rightturnH2(const RT& phx, const RT& phy, const RT& phw,
            const RT& qhx, const RT& qhy, const RT& qhw,
            const RT& rhx, const RT& rhy, const RT& rhw )
{
   return right_turnH2(phx, phy, phw, qhx, qhy, qhw, rhx, rhy, rhw);
}
#endif

template <class RT>
CGAL_KERNEL_INLINE
bool
collinearH2(const RT& phx, const RT& phy, const RT& phw,
            const RT& qhx, const RT& qhy, const RT& qhw,
            const RT& rhx, const RT& rhy, const RT& rhw )
{
  const RT  RT0 = RT(0);
  
  // | A B |
  // | C D |
  
  RT  A = phx*rhw - phw*rhx;
  RT  B = phy*rhw - phw*rhy;
  RT  C = qhx*rhw - qhw*rhx;
  RT  D = qhy*rhw - qhw*rhy;
  
  RT  det =  A*D - B*C;
  
  
  return ( det == RT0 );
}
template <class RT>
CGAL_KERNEL_INLINE
Bounded_side
side_of_bounded_circleH2( const RT& qhx, const RT& qhy, const RT& qhw,
                          const RT& rhx, const RT& rhy, const RT& rhw,
                          const RT& shx, const RT& shy, const RT& shw,
                          const RT& thx, const RT& thy, const RT& thw )
{
  CGAL_kernel_precondition( ! collinearH2(qhx, qhy, ghw,
                                               rhx, rhy, rhw,
                                               shx, shy, shw) );
  
  // compute sign of      |qx  qy  qx^2+qy^2  1 |   | a b c d |
  //                      |      --  r  --      | = | e f g h |
  //     determinant      |      --  s  --      | = | i j k l |
  //                      |      --  t  --      |   | m n o p |
  //           where
  
  RT a = qhx*qhw;
  RT b = qhy*qhw;
  RT c = qhx*qhx + qhy*qhy;
  RT d = qhw*qhw;
  
  RT e = rhx*rhw;
  RT f = rhy*rhw;
  RT g = rhx*rhx + rhy*rhy;
  RT h = rhw*rhw;
  
  RT i = shx*shw;
  RT j = shy*shw;
  RT k = shx*shx + shy*shy;
  RT l = shw*shw;
  
  RT m = thx*thw;
  RT n = thy*thw;
  RT o = thx*thx + thy*thy;
  RT p = thw*thw;
  RT det =   a * ( f*(k*p - l*o) + j*(h*o - g*p) + n*(g*l - h*k) )
           - e * ( b*(k*p - l*o) + j*(d*o - c*p) + n*(c*l - d*k) )
           + i * ( b*(g*p - h*o) + f*(d*o - c*p) + n*(c*h - d*g) )
           - m * ( b*(g*l - h*k) + f*(d*k - c*l) + j*(c*h - d*g) );
  
  if ( det == RT0 )
  {
      return ON_BOUNDARY;
  }
  else
  {
      if (orientation(q,r,s) == CLOCKWISE)
      {
          det = -det;
      }
      return (RT0 < det ) ? ON_BOUNDED_SIDE : ON_UNBOUNDED_SIDE;
  }
}

template <class RT>
CGAL_KERNEL_INLINE
Oriented_side
side_of_oriented_circleH2(const RT& qhx, const RT& qhy, const RT& qhw,
                          const RT& rhx, const RT& rhy, const RT& rhw,
                          const RT& shx, const RT& shy, const RT& shw,
                          const RT& thx, const RT& thy, const RT& thw )
{
  CGAL_kernel_precondition( ! collinearH2(qhx, qhy, ghw,
                                               rhx, rhy, rhw,
                                               shx, shy, shw) );
  
  // compute sign of      |qx  qy  qx^2+qy^2  1 |   | a b c d |
  //                      |      --  r  --      | = | e f g h |
  //     determinant      |      --  s  --      | = | i j k l |
  //                      |      --  t  --      |   | m n o p |
  //           where
  
  RT a = qhx*qhw;
  RT b = qhy*qhw;
  RT c = qhx*qhx + qhy*qhy;
  RT d = qhw*qhw;
  
  RT e = rhx*rhw;
  RT f = rhy*rhw;
  RT g = rhx*rhx + rhy*rhy;
  RT h = rhw*rhw;
  
  RT i = shx*shw;
  RT j = shy*shw;
  RT k = shx*shx + shy*shy;
  RT l = shw*shw;
  
  RT m = thx*thw;
  RT n = thy*thw;
  RT o = thx*thx + thy*thy;
  RT p = thw*thw;
  RT det =   a * ( f*(k*p - l*o) + j*(h*o - g*p) + n*(g*l - h*k) )
           - e * ( b*(k*p - l*o) + j*(d*o - c*p) + n*(c*l - d*k) )
           + i * ( b*(g*p - h*o) + f*(d*o - c*p) + n*(c*h - d*g) )
           - m * ( b*(g*l - h*k) + f*(d*k - c*l) + j*(c*h - d*g) );
  
  if ( det < RT0 )  return ON_NEGATIVE_SIDE;
  else return (RT0 < det ) ? ON_POSITIVE_SIDE :
                             ON_ORIENTED_BOUNDARY;
}
template <class RT>
CGAL_KERNEL_INLINE
Comparison_result
compare_lexicographically_xyH2(const RT& phx, const RT& phy, const RT& phw,
                               const RT& qhx, const RT& qhy, const RT& qhw)
{
  RT pV = phx*qhw;
  RT qV = qhx*phw;
  if ( pV == qV )
  {
      pV = phy*qhw;
      qV = qhy*phw;
  }
  if ( pV < qV )
  {
      return SMALLER;
  }
  else
  {
      return (qV < pV) ? LARGER : EQUAL;
  }
}

template <class RT>
CGAL_KERNEL_INLINE
Comparison_result
compare_xH2( const RT& phx, const RT& phw,
             const RT& qhx, const RT& qhw )
{
  RT com = phx * qhw - qhx * phw;
  if ( com < RT0 )
  {
      return SMALLER;
  }
  else if ( RT0 < com )
  {
      return LARGER;
  }
  return EQUAL;
}

// No compare_yH2; use compare_xH2( py, pw, qy, qw)

template < class RT >
CGAL_KERNEL_INLINE
Comparison_result
compare_deltax_deltayH2(const RT& phx, const RT& phw,
                        const RT& qhx, const RT& qhw,
                        const RT& rhy, const RT& rhw,
                        const RT& shy, const RT& shw )
{
  const RT  tbc1 = CGAL_NTS abs(phx*qhw - qhx*phw) * rhw*shw;
  const RT  tbc2 = CGAL_NTS abs(rhy*shw - shy*rhw) * phw*qhw;
  return (tbc2 < tbc1) ? LARGER
                       : (tbc1 == tbc2) ? EQUAL : SMALLER;

}

template <class RT>
CGAL_KERNEL_INLINE
bool
collinear_are_ordered_along_lineH2(
     const RT& phx, const RT& phy, const RT& phw,
     const RT& qhx, const RT& qhy, const RT& qhw,
     const RT& rhx, const RT& rhy, const RT& rhw
                                       )
{
  if ( !(phx * rhw == rhx * phw ) )          // non-vertical ?
  {
     return !( (  ( phx * qhw < qhx * phw)
                &&( rhx * qhw < qhx * rhw))
             ||(  ( qhx * phw < phx * qhw)
                &&( qhx * rhw < rhx * qhw)) );
  }
  else if ( !(phy * rhw == rhy * phw ) )
  {
     return !( (  ( phy * qhw < qhy * phw)
                &&( rhy * qhw < qhy * rhw))
             ||(  ( qhy * phw < phy * qhw)
                &&( qhy * rhw < rhy * qhw)) );
  }
  else
     return (( phx*qhw == qhx*phw) && ( phy*qhw == qhy*phw));
}

template <class RT>
CGAL_KERNEL_INLINE
bool
collinear_are_strictly_ordered_along_lineH2(
     const RT& phx, const RT& phy, const RT& phw,
     const RT& qhx, const RT& qhy, const RT& qhw,
     const RT& rhx, const RT& rhy, const RT& rhw)
{
  if ( !(phx * rhw == rhx * phw ) )
  {
     return (   ( phx * qhw < qhx * phw)
              &&( qhx * rhw < rhx * qhw))
          ||(   ( qhx * phw < phx * qhw)    // ( phx * qhw > qhx * phw)
              &&( rhx * qhw < qhx * rhw));  // ( qhx * rhw > rhx * qhw)
  }
  else
  {
     return (   ( phy * qhw < qhy * phw)
              &&( qhy * rhw < rhy * qhw))
          ||(   ( qhy * phw < phy * qhw)    // ( phy * qhw > qhy * phw)
              &&( rhy * qhw < qhy * rhw));  // ( qhy * rhw > rhy * qhw)
  }
}



CGAL_END_NAMESPACE

// Filtered_exact<> is not operational for Homogeneous at the moment.
// #ifdef CGAL_ARITHMETIC_FILTER_H
// #include <CGAL/Arithmetic_filter/predicates_on_rtH2.h>
// #endif

#endif // CGAL_PREDICATES_ON_RTH2_H