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cgal/Packages/H2/include/CGAL/predicates_on_rtH2.h

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// ======================================================================
//
// 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/predicates_on_rtH2.h
// revision : $Revision$
// revision_date : $Date$
// author(s) : Stefan Schirra
//
//
// coordinator : MPI, Saarbruecken (<Stefan.Schirra@mpi-sb.mpg.de>)
// ======================================================================
#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
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