// 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/H3/include/CGAL/Homogeneous/distance_predicatesH3.h,v $
// $Revision: 1.5 $ $Date: 2003/11/17 19:31:55 $
// $Name: $
//
// Author(s) : Stefan Schirra
#ifndef CGAL_DISTANCE_PREDICATESH3_H
#define CGAL_DISTANCE_PREDICATESH3_H
CGAL_BEGIN_NAMESPACE
template <class R>
Comparison_result
compare_distance_to_point(const PointH3<R>& ,
const PointH3<R>& ,
const PointH3<R>& );
template <class R>
bool
has_larger_distance_to_point(const PointH3<R>& ,
const PointH3<R>& ,
const PointH3<R>& );
template <class R>
bool
has_smaller_distance_to_point(const PointH3<R>& ,
const PointH3<R>& ,
const PointH3<R>& );
template <class R>
Comparison_result
compare_signed_distance_to_plane(const PlaneH3<R>& ,
const PointH3<R>& ,
const PointH3<R>& );
template <class R>
bool
has_larger_signed_distance_to_plane(const PlaneH3<R>& ,
const PointH3<R>& ,
const PointH3<R>& );
template <class R>
bool
has_smaller_signed_distance_to_plane(const PlaneH3<R>&,
const PointH3<R>& ,
const PointH3<R>& );
template <class R>
Comparison_result
compare_signed_distance_to_plane(const PointH3<R>& ,
const PointH3<R>& ,
const PointH3<R>& ,
const PointH3<R>& ,
const PointH3<R>& );
template <class R>
bool
has_larger_signed_distance_to_plane(const PointH3<R>& ,
const PointH3<R>& ,
const PointH3<R>& ,
const PointH3<R>& ,
const PointH3<R>& );
template <class R>
bool
has_smaller_signed_distance_to_plane(const PointH3<R>& ,
const PointH3<R>& ,
const PointH3<R>& ,
const PointH3<R>& ,
const PointH3<R>& );
template <class R>
CGAL_KERNEL_MEDIUM_INLINE
Comparison_result
compare_distance_to_point(const PointH3<R>& p,
const PointH3<R>& q,
const PointH3<R>& r)
{
typedef typename R::RT RT;
const RT phx = p.hx();
const RT phy = p.hy();
const RT phz = p.hz();
const RT phw = p.hw();
const RT qhx = q.hx();
const RT qhy = q.hy();
const RT qhz = q.hz();
const RT qhw = q.hw();
const RT rhx = r.hx();
const RT rhy = r.hy();
const RT rhz = r.hz();
const RT rhw = r.hw();
const RT RT0 = RT(0);
const RT RT2 = RT(2);
RT dosd = // difference of squared distances
rhw*rhw * ( phw * ( qhx*qhx + qhy*qhy + qhz*qhz )
- RT2 * qhw * ( phx*qhx + phy*qhy + phz*qhz )
)
- qhw*qhw * ( phw * ( rhx*rhx + rhy*rhy + rhz*rhz )
- RT2 * rhw * ( phx*rhx + phy*rhy + phz*rhz )
);
if ( RT0 < dosd )
{ return LARGER; }
else
{ return (dosd < RT0) ? SMALLER : EQUAL; }
}
template < class R>
CGAL_KERNEL_MEDIUM_INLINE
bool
has_larger_distance_to_point(const PointH3<R>& p,
const PointH3<R>& q,
const PointH3<R>& r)
{
typedef typename R::RT RT;
const RT phx = p.hx();
const RT phy = p.hy();
const RT phz = p.hz();
const RT phw = p.hw();
const RT qhx = q.hx();
const RT qhy = q.hy();
const RT qhz = q.hz();
const RT qhw = q.hw();
const RT rhx = r.hx();
const RT rhy = r.hy();
const RT rhz = r.hz();
const RT rhw = r.hw();
const RT RT0 = RT(0);
const RT RT2 = RT(2);
RT dosd = // difference of squared distances
rhw*rhw * ( phw * ( qhx*qhx + qhy*qhy + qhz*qhz )
- RT2 * qhw * ( phx*qhx + phy*qhy + phz*qhz )
)
- qhw*qhw * ( phw * ( rhx*rhx + rhy*rhy + rhz*rhz )
- RT2 * rhw * ( phx*rhx + phy*rhy + phz*rhz )
);
return ( RT0 < dosd );
}
template < class R>
CGAL_KERNEL_MEDIUM_INLINE
bool
has_smaller_distance_to_point(const PointH3<R>& p,
const PointH3<R>& q,
const PointH3<R>& r)
{
typedef typename R::RT RT;
const RT phx = p.hx();
const RT phy = p.hy();
const RT phz = p.hz();
const RT phw = p.hw();
const RT qhx = q.hx();
const RT qhy = q.hy();
const RT qhz = q.hz();
const RT qhw = q.hw();
const RT rhx = r.hx();
const RT rhy = r.hy();
const RT rhz = r.hz();
const RT rhw = r.hw();
const RT RT0 = RT(0);
const RT RT2 = RT(2);
RT dosd = // difference of squared distances
rhw*rhw * ( phw * ( qhx*qhx + qhy*qhy + qhz*qhz )
- RT2 * qhw * ( phx*qhx + phy*qhy + phz*qhz )
)
- qhw*qhw * ( phw * ( rhx*rhx + rhy*rhy + rhz*rhz )
- RT2 * rhw * ( phx*rhx + phy*rhy + phz*rhz )
);
return ( dosd < RT0 );
}
template < class R>
CGAL_KERNEL_INLINE
Comparison_result
compare_signed_distance_to_plane(const PlaneH3<R>& pl,
const PointH3<R>& p,
const PointH3<R>& q)
{
typedef typename R::RT RT;
const RT pla = pl.a();
const RT plb = pl.b();
const RT plc = pl.c();
const RT phx = p.hx();
const RT phy = p.hy();
const RT phz = p.hz();
const RT phw = p.hw();
const RT qhx = q.hx();
const RT qhy = q.hy();
const RT qhz = q.hz();
const RT qhw = q.hw();
const RT RT0 = RT(0);
RT scaled_dist_p_minus_scaled_dist_q =
pla*( phx*qhw - qhx*phw )
+ plb*( phy*qhw - qhy*phw )
+ plc*( phz*qhw - qhz*phw );
if ( scaled_dist_p_minus_scaled_dist_q < RT0 )
{ return SMALLER; }
else
{ return (RT0 < scaled_dist_p_minus_scaled_dist_q ) ? LARGER : EQUAL;}
}
template <class R>
bool
has_larger_signed_distance_to_plane(const PlaneH3<R>& pl,
const PointH3<R>& p,
const PointH3<R>& q )
{
typedef typename R::RT RT;
const RT pla = pl.a();
const RT plb = pl.b();
const RT plc = pl.c();
const RT phx = p.hx();
const RT phy = p.hy();
const RT phz = p.hz();
const RT phw = p.hw();
const RT qhx = q.hx();
const RT qhy = q.hy();
const RT qhz = q.hz();
const RT qhw = q.hw();
const RT RT0 = RT(0);
RT scaled_dist_p_minus_scaled_dist_q =
pla*( phx*qhw - qhx*phw )
+ plb*( phy*qhw - qhy*phw )
+ plc*( phz*qhw - qhz*phw );
return ( RT0 < scaled_dist_p_minus_scaled_dist_q );
}
template <class R>
bool
has_smaller_signed_distance_to_plane(const PlaneH3<R>& pl,
const PointH3<R>& p,
const PointH3<R>& q )
{
typedef typename R::RT RT;
const RT pla = pl.a();
const RT plb = pl.b();
const RT plc = pl.c();
const RT phx = p.hx();
const RT phy = p.hy();
const RT phz = p.hz();
const RT phw = p.hw();
const RT qhx = q.hx();
const RT qhy = q.hy();
const RT qhz = q.hz();
const RT qhw = q.hw();
const RT RT0 = RT(0);
RT scaled_dist_p_minus_scaled_dist_q =
pla*( phx*qhw - qhx*phw )
+ plb*( phy*qhw - qhy*phw )
+ plc*( phz*qhw - qhz*phw );
return ( scaled_dist_p_minus_scaled_dist_q < RT0 );
}
template <class R>
inline
Comparison_result
compare_signed_distance_to_plane(const PointH3<R>& p,
const PointH3<R>& q,
const PointH3<R>& r,
const PointH3<R>& s,
const PointH3<R>& t)
{
CGAL_kernel_precondition( !collinear(p,q,r) );
PlaneH3<R> P(p,q,r);
return cmp_signed_dist_to_plane( P, s, t);
}
template <class R>
inline
bool
has_larger_signed_distance_to_plane(const PointH3<R>& p,
const PointH3<R>& q,
const PointH3<R>& r,
const PointH3<R>& s,
const PointH3<R>& t)
{ return cmp_signed_dist_to_plane(p,q,r,s,t) == LARGER; }
template <class R>
inline
bool
has_smaller_signed_distance_to_plane(const PointH3<R>& p,
const PointH3<R>& q,
const PointH3<R>& r,
const PointH3<R>& s,
const PointH3<R>& t)
{ return cmp_signed_dist_to_plane(p,q,r,s,t) == SMALLER; }
CGAL_END_NAMESPACE
#endif //CGAL_DISTANCE_PREDICATESH3_H
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