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predicates_on_pointsH2.h
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predicates_on_pointsH2.h
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// Copyright (c) 1999,2016
// Utrecht University (The Netherlands),
// ETH Zurich (Switzerland),
// INRIA Sophia-Antipolis (France),
// Max-Planck-Institute Saarbruecken (Germany),
// and Tel-Aviv University (Israel). All rights reserved.
//
// This file is part of CGAL (www.cgal.org)
//
// $URL$
// $Id$
// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s) : Stefan Schirra, Olivier Devillers, Mariette Yvinec
#ifndef CGAL_PREDICATES_ON_POINTSH2_H
#define CGAL_PREDICATES_ON_POINTSH2_H
#include <CGAL/Homogeneous/PointH2.h>
namespace CGAL {
template < class R>
CGAL_KERNEL_INLINE
bool
equal_xy(const PointH2<R>& p,
const PointH2<R>& q)
{
typedef typename R::RT RT;
// Using these references allows to spare calls to [pq].hw().
const RT& phw = p.hw();
const RT& qhw = q.hw();
return (p.hx()*qhw == q.hx()*phw) && (p.hy()*qhw == q.hy()*phw);
}
template <class R>
CGAL_KERNEL_MEDIUM_INLINE
Oriented_side
_where_wrt_L_wedge( const PointH2<R>& p, const PointH2<R>& q )
{
Sign xs = CGAL_NTS sign( q.hx()*p.hw() - p.hx()*q.hw() ); // sign( qx - px )
Sign ys = CGAL_NTS sign( q.hy()*p.hw() - p.hy()*q.hw() ); // sign( qy - py )
if (( xs == NEGATIVE ) || ( ys == NEGATIVE ))
return ON_NEGATIVE_SIDE;
if (( xs == POSITIVE ) && ( ys == POSITIVE ))
return ON_POSITIVE_SIDE;
return ON_ORIENTED_BOUNDARY;
}
template <class RT>
Comparison_result
compare_power_distanceH2(const RT& phx, const RT& phy, const RT& phw,
const Quotient<RT>& pwt,
const RT& qhx, const RT& qhy, const RT& qhw,
const Quotient<RT>& qwt,
const RT& rhx, const RT& rhy, const RT& rhw)
{
// returns SMALLER if r is closer to p w.r.t. the power metric
RT dphx = rhx * phw - phx * rhw;
RT dphy = rhy * phw - phy * rhw;
RT dqhx = rhx * qhw - qhx * rhw;
RT dqhy = rhy * qhw - qhy * rhw;
RT dphw = CGAL_NTS square(phw);
RT dqhw = CGAL_NTS square(qhw);
RT drhw = CGAL_NTS square(rhw);
RT npwt = pwt.numerator();
RT dpwt = pwt.denominator();
RT nqwt = qwt.numerator();
RT dqwt = qwt.denominator();
RT dh1 = (CGAL_NTS square(dphx) + CGAL_NTS square(dphy))*dpwt - npwt * dphw * drhw;
RT dh2 = (CGAL_NTS square(dqhx) + CGAL_NTS square(dqhy))*dqwt - nqwt * dqhw * drhw;
return CGAL_NTS compare(dh1 * dqhw * dqwt, dh2 * dphw * dpwt );
}
template <class RT>
Oriented_side
power_testH2( const RT &phx, const RT &phy, const RT &phw, const Quotient<RT> &pwt,
const RT &qhx, const RT &qhy, const RT &qhw, const Quotient<RT> &qwt,
const RT &rhx, const RT &rhy, const RT &rhw, const Quotient<RT> &rwt,
const RT &thx, const RT &thy, const RT &thw, const Quotient<RT> &twt)
{
RT npwt = pwt.numerator();
RT dpwt = pwt.denominator();
RT nqwt = qwt.numerator();
RT dqwt = qwt.denominator();
RT nrwt = rwt.numerator();
RT drwt = rwt.denominator();
RT ntwt = twt.numerator();
RT dtwt = twt.denominator();
RT dphx = phx*phw;
RT dphy = phy*phw;
RT dphw = CGAL_NTS square(phw);
RT dpz = (CGAL_NTS square(phx) + CGAL_NTS square(phy))*dpwt - npwt*dphw;
RT dqhx = qhx*qhw;
RT dqhy = qhy*qhw;
RT dqhw = CGAL_NTS square(qhw);
RT dqz = (CGAL_NTS square(qhx) + CGAL_NTS square(qhy))*dqwt - nqwt*dqhw;
RT drhx = rhx*rhw;
RT drhy = rhy*rhw;
RT drhw = CGAL_NTS square(rhw);
RT drz = (CGAL_NTS square(rhx) + CGAL_NTS square(rhy)) *drwt - nrwt*drhw;
RT dthx = thx*thw;
RT dthy = thy*thw;
RT dthw = CGAL_NTS square(thw);
RT dtz = (CGAL_NTS square(thx) + CGAL_NTS square(thy))*dtwt - ntwt*dthw;
dthx *= dtwt;
dthy *= dtwt;
dthw *= dtwt;
return sign_of_determinant(dphx, dphy, dpz, dphw,
dqhx, dqhy, dqz, dqhw,
drhx, drhy, drz, drhw,
dthx, dthy, dtz, dthw);
}
template <class RT>
Oriented_side
power_testH2( const RT &phx, const RT &phy, const RT &phw, const Quotient<RT> &pwt,
const RT &qhx, const RT &qhy, const RT &qhw, const Quotient<RT> &qwt,
const RT &thx, const RT &thy, const RT &thw, const Quotient<RT> &twt)
{
RT npwt = pwt.numerator();
RT dpwt = pwt.denominator();
RT nqwt = qwt.numerator();
RT dqwt = qwt.denominator();
RT ntwt = twt.numerator();
RT dtwt = twt.denominator();
// Test if we can project on the (x) axis. If not, then on the
// (y) axis
RT pa, qa, ta;
if (phx * qhw != qhx * phw )
{
pa = phx*phw;
qa = qhx*qhw;
ta = thx*thw;
}
else
{
pa = phy*phw;
qa = qhy*qhw;
ta = thy*thw;
}
RT dphw = CGAL_NTS square(phw);
RT dpz = (CGAL_NTS square(phx) + CGAL_NTS square(phy))*dpwt - npwt*dphw;
RT dqhw = CGAL_NTS square(qhw);
RT dqz = (CGAL_NTS square(qhx) + CGAL_NTS square(qhy))*dqwt - nqwt*dqhw;
RT dthw = CGAL_NTS square(thw);
RT dtz = (CGAL_NTS square(thx) + CGAL_NTS square(thy))*dtwt - ntwt*dthw;
pa *= dtwt;
qa *= dtwt;
ta *= dtwt;
return CGAL_NTS compare(pa, qa) * sign_of_determinant(pa, dpz, dphw,
qa, dqz, dqhw,
ta, dtz, dthw);
}
#if 0
// Unused, undocumented, un-functorized.
template < class R >
CGAL_KERNEL_MEDIUM_INLINE
Comparison_result
compare_deltax_deltay(const PointH2<R>& p,
const PointH2<R>& q,
const PointH2<R>& r,
const PointH2<R>& s)
{
return CGAL_NTS compare(
CGAL_NTS abs(p.hx()*q.hw() - q.hx()*p.hw()) * r.hw()*s.hw(),
CGAL_NTS abs(r.hy()*s.hw() - s.hy()*r.hw()) * p.hw()*q.hw());
}
#endif
} //namespace CGAL
#endif // CGAL_PREDICATES_ON_POINTSH2_H