198 lines
5.9 KiB
C++
198 lines
5.9 KiB
C++
// Copyright (c) 1999,2016
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// Utrecht University (The Netherlands),
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// ETH Zurich (Switzerland),
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// INRIA Sophia-Antipolis (France),
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// Max-Planck-Institute Saarbruecken (Germany),
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// and Tel-Aviv University (Israel). All rights reserved.
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//
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// This file is part of CGAL (www.cgal.org)
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//
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// $URL: https://github.com/CGAL/cgal/blob/v5.1/Homogeneous_kernel/include/CGAL/Homogeneous/predicates_on_pointsH2.h $
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// $Id: predicates_on_pointsH2.h 0779373 2020-03-26T13:31:46+01:00 Sébastien Loriot
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// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
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//
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//
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// Author(s) : Stefan Schirra, Olivier Devillers, Mariette Yvinec
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#ifndef CGAL_PREDICATES_ON_POINTSH2_H
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#define CGAL_PREDICATES_ON_POINTSH2_H
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#include <CGAL/Homogeneous/PointH2.h>
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namespace CGAL {
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template < class R>
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CGAL_KERNEL_INLINE
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bool
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equal_xy(const PointH2<R>& p,
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const PointH2<R>& q)
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{
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typedef typename R::RT RT;
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// Using these references allows to spare calls to [pq].hw().
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const RT& phw = p.hw();
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const RT& qhw = q.hw();
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return (p.hx()*qhw == q.hx()*phw) && (p.hy()*qhw == q.hy()*phw);
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}
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template <class R>
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CGAL_KERNEL_MEDIUM_INLINE
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Oriented_side
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_where_wrt_L_wedge( const PointH2<R>& p, const PointH2<R>& q )
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{
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Sign xs = CGAL_NTS sign( q.hx()*p.hw() - p.hx()*q.hw() ); // sign( qx - px )
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Sign ys = CGAL_NTS sign( q.hy()*p.hw() - p.hy()*q.hw() ); // sign( qy - py )
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if (( xs == NEGATIVE ) || ( ys == NEGATIVE ))
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return ON_NEGATIVE_SIDE;
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if (( xs == POSITIVE ) && ( ys == POSITIVE ))
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return ON_POSITIVE_SIDE;
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return ON_ORIENTED_BOUNDARY;
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}
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template <class RT>
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Comparison_result
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compare_power_distanceH2(const RT& phx, const RT& phy, const RT& phw,
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const Quotient<RT>& pwt,
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const RT& qhx, const RT& qhy, const RT& qhw,
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const Quotient<RT>& qwt,
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const RT& rhx, const RT& rhy, const RT& rhw)
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{
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// returns SMALLER if r is closer to p w.r.t. the power metric
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RT dphx = rhx * phw - phx * rhw;
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RT dphy = rhy * phw - phy * rhw;
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RT dqhx = rhx * qhw - qhx * rhw;
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RT dqhy = rhy * qhw - qhy * rhw;
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RT dphw = CGAL_NTS square(phw);
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RT dqhw = CGAL_NTS square(qhw);
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RT drhw = CGAL_NTS square(rhw);
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RT npwt = pwt.numerator();
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RT dpwt = pwt.denominator();
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RT nqwt = qwt.numerator();
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RT dqwt = qwt.denominator();
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RT dh1 = (CGAL_NTS square(dphx) + CGAL_NTS square(dphy))*dpwt - npwt * dphw * drhw;
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RT dh2 = (CGAL_NTS square(dqhx) + CGAL_NTS square(dqhy))*dqwt - nqwt * dqhw * drhw;
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return CGAL_NTS compare(dh1 * dqhw * dqwt, dh2 * dphw * dpwt );
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}
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template <class RT>
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Oriented_side
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power_testH2( const RT &phx, const RT &phy, const RT &phw, const Quotient<RT> &pwt,
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const RT &qhx, const RT &qhy, const RT &qhw, const Quotient<RT> &qwt,
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const RT &rhx, const RT &rhy, const RT &rhw, const Quotient<RT> &rwt,
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const RT &thx, const RT &thy, const RT &thw, const Quotient<RT> &twt)
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{
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RT npwt = pwt.numerator();
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RT dpwt = pwt.denominator();
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RT nqwt = qwt.numerator();
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RT dqwt = qwt.denominator();
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RT nrwt = rwt.numerator();
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RT drwt = rwt.denominator();
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RT ntwt = twt.numerator();
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RT dtwt = twt.denominator();
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RT dphx = phx*phw;
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RT dphy = phy*phw;
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RT dphw = CGAL_NTS square(phw);
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RT dpz = (CGAL_NTS square(phx) + CGAL_NTS square(phy))*dpwt - npwt*dphw;
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RT dqhx = qhx*qhw;
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RT dqhy = qhy*qhw;
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RT dqhw = CGAL_NTS square(qhw);
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RT dqz = (CGAL_NTS square(qhx) + CGAL_NTS square(qhy))*dqwt - nqwt*dqhw;
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RT drhx = rhx*rhw;
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RT drhy = rhy*rhw;
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RT drhw = CGAL_NTS square(rhw);
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RT drz = (CGAL_NTS square(rhx) + CGAL_NTS square(rhy)) *drwt - nrwt*drhw;
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RT dthx = thx*thw;
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RT dthy = thy*thw;
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RT dthw = CGAL_NTS square(thw);
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RT dtz = (CGAL_NTS square(thx) + CGAL_NTS square(thy))*dtwt - ntwt*dthw;
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dthx *= dtwt;
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dthy *= dtwt;
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dthw *= dtwt;
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return sign_of_determinant(dphx, dphy, dpz, dphw,
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dqhx, dqhy, dqz, dqhw,
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drhx, drhy, drz, drhw,
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dthx, dthy, dtz, dthw);
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}
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template <class RT>
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Oriented_side
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power_testH2( const RT &phx, const RT &phy, const RT &phw, const Quotient<RT> &pwt,
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const RT &qhx, const RT &qhy, const RT &qhw, const Quotient<RT> &qwt,
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const RT &thx, const RT &thy, const RT &thw, const Quotient<RT> &twt)
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{
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RT npwt = pwt.numerator();
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RT dpwt = pwt.denominator();
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RT nqwt = qwt.numerator();
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RT dqwt = qwt.denominator();
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RT ntwt = twt.numerator();
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RT dtwt = twt.denominator();
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// Test if we can project on the (x) axis. If not, then on the
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// (y) axis
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RT pa, qa, ta;
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if (phx * qhw != qhx * phw )
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{
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pa = phx*phw;
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qa = qhx*qhw;
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ta = thx*thw;
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}
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else
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{
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pa = phy*phw;
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qa = qhy*qhw;
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ta = thy*thw;
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}
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RT dphw = CGAL_NTS square(phw);
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RT dpz = (CGAL_NTS square(phx) + CGAL_NTS square(phy))*dpwt - npwt*dphw;
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RT dqhw = CGAL_NTS square(qhw);
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RT dqz = (CGAL_NTS square(qhx) + CGAL_NTS square(qhy))*dqwt - nqwt*dqhw;
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RT dthw = CGAL_NTS square(thw);
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RT dtz = (CGAL_NTS square(thx) + CGAL_NTS square(thy))*dtwt - ntwt*dthw;
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pa *= dtwt;
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qa *= dtwt;
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ta *= dtwt;
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return CGAL_NTS compare(pa, qa) * sign_of_determinant(pa, dpz, dphw,
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qa, dqz, dqhw,
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ta, dtz, dthw);
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}
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#if 0
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// Unused, undocumented, un-functorized.
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template < class R >
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CGAL_KERNEL_MEDIUM_INLINE
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Comparison_result
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compare_deltax_deltay(const PointH2<R>& p,
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const PointH2<R>& q,
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const PointH2<R>& r,
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const PointH2<R>& s)
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{
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return CGAL_NTS compare(
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CGAL_NTS abs(p.hx()*q.hw() - q.hx()*p.hw()) * r.hw()*s.hw(),
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CGAL_NTS abs(r.hy()*s.hw() - s.hy()*r.hw()) * p.hw()*q.hw());
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}
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#endif
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} //namespace CGAL
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#endif // CGAL_PREDICATES_ON_POINTSH2_H
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