205 lines
5.4 KiB
C++
Executable File
205 lines
5.4 KiB
C++
Executable File
// 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); you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public License as
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// published by the Free Software Foundation; either version 3 of the License,
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// or (at your option) any later version.
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//
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// Licensees holding a valid commercial license may use this file in
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// accordance with the commercial license agreement provided with the software.
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//
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// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
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// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
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//
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// $URL$
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// $Id$
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// SPDX-License-Identifier: LGPL-3.0+
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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_POINTSH3_H
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#define CGAL_PREDICATES_ON_POINTSH3_H
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#include <CGAL/Homogeneous/PointH3.h>
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#include <CGAL/predicates/kernel_ftC3.h>
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namespace CGAL {
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template < class R >
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CGAL_KERNEL_MEDIUM_INLINE
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bool lexicographically_xy_smaller(const PointH3<R> &p,
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const PointH3<R> &q)
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{
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typedef typename R::RT RT;
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RT pV = p.hx()*q.hw();
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RT qV = q.hx()*p.hw();
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if ( pV < qV )
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{
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return true;
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}
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if ( qV < pV )
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{
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return false;
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}
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// same x
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pV = p.hy()*q.hw();
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qV = q.hy()*p.hw();
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if ( pV < qV )
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{
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return true;
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}
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return false;
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}
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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_xy(const PointH3<R>& p, const PointH3<R>& q)
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{
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typedef typename R::RT RT;
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RT pV = p.hx()*q.hw();
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RT qV = q.hx()*p.hw();
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if ( pV < qV )
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{
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return SMALLER;
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}
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if ( qV < pV ) // ( pV > qV )
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{
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return LARGER;
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}
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// same x
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pV = p.hy()*q.hw();
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qV = q.hy()*p.hw();
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if ( pV < qV )
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{
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return SMALLER;
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}
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if ( qV < pV ) // ( pV > qV )
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{
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return LARGER;
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}
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// same x and y
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return EQUAL;
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}
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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 PointH3<R> &p, const PointH3<R> &q)
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{
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return (p.hx() * q.hw() == q.hx() * p.hw() )
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&& (p.hy() * q.hw() == q.hy() * p.hw() );
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}
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template < class R > // ??? -> ==
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CGAL_KERNEL_INLINE
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bool
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equal_xyz(const PointH3<R> &p, const PointH3<R> &q)
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{
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return (p.hx() * q.hw() == q.hx() * p.hw() )
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&& (p.hy() * q.hw() == q.hy() * p.hw() )
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&& (p.hz() * q.hw() == q.hz() * p.hw() );
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}
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template < class R >
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CGAL_KERNEL_INLINE
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bool
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less_x(const PointH3<R> &p, const PointH3<R> &q)
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{ return (p.hx() * q.hw() < q.hx() * p.hw() ); }
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template < class R >
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CGAL_KERNEL_INLINE
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bool
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less_y(const PointH3<R> &p, const PointH3<R> &q)
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{ return (p.hy() * q.hw() < q.hy() * p.hw() ); }
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template < class R >
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CGAL_KERNEL_INLINE
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bool
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less_z(const PointH3<R> &p, const PointH3<R> &q)
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{ return (p.hz() * q.hw() < q.hz() * p.hw() ); }
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template <class RT>
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Oriented_side
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power_side_of_oriented_power_sphereH3(
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const RT &phx, const RT &phy, const RT &phz, const RT &phw, const Quotient<RT> &pwt,
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const RT &qhx, const RT &qhy, const RT &qhz, const RT &qhw, const Quotient<RT> &qwt,
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const RT &rhx, const RT &rhy, const RT &rhz, const RT &rhw, const Quotient<RT> &rwt,
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const RT &shx, const RT ­, const RT &shz, const RT &shw, const Quotient<RT> &swt,
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const RT &thx, const RT &thy, const RT &thz, 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 nswt = swt.numerator();
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RT dswt = swt.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 dphz = phz*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) +
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CGAL_NTS square(phz))*dpwt - npwt*dphw;
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RT dqhx = qhx*qhw;
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RT dqhy = qhy*qhw;
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RT dqhz = qhz*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) +
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CGAL_NTS square(qhz))*dqwt - nqwt*dqhw;
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RT drhx = rhx*rhw;
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RT drhy = rhy*rhw;
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RT drhz = rhz*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) +
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CGAL_NTS square(rhz))*drwt - nrwt*drhw;
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RT dshx = shx*shw;
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RT dshy = shy*shw;
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RT dshz = shz*shw;
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RT dshw = CGAL_NTS square(shw);
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RT dsz = (CGAL_NTS square(shx) + CGAL_NTS square(shy) +
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CGAL_NTS square(shz))*dswt - nswt*dshw;
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RT dthx = thx*thw;
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RT dthy = thy*thw;
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RT dthz = thz*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) +
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CGAL_NTS square(thz))*dtwt - ntwt*dthw;
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dthx *= dtwt;
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dthy *= dtwt;
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dthz *= dtwt;
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dthw *= dtwt;
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return - sign_of_determinant(dphx, dphy, dphz, dpz, dphw,
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dqhx, dqhy, dqhz, dqz, dqhw,
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drhx, drhy, drhz, drz, drhw,
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dshx, dshy, dshz, dsz, dshw,
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dthx, dthy, dthz, dtz, dthw);
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}
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// The 2 degenerate are not speed critical, and they are quite boring and error
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// prone to write, so we use the Cartesian version, using FT.
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} //namespace CGAL
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#endif // CGAL_PREDICATES_ON_POINTSH3_H
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