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// Copyright (c) 1999 INRIA Sophia-Antipolis (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org); you may redistribute it under
// the terms of the Q Public License version 1.0.
// See the file LICENSE.QPL 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.
//
// $URL: svn+ssh://scm.gforge.inria.fr/svn/cgal/branches/CGAL-3.5-branch/Triangulation_2/include/CGAL/predicates/Regular_triangulation_rtH2.h $
// $Id: Regular_triangulation_rtH2.h 46206 2008-10-11 20:21:08Z spion $
//
//
// Author(s) : Sylvain Pion
// Mariette Yvinec <Mariette.Yvinec@sophia.inria.fr>
#ifndef CGAL_REGULAR_TRIANGULATION_RTH2_H
#define CGAL_REGULAR_TRIANGULATION_RTH2_H
// This file contains the low level homogeneous predicates
// used by the 2D regular triangulation.
CGAL_BEGIN_NAMESPACE
template <class RT>
Comparison_result
compare_power_distanceH2(const RT& phx, const RT& phy, const RT& phw,
const RT& pwt,
const RT& qhx, const RT& qhy, const RT& qhw,
const 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 dh1 = CGAL_NTS square(dphx) + CGAL_NTS square(dphy) - pwt * dphw * drhw;
RT dh2 = CGAL_NTS square(dqhx) + CGAL_NTS square(dqhy) - qwt * dqhw * drhw;
return CGAL_NTS compare(dh1, dh2);
}
template <class RT>
Oriented_side
power_testH2( const RT &phx, const RT &phy, const RT &phw, const RT &pwt,
const RT &qhx, const RT &qhy, const RT &qhw, const RT &qwt,
const RT &rhx, const RT &rhy, const RT &rhw, const RT &rwt,
const RT &thx, const RT &thy, const RT &thw, const RT &twt)
{
RT dphx = phx*phw;
RT dphy = phy*phw;
RT dphw = CGAL_NTS square(phw);
RT dpz = CGAL_NTS square(phx) + CGAL_NTS square(phy) - pwt*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) - qwt*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) - rwt*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) - twt*dthw;
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 RT &pwt,
const RT &qhx, const RT &qhy, const RT &qhw, const RT &qwt,
const RT &thx, const RT &thy, const RT &thw, const RT &twt)
{
// 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) - pwt*dphw;
RT dqhw = CGAL_NTS square(qhw);
RT dqz = CGAL_NTS square(qhx) + CGAL_NTS square(qhy) - qwt*dqhw;
RT dthw = CGAL_NTS square(thw);
RT dtz = CGAL_NTS square(thx) + CGAL_NTS square(thy) - twt*dthw;
return CGAL_NTS compare(pa, qa) * sign_of_determinant(pa, dpz, dphw,
qa, dqz, dqhw,
ta, dtz, dthw);
}
CGAL_END_NAMESPACE
#endif // CGAL_REGULAR_TRIANGULATION_RTH2_H
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