141 lines
4.0 KiB
C++
Executable File
141 lines
4.0 KiB
C++
Executable File
// Copyright (c) 1999
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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) : Sven Schoenherr
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// Stefan Schirra
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#ifndef CGAL_BASIC_CONSTRUCTIONSH2_H
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#define CGAL_BASIC_CONSTRUCTIONSH2_H
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#include <CGAL/Homogeneous/PointH2.h>
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#include <CGAL/Homogeneous/LineH2.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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typename R::Point_2
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gp_linear_intersection(const LineH2<R>& l1, const LineH2<R>& l2)
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{
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return typename R::Point_2( l1.b()*l2.c() - l2.b()*l1.c(),
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l2.a()*l1.c() - l1.a()*l2.c(),
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l1.a()*l2.b() - l2.a()*l1.b() );
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}
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template <class R>
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CGAL_KERNEL_MEDIUM_INLINE
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typename R::FT
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squared_distance( const PointH2<R>& p, const PointH2<R>& q )
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{
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typedef typename R::RT RT;
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typedef typename R::FT FT;
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const RT & phx = p.hx();
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const RT & phy = p.hy();
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const RT & phw = p.hw();
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const RT & qhx = q.hx();
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const RT & qhy = q.hy();
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const RT & qhw = q.hw();
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RT sq_dist_numerator =
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phx * phx * qhw * qhw
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- RT(2) * phx * qhx * phw * qhw
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+ qhx * qhx * phw * phw
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+ phy * phy * qhw * qhw
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- RT(2) * phy * qhy * phw * qhw
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+ qhy * qhy * phw * phw ;
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RT sq_dist_denominator = qhw * qhw * phw * phw ;
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return FT( sq_dist_numerator ) / FT( sq_dist_denominator );
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}
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template < class RT, class We>
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void
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weighted_circumcenterH2( const RT &phx, const RT &phy, const RT &phw,
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const We &pwt,
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const RT &qhx, const RT &qhy, const RT &qhw,
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const We &qwt,
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const RT &rhx, const RT &rhy, const RT &rhw,
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const We &rwt,
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RT &vvx, RT &vvy, RT &vvw )
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{
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// RT qx_px = ( qhx*qhw*phw*phw - phx*phw*qhw*qhw );
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// RT qy_py = ( qhy*qhw*phw*phw - phy*phw*qhw*qhw );
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// RT rx_px = ( rhx*rhw*phw*phw - phx*phw*rhw*rhw );
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// RT ry_py = ( rhy*rhw*phw*phw - phy*phw*rhw*rhw );
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// //intersection of the two radical axis of (qp) and (rp)
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// RT px2_py2_rx2_ry_2 =
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// phx*phx*rhw*rhw + phy*phy*rhw*rhw - rhx*rhx*phw*phw -
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// rhy*rhy*phw*phw - RT(pwt*pwt) + RT(rwt*rwt);
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// RT px2_py2_qx2_qy_2 =
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// phx*phx*qhw*qhw + phy*phy*qhw*qhw - qhx*qhx*phw*phw -
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// qhy*qhy*phw*phw - RT(pwt*pwt) + RT(qwt*qwt);
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// vvx = qy_py * px2_py2_rx2_ry_2 - ry_py * px2_py2_qx2_qy_2;
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// vvy = rx_px * px2_py2_qx2_qy_2 - qx_px * px2_py2_rx2_ry_2;
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// vvw = RT(2) * ( qx_px * ry_py - rx_px * qy_py );
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RT a1, b1, c1;
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RT a2, b2, c2;
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radical_axisH2(phx,phy,phw,pwt,qhx,qhy,qhw,qwt,a1,b1,c1);
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radical_axisH2(phx,phy,phw,pwt,rhx,rhy,rhw,rwt,a2,b2,c2);
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vvx = b1*c2 - c1*b2;
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vvy = c1*a2 - c2*a1;
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vvw = a1*b2 - a2*b1;
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}
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template < class RT , class FT>
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void
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radical_axisH2(const RT &phx, const RT &phy, const RT &phw, const FT &pwt,
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const RT &qhx, const RT &qhy, const RT &qhw, const FT &qwt,
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RT &a, RT &b, RT &c )
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{
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Rational_traits<FT> rt;
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RT npwt = rt.numerator(pwt);
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RT dpwt = rt.denominator(pwt);
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RT nqwt = rt.numerator(qwt);
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RT dqwt = rt.denominator(qwt);
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a = RT(2) * ( phx*phw*qhw*qhw - qhx*qhw*phw*phw );
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b = RT(2) * ( phy*phw*qhw*qhw - qhy*qhw*phw*phw );
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c = (- phx*phx*qhw*qhw - phy*phy*qhw*qhw
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+ qhx*qhx*phw*phw + qhy*qhy*phw*phw) * dpwt * dqwt
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+ npwt*dqwt*phw*phw*qhw*qhw - nqwt*dpwt*phw*phw*qhw*qhw;
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}
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} //namespace CGAL
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#endif // CGAL_BASIC_CONSTRUCTIONSH2_H
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