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// Copyright (c) 1999 // 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: https://github.com/CGAL/cgal/blob/v6.1/Homogeneous_kernel/include/CGAL/Homogeneous/basic_constructionsH2.h $ // $Id: include/CGAL/Homogeneous/basic_constructionsH2.h b26b07a1242 $ // SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Sven Schoenherr // Stefan Schirra #ifndef CGAL_BASIC_CONSTRUCTIONSH2_H #define CGAL_BASIC_CONSTRUCTIONSH2_H #include #include namespace CGAL { template CGAL_KERNEL_MEDIUM_INLINE typename R::Point_2 gp_linear_intersection(const LineH2& l1, const LineH2& l2) { return typename R::Point_2( l1.b()*l2.c() - l2.b()*l1.c(), l2.a()*l1.c() - l1.a()*l2.c(), l1.a()*l2.b() - l2.a()*l1.b() ); } template CGAL_KERNEL_MEDIUM_INLINE typename R::FT squared_distance( const PointH2& p, const PointH2& q ) { typedef typename R::RT RT; typedef typename R::FT FT; const RT & phx = p.hx(); const RT & phy = p.hy(); const RT & phw = p.hw(); const RT & qhx = q.hx(); const RT & qhy = q.hy(); const RT & qhw = q.hw(); RT sq_dist_numerator = phx * phx * qhw * qhw - RT(2) * phx * qhx * phw * qhw + qhx * qhx * phw * phw + phy * phy * qhw * qhw - RT(2) * phy * qhy * phw * qhw + qhy * qhy * phw * phw ; RT sq_dist_denominator = qhw * qhw * phw * phw ; return FT( sq_dist_numerator ) / FT( sq_dist_denominator ); } template < class RT, class We> void weighted_circumcenterH2( const RT &phx, const RT &phy, const RT &phw, const We &pwt, const RT &qhx, const RT &qhy, const RT &qhw, const We &qwt, const RT &rhx, const RT &rhy, const RT &rhw, const We &rwt, RT &vvx, RT &vvy, RT &vvw ) { // RT qx_px = ( qhx*qhw*phw*phw - phx*phw*qhw*qhw ); // RT qy_py = ( qhy*qhw*phw*phw - phy*phw*qhw*qhw ); // RT rx_px = ( rhx*rhw*phw*phw - phx*phw*rhw*rhw ); // RT ry_py = ( rhy*rhw*phw*phw - phy*phw*rhw*rhw ); // //intersection of the two radical axis of (qp) and (rp) // RT px2_py2_rx2_ry_2 = // phx*phx*rhw*rhw + phy*phy*rhw*rhw - rhx*rhx*phw*phw - // rhy*rhy*phw*phw - RT(pwt*pwt) + RT(rwt*rwt); // RT px2_py2_qx2_qy_2 = // phx*phx*qhw*qhw + phy*phy*qhw*qhw - qhx*qhx*phw*phw - // qhy*qhy*phw*phw - RT(pwt*pwt) + RT(qwt*qwt); // vvx = qy_py * px2_py2_rx2_ry_2 - ry_py * px2_py2_qx2_qy_2; // vvy = rx_px * px2_py2_qx2_qy_2 - qx_px * px2_py2_rx2_ry_2; // vvw = RT(2) * ( qx_px * ry_py - rx_px * qy_py ); RT a1, b1, c1; RT a2, b2, c2; radical_axisH2(phx,phy,phw,pwt,qhx,qhy,qhw,qwt,a1,b1,c1); radical_axisH2(phx,phy,phw,pwt,rhx,rhy,rhw,rwt,a2,b2,c2); vvx = b1*c2 - c1*b2; vvy = c1*a2 - c2*a1; vvw = a1*b2 - a2*b1; } template < class RT , class FT> void radical_axisH2(const RT &phx, const RT &phy, const RT &phw, const FT &pwt, const RT &qhx, const RT &qhy, const RT &qhw, const FT &qwt, RT &a, RT &b, RT &c ) { Rational_traits rt; RT npwt = rt.numerator(pwt); RT dpwt = rt.denominator(pwt); RT nqwt = rt.numerator(qwt); RT dqwt = rt.denominator(qwt); a = RT(2) * ( phx*phw*qhw*qhw - qhx*qhw*phw*phw ); b = RT(2) * ( phy*phw*qhw*qhw - qhy*qhw*phw*phw ); c = (- phx*phx*qhw*qhw - phy*phy*qhw*qhw + qhx*qhx*phw*phw + qhy*qhy*phw*phw) * dpwt * dqwt + npwt*dqwt*phw*phw*qhw*qhw - nqwt*dpwt*phw*phw*qhw*qhw; } } //namespace CGAL #endif // CGAL_BASIC_CONSTRUCTIONSH2_H