// Copyright (c) 1999 INRIA Sophia-Antipolis (France). // All rights reserved. // // This file is part of CGAL (www.cgal.org). // You can redistribute it and/or modify it under the terms of the GNU // General Public License as published by the Free Software Foundation, // either version 3 of the License, or (at your option) any later version. // // 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. // // $URL$ // $Id$ // // // Author(s) : Sylvain Pion // Mariette Yvinec #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. namespace CGAL { template 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 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 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); } } //namespace CGAL #endif // CGAL_REGULAR_TRIANGULATION_RTH2_H