// 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_FTC2_H #define CGAL_REGULAR_TRIANGULATION_FTC2_H // This file contains the low level cartesian predicates // used by the 2D regular triangulation. namespace CGAL { template Comparison_result compare_power_distanceC2(const FT& px, const FT& py, const FT& pwt, const FT& qx, const FT& qy, const FT& qwt, const FT& rx, const FT& ry) { // returns SMALLER if r is closer to p w.r.t. the power metric FT d1 = CGAL_NTS square(rx - px) + CGAL_NTS square(ry - py) - pwt; FT d2 = CGAL_NTS square(rx - qx) + CGAL_NTS square(ry - qy) - qwt; return CGAL_NTS compare(d1, d2); } template Oriented_side power_testC2( const FT &px, const FT &py, const FT &pwt, const FT &qx, const FT &qy, const FT &qwt, const FT &rx, const FT &ry, const FT &rwt, const FT &tx, const FT &ty, const FT &twt) { // Note: maybe this can be further optimized like the usual in_circle() ? // We translate the 4 points so that T becomes the origin. FT dpx = px - tx; FT dpy = py - ty; FT dpz = CGAL_NTS square(dpx) + CGAL_NTS square(dpy) - pwt + twt; FT dqx = qx - tx; FT dqy = qy - ty; FT dqz = CGAL_NTS square(dqx) + CGAL_NTS square(dqy) - qwt + twt; FT drx = rx - tx; FT dry = ry - ty; FT drz = CGAL_NTS square(drx) + CGAL_NTS square(dry) - rwt + twt; return sign_of_determinant(dpx, dpy, dpz, dqx, dqy, dqz, drx, dry, drz); } template Oriented_side power_testC2( const FT &px, const FT &py, const FT &pwt, const FT &qx, const FT &qy, const FT &qwt, const FT &tx, const FT &ty, const FT &twt) { // Same translation as above. FT dpx = px - tx; FT dpy = py - ty; FT dpz = CGAL_NTS square(dpx) + CGAL_NTS square(dpy) - pwt + twt; FT dqx = qx - tx; FT dqy = qy - ty; FT dqz = CGAL_NTS square(dqx) + CGAL_NTS square(dqy) - qwt + twt; // We do an orthogonal projection on the (x) axis, if possible. Comparison_result cmpx = CGAL_NTS compare(px, qx); if (cmpx != EQUAL) return cmpx * sign_of_determinant(dpx, dpz, dqx, dqz); // If not possible, then on the (y) axis. Comparison_result cmpy = CGAL_NTS compare(py, qy); return cmpy * sign_of_determinant(dpy, dpz, dqy, dqz); } } //namespace CGAL #endif // CGAL_REGULAR_TRIANGULATION_FTC2_H