// 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 #ifndef CGAL_REGULAR_TRIANGULATION_FTC3_H #define CGAL_REGULAR_TRIANGULATION_FTC3_H #include #include // This file contains the low level cartesian predicates // used by the 3D regular triangulation. namespace CGAL { // return minus the sign of the 5x5 determinant [P,Q,R,S,T] // where column [P] = transpose[px,py,pz,p^2 -wp,1] template Oriented_side power_testC3( const FT &px, const FT &py, const FT &pz, const FT &pwt, const FT &qx, const FT &qy, const FT &qz, const FT &qwt, const FT &rx, const FT &ry, const FT &rz, const FT &rwt, const FT &sx, const FT &sy, const FT &sz, const FT &swt, const FT &tx, const FT &ty, const FT &tz, const FT &twt) { // We translate the points so that T becomes the origin. FT dpx = px - tx; FT dpy = py - ty; FT dpz = pz - tz; FT dpt = CGAL_NTS square(dpx) + CGAL_NTS square(dpy) + CGAL_NTS square(dpz) + (twt - pwt); FT dqx = qx - tx; FT dqy = qy - ty; FT dqz = qz - tz; FT dqt = CGAL_NTS square(dqx) + CGAL_NTS square(dqy) + CGAL_NTS square(dqz) + (twt - qwt); FT drx = rx - tx; FT dry = ry - ty; FT drz = rz - tz; FT drt = CGAL_NTS square(drx) + CGAL_NTS square(dry) + CGAL_NTS square(drz) + (twt - rwt); FT dsx = sx - tx; FT dsy = sy - ty; FT dsz = sz - tz; FT dst = CGAL_NTS square(dsx) + CGAL_NTS square(dsy) + CGAL_NTS square(dsz) + (twt - swt); return - sign_of_determinant(dpx, dpy, dpz, dpt, dqx, dqy, dqz, dqt, drx, dry, drz, drt, dsx, dsy, dsz, dst); } template Oriented_side power_testC3( const FT &px, const FT &py, const FT &pz, const FT &pwt, const FT &qx, const FT &qy, const FT &qz, const FT &qwt, const FT &rx, const FT &ry, const FT &rz, const FT &rwt, const FT &tx, const FT &ty, const FT &tz, const FT &twt) { // Same translation as above. FT dpx = px - tx; FT dpy = py - ty; FT dpz = pz - tz; FT dpt = CGAL_NTS square(dpx) + CGAL_NTS square(dpy) + CGAL_NTS square(dpz) + (twt - pwt); FT dqx = qx - tx; FT dqy = qy - ty; FT dqz = qz - tz; FT dqt = CGAL_NTS square(dqx) + CGAL_NTS square(dqy) + CGAL_NTS square(dqz) + (twt - qwt); FT drx = rx - tx; FT dry = ry - ty; FT drz = rz - tz; FT drt = CGAL_NTS square(drx) + CGAL_NTS square(dry) + CGAL_NTS square(drz) + (twt - rwt); Sign cmp; // Projection on the (xy) plane. cmp = sign_of_determinant(dpx, dpy, dpt, dqx, dqy, dqt, drx, dry, drt); if (cmp != ZERO) return cmp * sign_of_determinant(px-rx, py-ry, qx-rx, qy-ry); // Projection on the (xz) plane. cmp = sign_of_determinant(dpx, dpz, dpt, dqx, dqz, dqt, drx, drz, drt); if (cmp != ZERO) return cmp * sign_of_determinant(px-rx, pz-rz, qx-rx, qz-rz); // Projection on the (yz) plane. cmp = sign_of_determinant(dpy, dpz, dpt, dqy, dqz, dqt, dry, drz, drt); return cmp * sign_of_determinant(py-ry, pz-rz, qy-ry, qz-rz); } template Oriented_side power_testC3( const FT &px, const FT &py, const FT &pz, const FT &pwt, const FT &qx, const FT &qy, const FT &qz, const FT &qwt, const FT &tx, const FT &ty, const FT &tz, const FT &twt) { // Same translation as above. FT dpx = px - tx; FT dpy = py - ty; FT dpz = pz - tz; FT dpt = CGAL_NTS square(dpx) + CGAL_NTS square(dpy) + CGAL_NTS square(dpz) + (twt - pwt); FT dqx = qx - tx; FT dqy = qy - ty; FT dqz = qz - tz; FT dqt = CGAL_NTS square(dqx) + CGAL_NTS square(dqy) + CGAL_NTS square (dqz) + (twt - qwt); Comparison_result cmp; // We do an orthogonal projection on the (x) axis, if possible. cmp = CGAL_NTS compare(px, qx); if (cmp != EQUAL) return cmp * sign_of_determinant(dpx, dpt, dqx, dqt); // We do an orthogonal projection on the (y) axis, if possible. cmp = CGAL_NTS compare(py, qy); if (cmp != EQUAL) return cmp * sign_of_determinant(dpy, dpt, dqy, dqt); // We do an orthogonal projection on the (z) axis. cmp = CGAL_NTS compare(pz, qz); return cmp * sign_of_determinant(dpz, dpt, dqz, dqt); } template Oriented_side power_testC3(const FT &pwt, const FT &qwt) { return CGAL_NTS compare(qwt, pwt); } } //namespace CGAL #endif // CGAL_REGULAR_TRIANGULATION_FTC3_H