634 lines
20 KiB
C++
Executable File
634 lines
20 KiB
C++
Executable File
// Copyright (c) 2000,2001
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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) : Bernd Gaertner, Sven Schoenherr <sven@inf.ethz.ch>
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#ifndef CGAL_CONICCPA2_H
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#define CGAL_CONICCPA2_H
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// includes
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#include <CGAL/Kernel/Conic_misc.h>
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#include <CGAL/kernel_assertions.h>
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namespace CGAL {
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template < class PT, class DA>
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class ConicCPA2;
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template < class PT, class DA>
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class _Min_ellipse_2_adapterC2__Ellipse;
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template < class _PT, class _DA>
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class ConicCPA2
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{
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public:
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// types
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typedef _PT PT;
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typedef _DA DA;
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typedef typename _DA::FT FT;
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//private:
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//friend class Conic_2< CGAL::Cartesian<FT> >;
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friend class _Min_ellipse_2_adapterC2__Ellipse<PT,DA>;
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DA dao;
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FT _r, _s, _t, _u, _v, _w;
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Conic_type type;
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CGAL::Orientation o;
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bool empty, trivial, degenerate;
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void
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set_linear_combination (const FT& a1, const ConicCPA2<PT,DA>& c1,
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const FT& a2, const ConicCPA2<PT,DA>& c2)
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{
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_r = a1 * c1.r() + a2 * c2.r();
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_s = a1 * c1.s() + a2 * c2.s();
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_t = a1 * c1.t() + a2 * c2.t();
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_u = a1 * c1.u() + a2 * c2.u();
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_v = a1 * c1.v() + a2 * c2.v();
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_w = a1 * c1.w() + a2 * c2.w();
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}
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static void set_two_linepairs (const PT& p1,
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const PT& p2,
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const PT& p3,
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const PT& p4,
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ConicCPA2<PT,DA>& pair1,
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ConicCPA2<PT,DA>& pair2)
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{
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FT x1, y1, x2, y2, x3, y3, x4, y4;
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const DA& da = pair1.da();
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da.get (p1, x1, y1);
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da.get (p2, x2, y2);
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da.get (p3, x3, y3);
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da.get (p4, x4, y4);
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CGAL::Orientation side1_24 = (CGAL::Orientation)(CGAL_NTS sign
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(-x1*y4+x2*y4
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+x4*y1-x2*y1
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+x1*y2-x4*y2)),
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side3_24 = (CGAL::Orientation)(CGAL_NTS sign
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(-x3*y4+x2*y4
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+x4*y3-x2*y3
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+x3*y2-x4*y2));
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if (side1_24 != side3_24) {
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// (counter)clockwise order
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pair1.set_linepair (p1, p2, p3, p4);
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pair2.set_linepair (p2, p3, p4, p1);
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} else {
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CGAL::Orientation side1_32 = (CGAL::Orientation)(CGAL_NTS sign
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(-x1*y2+x3*y2
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+x2*y1-x3*y1
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+x1*y3-x2*y3));
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if (side1_32 != side3_24) {
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// p1, p2 need to be swapped
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pair1.set_linepair (p2, p1, p3, p4);
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pair2.set_linepair (p1, p3, p4, p2);
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} else {
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// p2, p3 need to be swapped
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pair1.set_linepair (p1, p3, p2, p4);
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pair2.set_linepair (p3, p2, p4, p1);
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}
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}
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}
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void set_ellipse (const ConicCPA2<PT,DA>& pair1,
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const ConicCPA2<PT,DA>& pair2)
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{
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FT b = FT(2) * (pair1.r() * pair2.s() + pair1.s() * pair2.r()) -
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pair1.t() * pair2.t();
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set_linear_combination (pair2.det()-b, pair1,
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pair1.det()-b, pair2);
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}
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void set (const ConicCPA2<PT,DA>& c1,
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const ConicCPA2<PT,DA>& c2,
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const PT& p)
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{
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set_linear_combination (c2.evaluate(p), c1, -c1.evaluate(p), c2);
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}
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CGAL::Sign vol_derivative (FT dr, FT ds, FT dt,
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FT du, FT dv, FT dw) const
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{
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FT a1 = FT(4)*r()*ds+FT(4)*dr*s()-FT(2)*t()*dt,
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a0 = FT(4)*r()*s()-t()*t(),
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b1 = (FT(4)*r()*s()-t()*t())*dw+(FT(4)*r()*ds+FT(4)*dr*s()-
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FT(2)*t()*dt)*w()-u()*u()*ds -
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FT(2)*u()*du*s()-v()*v()*dr-FT(2)*v()*dv*r()+u()*v()*dt+
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(u()*dv+du*v())*t(),
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b0 = (FT(4)*r()*s()-t()*t())*w()
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-u()*u()*s()-v()*v()*r()+u()*v()*t(),
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c0 = -FT(2)*a0*b1 + FT(3)*a1*b0;
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return CGAL_NTS sign ((int)-CGAL_NTS sign (c0)*o);
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}
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double vol_minimum (FT dr, FT ds, FT dt, FT du, FT dv, FT dw) const
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{
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FT a2 = FT(4)*dr*ds-dt*dt,
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a1 = FT(4)*r()*ds+FT(4)*dr*s()-FT(2)*t()*dt,
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a0 = FT(4)*r()*s()-t()*t(),
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b3 = (FT(4)*dr*ds-dt*dt)*dw-du*du*ds-dv*dv*dr+du*dv*dt,
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b2 = (FT(4)*r()*ds+FT(4)*dr*s()-FT(2)*t()*dt)*dw+
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(FT(4)*dr*ds-dt*dt)*w()-FT(2)*u()*du*ds-du*du*s()-
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FT(2)*v()*dv*dr-dv*dv*r()+(u()*dv+du*v())*dt+du*dv*t(),
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b1 = (FT(4)*r()*s()-t()*t())*dw+(FT(4)*r()*ds+FT(4)*dr*s()-
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FT(2)*t()*dt)*w()-u()*u()*ds -
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FT(2)*u()*du*s()-v()*v()*dr-FT(2)*v()*dv*r()+u()*v()*dt+
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(u()*dv+du*v())*t(),
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b0 = (FT(4)*r()*s()-t()*t())*w()
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-u()*u()*s()-v()*v()*r()+u()*v()*t(),
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c3 = -FT(3)*a1*b3 + FT(2)*a2*b2,
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c2 = -FT(6)*a0*b3 - a1*b2 + FT(4)*a2*b1,
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c1 = -FT(4)*a0*b2 + a1*b1 + FT(6)*a2*b0,
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c0 = -FT(2)*a0*b1 + FT(3)*a1*b0;
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double roots[3];
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int nr_roots = solve_cubic
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(CGAL::to_double(c3), CGAL::to_double(c2),
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CGAL::to_double(c1), CGAL::to_double(c0),
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roots[0], roots[1], roots[2]);
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CGAL_kernel_precondition (nr_roots > 0); // minimum exists
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return best_value (roots, nr_roots,
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CGAL::to_double(a2), CGAL::to_double(a1),
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CGAL::to_double(a0), CGAL::to_double(b3),
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CGAL::to_double(b2), CGAL::to_double(b1),
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CGAL::to_double(b0));
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}
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protected:
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FT det () const
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{
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return FT(4)*s()*r() - t()*t();
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}
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void analyse( )
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{
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FT d = det();
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type = (Conic_type)(CGAL_NTS sign(d));
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switch (type) {
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case HYPERBOLA:
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{
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trivial = empty = false;
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FT z_prime = d*w() - u()*u()*s() - v()*v()*r() + u()*v()*t();
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o = (CGAL::Orientation)(CGAL_NTS sign (z_prime));
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degenerate = (o == CGAL::ZERO);
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}
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break;
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case PARABOLA:
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{
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if (!CGAL_NTS is_zero (r())) {
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trivial = false;
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degenerate = (t()*u() == FT(2)*r()*v());
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if (degenerate) {
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CGAL::Sign discr = (CGAL::Sign)
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CGAL_NTS sign(u()*u()-FT(4)*r()*w());
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switch (discr) {
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case CGAL::NEGATIVE:
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empty = true;
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o = (CGAL::Orientation)(CGAL_NTS sign (w()));
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break;
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case CGAL::ZERO:
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empty = false;
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o = (CGAL::Orientation)(CGAL_NTS sign (r()));
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break;
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case CGAL::POSITIVE:
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empty = false;
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o = CGAL::ZERO;
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break;
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}
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} else {
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empty = false;
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o = (CGAL::Orientation)(-CGAL_NTS sign (r()));
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}
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} else if (!CGAL_NTS is_zero (s())) {
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trivial = false;
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degenerate = (t()*v() == FT(2)*s()*u());
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if (degenerate) {
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CGAL::Sign discr = (CGAL::Sign)
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CGAL_NTS sign(v()*v()-FT(4)*s()*w());
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switch (discr) {
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case CGAL::NEGATIVE:
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empty = true;
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o = (CGAL::Orientation)(CGAL_NTS sign (w()));
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break;
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case CGAL::ZERO:
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empty = false;
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o = (CGAL::Orientation)(CGAL_NTS sign (s()));
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break;
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case CGAL::POSITIVE:
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empty = false;
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o = CGAL::ZERO;
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break;
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}
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} else {
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empty = false;
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o = (CGAL::Orientation)(-CGAL_NTS sign (s()));
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}
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} else { // r=0, s=0
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degenerate = true;
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bool uv_zero = CGAL_NTS is_zero (u())
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&& CGAL_NTS is_zero (v());
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trivial = uv_zero && CGAL_NTS is_zero (w());
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empty = uv_zero && !trivial;
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if (empty)
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o = (CGAL::Orientation)(CGAL_NTS sign (w()));
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else if (trivial)
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o = CGAL::POSITIVE;
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else
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o = CGAL::ZERO;
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}
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}
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break;
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case ELLIPSE:
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{
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trivial = false;
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FT z_prime = d*w() - u()*u()*s() - v()*v()*r() + u()*v()*t();
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if (CGAL_NTS is_positive (r())) {
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empty = CGAL_NTS sign (z_prime) == CGAL::POSITIVE;
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empty ? o = CGAL::POSITIVE : o = CGAL::NEGATIVE;
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} else {
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empty = CGAL_NTS sign (z_prime) == CGAL::NEGATIVE ;
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empty ? o = CGAL::NEGATIVE : o = CGAL::POSITIVE;
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}
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degenerate = empty || CGAL_NTS is_zero (z_prime);
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}
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break;
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}
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}
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FT evaluate (const PT& p) const
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{
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FT x, y;
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dao.get (p, x, y);
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return r()*x*x + s()*y*y + t()*x*y + u()*x + v()*y + w();
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}
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public:
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ConicCPA2 ( const DA& da = DA()) : dao( da) { }
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ConicCPA2 (FT r, FT s, FT t, FT u, FT v, FT w, const DA& da = DA())
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: dao( da), _r(r), _s(s), _t(t), _u(u), _v(v), _w(w)
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{
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analyse();
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}
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const DA& da() const
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{
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return dao;
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}
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FT r() const { return _r;}
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FT s() const { return _s;}
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FT t() const { return _t;}
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FT u() const { return _u;}
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FT v() const { return _v;}
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FT w() const { return _w;}
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PT center () const
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{
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CGAL_kernel_precondition (type != PARABOLA);
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// PT p;
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// replaced previous line by following hack (no idea
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// why original version doesn't work)
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typename DA::Point p;
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FT two = FT(2);
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FT div = -det();
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dao.set( p, (two*s()*u() - t()*v()) / div,
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(two*r()*v() - t()*u()) / div);
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return p;
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}
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Conic_type conic_type () const
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{
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return type;
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}
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bool is_hyperbola () const
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{
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return (type == HYPERBOLA);
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}
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bool is_parabola () const
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{
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return (type == PARABOLA);
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}
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bool is_ellipse () const
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{
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return (type == ELLIPSE);
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}
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bool is_circle () const
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{
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return (type == ELLIPSE && (r()==s()) && CGAL_NTS is_zero (t()));
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}
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bool is_empty () const
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{
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return empty;
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}
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bool is_trivial () const
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{
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return trivial;
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}
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bool is_degenerate () const
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{
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return degenerate;
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}
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CGAL::Orientation orientation () const
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{
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return o;
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}
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CGAL::Oriented_side oriented_side (const PT& p) const
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{
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return (CGAL::Oriented_side)(CGAL_NTS sign (evaluate (p)));
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}
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bool has_on_positive_side (const PT& p) const
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{
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return (CGAL_NTS is_positive (evaluate(p)));
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}
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bool has_on_negative_side (const PT& p) const
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{
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return (CGAL_NTS is_negative (evaluate(p)));
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}
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bool has_on_boundary (const PT& p) const
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{
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return (CGAL_NTS is_zero (evaluate(p)));
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}
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bool has_on (const PT& p) const
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{
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return (CGAL_NTS is_zero (evaluate(p)));
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}
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Convex_side convex_side (const PT& p) const
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{
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switch (o) {
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case CGAL::POSITIVE:
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return (Convex_side)( CGAL_NTS sign (evaluate (p)));
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case CGAL::NEGATIVE:
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return (Convex_side)(-CGAL_NTS sign (evaluate (p)));
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case CGAL::ZERO:
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return (Convex_side)( CGAL_NTS sign (CGAL_NTS abs (evaluate(p))));
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}
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// keeps g++ happy
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return( Convex_side( 0));
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}
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bool has_on_convex_side (const PT& p) const
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{
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return (convex_side (p) == ON_CONVEX_SIDE);
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}
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bool has_on_nonconvex_side (const PT& p) const
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{
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return (convex_side (p) == ON_NONCONVEX_SIDE);
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}
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bool operator == ( const ConicCPA2<_PT,_DA>& c) const
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{
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// find coefficient != 0
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FT factor1(0);
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if ( ! CGAL_NTS is_zero( r())) factor1 = r(); else
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if ( ! CGAL_NTS is_zero( s())) factor1 = s(); else
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if ( ! CGAL_NTS is_zero( t())) factor1 = t(); else
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if ( ! CGAL_NTS is_zero( u())) factor1 = u(); else
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if ( ! CGAL_NTS is_zero( v())) factor1 = v(); else
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if ( ! CGAL_NTS is_zero( w())) factor1 = w(); else
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CGAL_kernel_assertion_msg( false, "all coefficients zero");
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// find coefficient != 0
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FT factor2(0);
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if ( ! CGAL_NTS is_zero( c.r())) factor2 = c.r(); else
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if ( ! CGAL_NTS is_zero( c.s())) factor2 = c.s(); else
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if ( ! CGAL_NTS is_zero( c.t())) factor2 = c.t(); else
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if ( ! CGAL_NTS is_zero( c.u())) factor2 = c.u(); else
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if ( ! CGAL_NTS is_zero( c.v())) factor2 = c.v(); else
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if ( ! CGAL_NTS is_zero( c.w())) factor2 = c.w(); else
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CGAL_kernel_assertion_msg( false, "all coefficients zero");
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return( ( r()*factor2 == c.r()*factor1)
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&& ( s()*factor2 == c.s()*factor1)
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&& ( t()*factor2 == c.t()*factor1)
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&& ( u()*factor2 == c.u()*factor1)
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&& ( v()*factor2 == c.v()*factor1)
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&& ( w()*factor2 == c.w()*factor1));
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}
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void set (FT r_, FT s_, FT t_, FT u_, FT v_, FT w_)
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{
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_r = r_; _s = s_; _t = t_; _u = u_; _v = v_; _w = w_;
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analyse();
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}
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void set_opposite ()
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{
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_r = -r(); _s = -s(); _t = -t(); _u = -u(); _v = -v(); _w = -w();
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o = CGAL::opposite(orientation());
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}
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void set_circle (const PT& p1, const PT& p2, const PT& p3)
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{
|
|
// the circle will have r = s = det, t=0
|
|
FT x1, y1, x2, y2, x3, y3;
|
|
dao.get (p1, x1, y1);
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|
dao.get (p2, x2, y2);
|
|
dao.get (p3, x3, y3);
|
|
|
|
// precondition: p1, p2, p3 not collinear
|
|
FT det = -x3*y2+x1*y2+x2*y3-x1*y3+x3*y1-x2*y1;
|
|
CGAL_kernel_precondition (!CGAL_NTS is_zero (det));
|
|
|
|
// Cramer's rule
|
|
FT sqr1 = -x1*x1 - y1*y1;
|
|
FT sqr2 = -x2*x2 - y2*y2;
|
|
FT sqr3 = -x3*x3 - y3*y3;
|
|
|
|
_u = -sqr3*y2+sqr1*y2+sqr2*y3-sqr1*y3+sqr3*y1-sqr2*y1;
|
|
_v = -x3*sqr2+x1*sqr2+x2*sqr3-x1*sqr3+x3*sqr1-x2*sqr1;
|
|
_w = -x3*y2*sqr1+x1*y2*sqr3+x2*y3*sqr1-x1*y3*sqr2+x3*y1*sqr2-x2*y1*sqr3;
|
|
_r = det;
|
|
_s = det;
|
|
_t = FT(0);
|
|
|
|
analyse();
|
|
CGAL_kernel_postcondition(is_circle());
|
|
CGAL_kernel_postcondition(has_on_boundary(p1));
|
|
CGAL_kernel_postcondition(has_on_boundary(p2));
|
|
CGAL_kernel_postcondition(has_on_boundary(p3));
|
|
}
|
|
|
|
void set_linepair (const PT& p1, const PT& p2, const PT& p3, const PT& p4)
|
|
{
|
|
FT x1, y1, x2, y2, x3, y3, x4, y4;
|
|
dao.get (p1, x1, y1);
|
|
dao.get (p2, x2, y2);
|
|
dao.get (p3, x3, y3);
|
|
dao.get (p4, x4, y4);
|
|
|
|
// precondition: p1 != p2, p3 != p4
|
|
CGAL_kernel_precondition
|
|
( ((x1 != x2) || (y1 != y2)) &&
|
|
((x3 != x4) || (y3 != y4)) );
|
|
|
|
FT x2_x1 = x2-x1;
|
|
FT x4_x3 = x4-x3;
|
|
FT y1_y2 = y1-y2;
|
|
FT y3_y4 = y3-y4;
|
|
FT x1y2_y1x2 = x1*y2-y1*x2;
|
|
FT x3y4_y3x4 = x3*y4-y3*x4;
|
|
|
|
_r = y1_y2 * y3_y4;
|
|
_s = x2_x1 * x4_x3;
|
|
_t = x2_x1 * y3_y4 + y1_y2 * x4_x3;
|
|
_u = x1y2_y1x2 * y3_y4 + y1_y2 * x3y4_y3x4;
|
|
_v = x1y2_y1x2 * x4_x3 + x2_x1 * x3y4_y3x4;
|
|
_w = x1y2_y1x2 * x3y4_y3x4;
|
|
|
|
analyse();
|
|
}
|
|
|
|
void set_ellipse (const PT& p1, const PT& p2, const PT& p3)
|
|
{
|
|
FT x1, y1, x2, y2, x3, y3;
|
|
dao.get (p1, x1, y1);
|
|
dao.get (p2, x2, y2);
|
|
dao.get (p3, x3, y3);
|
|
|
|
// precondition: p1, p2, p3 not collinear
|
|
FT det = -x3*y2+x1*y2+x2*y3-x1*y3+x3*y1-x2*y1;
|
|
CGAL_kernel_precondition (!CGAL_NTS is_zero (det));
|
|
|
|
FT x1x1 = x1*x1, y1y1 = y1*y1,
|
|
x2x2 = x2*x2, y2y2 = y2*y2,
|
|
x3x3 = x3*x3, y3y3 = y3*y3, // x_i^2, y_i^2
|
|
two = FT(2);
|
|
|
|
_r = y1y1 - y1*y2 - y1*y3 +
|
|
y2y2 - y2*y3 + y3y3;
|
|
|
|
_s = x1x1 - x1*x2 - x1*x3 +
|
|
x2x2 - x2*x3 + x3x3;
|
|
|
|
_t = -two*x1*y1 + x1*y2 + x1*y3 +
|
|
y1*x2 -two*x2*y2 + x2*y3 +
|
|
y1*x3 + y2*x3 -two*x3*y3;
|
|
|
|
_u = -(y2y2*x3 - x2*y2*y3 - y2*x3*y3 +
|
|
x1*y3y3 + x2*y3y3 + y1y1*x2 +
|
|
y1y1*x3 - x1*y1*y2 - y1*x2*y2 -
|
|
x1*y1*y3 - y1*x3*y3 + x1*y2y2);
|
|
|
|
_v = -(x2x2*y3 - x2*y2*x3 - x2*x3*y3 +
|
|
y1*x3x3 + y2*x3x3 + x1x1*y2 +
|
|
x1x1*y3 - x1*y1*x2 - x1*x2*y2 -
|
|
x1*y1*x3 - x1*x3*y3 + y1*x2x2);
|
|
|
|
_w = y1y1*x2*x3 - x1*y1*y2*x3 - y1*x2*y2*x3 +
|
|
y1*y2*x3x3 - x1*y1*x2*y3 + y1*x2x2*y3 -
|
|
y1*x2*x3*y3 + x1*y2y2*x3 + x1x1*y2*y3 -
|
|
x1*x2*y2*y3 - x1*y2*x3*y3 + x1*x2*y3y3;
|
|
|
|
type = ELLIPSE;
|
|
degenerate = trivial = empty = false;
|
|
o = CGAL::NEGATIVE;
|
|
if (CGAL_NTS is_positive (det)) set_opposite();
|
|
}
|
|
|
|
void set_ellipse (const PT& p1, const PT& p2,
|
|
const PT& p3, const PT& p4,
|
|
CGAL::Orientation _o = POSITIVE)
|
|
{
|
|
ConicCPA2<PT,DA> pair1, pair2;
|
|
set_two_linepairs (p1, p2, p3, p4, pair1, pair2);
|
|
set_ellipse (pair1, pair2);
|
|
analyse();
|
|
if (o != _o) set_opposite();
|
|
}
|
|
|
|
void set (const PT& p1, const PT& p2, const PT& p3, const PT& p4,
|
|
const PT& p5, CGAL::Orientation _o = POSITIVE)
|
|
{
|
|
ConicCPA2<PT,DA> c1; c1.set_linepair (p1, p2, p3, p4);
|
|
ConicCPA2<PT,DA> c2; c2.set_linepair (p1, p4, p2, p3);
|
|
set_linear_combination (c2.evaluate (p5), c1,
|
|
-c1.evaluate (p5), c2);
|
|
analyse();
|
|
// precondition: all points distinct <=> conic nontrivial
|
|
CGAL_kernel_precondition (!is_trivial());
|
|
if (o != _o) set_opposite();
|
|
}
|
|
|
|
|
|
|
|
};
|
|
|
|
#ifndef CGAL_NO_OSTREAM_INSERT_CONICCPA2
|
|
template< class _PT, class _DA>
|
|
std::ostream& operator << ( std::ostream& os, const ConicCPA2<_PT,_DA>& c)
|
|
{
|
|
return( os << c.r() << ' ' << c.s() << ' ' << c.t() << ' '
|
|
<< c.u() << ' ' << c.v() << ' ' << c.w());
|
|
}
|
|
|
|
template< class _PT, class _DA>
|
|
std::istream& operator >> ( std::istream& is, ConicCPA2<_PT,_DA>& c)
|
|
{
|
|
typedef typename _DA::FT FT;
|
|
|
|
FT r, s, t, u, v, w;
|
|
is >> r >> s >> t >> u >> v >> w;
|
|
c.set( r, s, t, u, v, w);
|
|
|
|
return( is);
|
|
}
|
|
#endif // CGAL_NO_OSTREAM_INSERT_CONICCPA2
|
|
|
|
} //namespace CGAL
|
|
|
|
#endif // CGAL_CONICCPA2_H
|
|
|
|
// ===== EOF ==================================================================
|