323 lines
7.2 KiB
C++
Executable File
323 lines
7.2 KiB
C++
Executable File
// Copyright (c) 2003,2004 INRIA Sophia-Antipolis (France).
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// All rights reserved.
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//
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// This file is part of CGAL (www.cgal.org).
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// You can redistribute it and/or modify it under the terms of the GNU
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// General Public License as published by the Free Software Foundation,
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// either version 3 of the License, 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: GPL-3.0+
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//
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//
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// Author(s) : Menelaos Karavelas <mkaravel@iacm.forth.gr>
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#ifndef CGAL_HYPERBOLA_2_H
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#define CGAL_HYPERBOLA_2_H
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#include <CGAL/license/Apollonius_graph_2.h>
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#include <CGAL/enum.h>
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#include <CGAL/determinant.h>
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#include <CGAL/Apollonius_site_2.h>
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#include <CGAL/Kernel_traits.h>
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namespace CGAL {
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template < class Gt >
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class Hyperbola_2
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{
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public:
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typedef Gt Geom_traits;
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typedef typename Gt::Site_2 Site_2;
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typedef typename Gt::Segment_2 Segment_2;
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typedef typename Gt::Point_2 Point_2;
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typedef typename Gt::FT FT;
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#if 0
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typedef typename Kernel_traits<Point>::Kernel Kernel;
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typedef CGAL::Apollonius_site_2<Kernel> Site_2;
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typedef typename Kernel::Segment_2 Segment_2;
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typedef Point Point_2;
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typedef typename Kernel::FT FT;
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#endif
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// typedef typename R::RT FT;
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// typedef double FT;
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// typedef CGAL::Point_2< Cartesian<double> > Point_2;
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// typedef CGAL::Segment_2< Cartesian< double > > Segment_2;
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protected:
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FT STEP;
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Point_2 f1, f2;
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FT r;
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Point_2 o;
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inline
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Point_2 lchain(const FT &t) const
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{
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std::vector< Point_2 > p = compute_points(t);
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if ( right(p[0]) ) return p[1];
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return p[0];
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}
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inline
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Point_2 rchain(const FT &t) const
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{
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std::vector< Point_2 > p = compute_points(t);
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if ( right(p[0]) ) return p[0];
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return p[1];
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}
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inline
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FT norm2(const Point_2& p) const
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{
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return (CGAL::square(p.x()) + CGAL::square(p.y()));
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}
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inline
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FT distance2(const Point_2& p1, const Point_2& p2) const
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{
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FT dx = p1.x()-p2.x();
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FT dy = p1.y()-p2.y();
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return (CGAL::square(dx) + CGAL::square(dy));
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}
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inline
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FT distance(const Point_2& p1, const Point_2& p2) const
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{
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return CGAL::sqrt( distance2(p1, p2) );
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}
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void compute_origin()
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{
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FT dx = f2.x() - f1.x();
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FT dy = f2.y() - f1.y();
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FT a = CGAL::sqrt(CGAL::square(dx) + CGAL::square(dy));
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FT t = (FT(1) + r / a) / FT(2);
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o = Point_2(dx * t + f1.x(), dy * t + f1.y());
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}
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std::vector< Point_2 > compute_points(const FT &d) const {
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FT d1 = distance(o, f1) + d;
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FT d2 = distance(o, f2) + d;
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d1 *= d1;
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d2 *= d2;
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Point_2 df = Point_2(f2.x() - f1.x(), f2.y()-f1.y());
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std::vector< Point_2 > p;
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if ( CGAL::is_negative(d) ) return p;
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if ( CGAL::is_zero(df.x()) ) {
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FT y = (d1 - d2 + norm2(f2) - norm2(f1)) / (FT(2) * df.y());
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FT D = d1 - CGAL::square(y - f1.y());
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D = CGAL::abs(D);
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FT x1 = CGAL::sqrt(D) + f1.x();
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FT x2 = -CGAL::sqrt(D) + f1.x();
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p.push_back(Point_2(x1, y));
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p.push_back(Point_2(x2, y));
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return p;
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}
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FT gamma = (d1 - d2 + norm2(f2) - norm2(f1)) / (FT(2) * df.x());
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FT gamma1 = gamma - f1.x();
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FT beta = df.y() / df.x();
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FT a = FT(1) + CGAL::square(beta);
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FT b = -FT(2) * (gamma1 * beta + f1.y());
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FT c = CGAL::square(f1.y()) + CGAL::square(gamma1) - d1;
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FT D = CGAL::square(b) - FT(4) * a * c;
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D = CGAL::abs(D);
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FT y1 = (-b + CGAL::sqrt(D)) / (FT(2) * a);
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FT y2 = (-b - CGAL::sqrt(D)) / (FT(2) * a);
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FT x1 = gamma - beta * y1;
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FT x2 = gamma - beta * y2;
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p.push_back(Point_2(x1, y1));
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p.push_back(Point_2(x2, y2));
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return p;
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}
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bool right(const Point_2& p) const
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{
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return
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CGAL::is_negative( determinant<FT>(f1.x(), f1.y(), 1,
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f2.x(), f2.y(), 1,
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p.x(), p.y(), 1) );
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}
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inline
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Point_2 midpoint(const Point_2& p1, const Point_2& p2) const
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{
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FT t1 = t(p1);
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FT t2 = t(p2);
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FT midt = (t1+t2)/2;
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return f(midt);
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}
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inline
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Point_2 f(FT t) const
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{
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if ( CGAL::is_negative(t) ) return rchain(-t);
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return lchain(t);
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}
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inline
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FT t(const Point_2 &p) const
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{
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FT tt = distance(f1, p) - distance(f1, o);
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if ( right(p) ) return -tt;
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return tt;
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}
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public:
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Hyperbola_2() { STEP = FT(2); }
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Hyperbola_2(const Site_2 &ff1, const Site_2 &ff2)
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{
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STEP = FT(2);
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this->r = ff1.weight() - ff2.weight();
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this->f1 = ff1.point();
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this->f2 = ff2.point();
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compute_origin();
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}
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Oriented_side
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side_of_hyperbola(const Point_2 &p) const
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{
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double dist = distance(p, f1) - distance(p, f2) - r;
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if ( dist < 0 ) return ON_NEGATIVE_SIDE;
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if ( dist > 0 ) return ON_POSITIVE_SIDE;
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return ON_ORIENTED_BOUNDARY;
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}
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template<class QTWIDGET>
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void generate_points_qt(const QTWIDGET& W,
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std::vector<Point_2>& pleft,
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std::vector<Point_2>& pright) const
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{
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std::vector< Point_2 > p;
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pleft.push_back(o);
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pright.push_back(o);
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double width = W.x_max() - W.x_min();
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double height = W.y_max() - W.y_min();
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FT STEP;
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if ( width < height ) {
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STEP = width / 500.0;
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} else {
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STEP = height / 500.0;
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}
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// double mind = distance(o, f1) - r1;
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for (int i = 1; i <= 100; i++) {
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p = compute_points(FT(i * i) * STEP);
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if ( p.size() > 0 ) {
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if ( right(p[0]) ) {
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pright.push_back(p[0]);
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pleft.push_back(p[1]);
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} else {
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pright.push_back(p[1]);
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pleft.push_back(p[0]);
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}
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}
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}
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}
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template<class QTWIDGET>
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void draw_qt(QTWIDGET& W) const
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{
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std::vector< Point_2 > pleft, pright;
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generate_points_qt(pleft, pright);
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for (unsigned int i = 0; i < pleft.size() - 1; i++) {
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W << Segment_2(pleft[i], pleft[i+1]);
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}
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for (unsigned int i = 0; i < pright.size() - 1; i++) {
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W << Segment_2(pright[i], pright[i+1]);
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}
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}
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void generate_points(std::vector<Point_2>& pleft,
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std::vector<Point_2>& pright) const
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{
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std::vector< Point_2 > p;
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pleft.push_back(o);
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pright.push_back(o);
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// double mind = distance(o, f1) - r1;
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for (int i = 1; i <= 100; i++) {
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p = compute_points(FT(i * i) * STEP);
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if ( p.size() > 0 ) {
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if ( right(p[0]) ) {
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pright.push_back(p[0]);
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pleft.push_back(p[1]);
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} else {
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pright.push_back(p[1]);
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pleft.push_back(p[0]);
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}
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}
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}
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}
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template< class Stream >
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void draw(Stream &W) const
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{
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std::vector< Point_2 > pleft, pright;
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generate_points(pleft,pright);
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for (unsigned int i = 0; i < pleft.size() - 1; i++) {
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W << Segment_2(pleft[i], pleft[i+1]);
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}
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for (unsigned int i = 0; i < pright.size() - 1; i++) {
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W << Segment_2(pright[i], pright[i+1]);
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}
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}
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};
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template< class Stream, class Gt >
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inline
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Stream& operator<<(Stream& s, const Hyperbola_2<Gt> &H)
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{
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H.draw(s);
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return s;
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}
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} //namespace CGAL
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#endif // CGAL_HYPERBOLA_2_H
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