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// Copyright (c) 2003,2004 INRIA Sophia-Antipolis (France). // All rights reserved. // // This file is part of CGAL (www.cgal.org). // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Apollonius_graph_2/include/CGAL/Parabola_2.h $ // $Id: include/CGAL/Parabola_2.h b26b07a1242 $ // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Menelaos Karavelas #ifndef CGAL_PARABOLA_2_H #define CGAL_PARABOLA_2_H #include #include #include #include #include namespace CGAL { template < class Gt > class Parabola_2 { private: typedef Parabola_2 Self; public: typedef typename Gt::Site_2 Site_2; typedef typename Gt::Point_2 Point_2; typedef typename Gt::Segment_2 Segment_2; typedef typename Gt::Line_2 Line_2; typedef typename Gt::FT FT; // typedef CGAL::Point_2< Cartesian > Point_2; // typedef CGAL::Segment_2< Cartesian > Segment_2; // typedef CGAL::Line_2< Cartesian > Line_2; private: typedef Algebraic_structure_traits AST; protected: // inline static // FT square(const FT &x) // { // return x * x; // } inline static FT divide(const FT& x, const FT& y, Integral_domain_without_division_tag) { return FT(CGAL::to_double(x) / CGAL::to_double(y)); } inline static FT divide(const FT& x, const FT& y, Field_tag) { return x / y; } inline static FT divide(const FT& x, const FT& y) { return divide(x,y, typename AST::Algebraic_category()); } inline static FT sqrt(const FT& x, Integral_domain_without_division_tag) { return CGAL::sqrt(CGAL::to_double(x)); } inline static FT sqrt(const FT& x, Field_with_sqrt_tag) { return CGAL::sqrt(x); } inline static FT sqrt(const FT& x) { return sqrt(x, typename AST::Algebraic_category()); } inline static FT norm2(const Point_2& p) { return CGAL::square(p.x()) + CGAL::square(p.y()); } inline static FT distance2(const Point_2& p1, const Point_2& p2) { FT dx = p1.x()-p2.x(); FT dy = p1.y()-p2.y(); return CGAL::square(dx) + CGAL::square(dy); } inline static FT distance(const Point_2& p1, const Point_2& p2) { return sqrt( distance2(p1, p2) ); } inline static FT distance(const Point_2& p, const Line_2& l) { return divide( p.x() * l.a() + p.y() * l.b() + l.c(), sqrt( CGAL::square(l.a()) + CGAL::square(l.b()) ) ); } // instance stuff Point_2 c; Line_2 l; Point_2 o; inline Point_2 lchain(const FT &t) const { std::vector< Point_2 > p = compute_points(t); if ( right(p[0]) ) return p[1]; return p[0]; } inline Point_2 rchain(const FT &t) const { std::vector< Point_2 > p = compute_points(t); if ( right(p[0]) ) return p[0]; return p[1]; } std::vector< Point_2 > compute_points(const FT &d) const { CGAL_assertion(d >= 0); FT d1 = distance(o, c) + d; FT d2 = distance(o, l) + d; d2 = d1; d1 *= d1; std::vector< Point_2 > p; if ( l.a() == FT(0) ) { FT y = d2 * int(CGAL::sign(l.b())) - divide(l.c(), l.b()); FT C = CGAL::square(y) - FT(2) * c.y() * y + CGAL::square(c.x()) + CGAL::square(c.y()) - d1; FT D = CGAL::square(c.x()) - C; D = CGAL::abs(D); FT x1 = sqrt(D) + c.x(); FT x2 = -sqrt(D) + c.x(); p.push_back(Point_2(x1, y)); p.push_back(Point_2(x2, y)); return p; } FT A = d2 * sqrt( CGAL::square(l.a()) + CGAL::square(l.b()) ) - l.c(); FT B = CGAL::square(c.x()) + CGAL::square(c.y()) - d1; FT alpha = FT(1) + CGAL::square(divide(l.b(), l.a())); FT beta = divide(A * l.b(), CGAL::square(l.a())) + c.y() - divide(c.x() * l.b(), l.a()); FT gamma = CGAL::square(divide(A, l.a())) + B - divide(FT(2) * c.x() * A, l.a()); FT D = CGAL::square(beta) - alpha * gamma; D = CGAL::abs(D); FT y1 = divide((beta + sqrt(D)), alpha); FT y2 = divide((beta - sqrt(D)), alpha); FT x1 = divide(A - l.b() * y1, l.a()); FT x2 = divide(A - l.b() * y2, l.a()); p.push_back(Point_2(x1, y1)); p.push_back(Point_2(x2, y2)); return p; } bool right(const Point_2& p) const { return CGAL::is_positive( determinant(c.x(), c.y(), FT(1), o.x(), o.y(), FT(1), p.x(), p.y(), FT(1)) ); } inline Point_2 midpoint(const Point_2& p1, const Point_2& p2) const { FT t1 = t(p1); FT t2 = t(p2); FT midt = divide(t1+t2, FT(2)); return f(midt); } inline Point_2 f(FT t) const { if ( CGAL::is_negative(t) ) return rchain(-t); return lchain(t); } inline FT t(const Point_2 &p) const { FT tt = distance(p, c) - distance(c, o); if ( right(p) ) return -tt; return tt; } void compute_origin() { FT d = divide(l.a() * c.x() + l.b() * c.y() + l.c(), FT(2) * ( CGAL::square(l.a()) + CGAL::square(l.b()) ) ); o = Point_2(c.x() - l.a() * d, c.y() - l.b() * d); } public: Parabola_2() {} template Parabola_2(const ApolloniusSite &p, const Line_2 &l1) { this->c = p.point(); FT d_a = CGAL::to_double(l1.a()); FT d_b = CGAL::to_double(l1.b()); FT len = sqrt(CGAL::square(d_a) + CGAL::square(d_b)); FT r = p.weight() * len; this->l = Line_2(-l1.a(), -l1.b(), -l1.c() + r); compute_origin(); } Parabola_2(const Point_2 &p, const Line_2 &line) { this->c = p; if ( line.has_on_positive_side(p) ) { this->l = line; } else { this->l = line.opposite(); } compute_origin(); } Oriented_side side_of_parabola(const Point_2& p) const { Point_2 q(CGAL::to_double(p.x()), CGAL::to_double(p.y())); FT d = distance(q, c) - CGAL::abs(distance(q, l)); if ( d < 0 ) return ON_NEGATIVE_SIDE; if ( d > 0 ) return ON_POSITIVE_SIDE; return ON_ORIENTED_BOUNDARY; } inline const Line_2& line() const { return l; } inline const Point_2& center() const { return c; } inline const Point_2& origin() const { return o; } template< class Stream > void draw(Stream& W) const { std::vector< Point_2 > p; std::vector< Point_2 > pleft, pright; pleft.push_back(origin()); pright.push_back(origin()); const FT STEP(2); for (int i = 1; i <= 100; i++) { p = compute_points(i * i * STEP); W << p[0]; W << p[1]; if ( p.size() > 0 ) { if ( right(p[0]) ) { pright.push_back(p[0]); pleft.push_back(p[1]); } else { pright.push_back(p[1]); pleft.push_back(p[0]); } } } for (unsigned int i = 0; i < pleft.size() - 1; i++) { W << Segment_2(pleft[i], pleft[i+1]); } for (unsigned int i = 0; i < pright.size() - 1; i++) { W << Segment_2(pright[i], pright[i+1]); } W << origin(); } }; template< class Stream, class Gt > inline Stream& operator<<(Stream& s, const Parabola_2 &P) { P.draw(s); return s; } } //namespace CGAL #endif // CGAL_PARABOLA_2_H