332 lines
7.2 KiB
C++
332 lines
7.2 KiB
C++
// 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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//
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// $URL: https://github.com/CGAL/cgal/blob/v5.1/Apollonius_graph_2/include/CGAL/Parabola_2.h $
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// $Id: Parabola_2.h 0779373 2020-03-26T13:31:46+01:00 Sébastien Loriot
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// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
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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_PARABOLA_2_H
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#define CGAL_PARABOLA_2_H
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#include <CGAL/license/Apollonius_graph_2.h>
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#include <vector>
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#include <CGAL/determinant.h>
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#include <CGAL/Algebraic_structure_traits.h>
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#include <CGAL/number_utils.h>
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namespace CGAL {
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template < class Gt >
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class Parabola_2
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{
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private:
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typedef Parabola_2<Gt> Self;
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public:
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typedef typename Gt::Site_2 Site_2;
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typedef typename Gt::Point_2 Point_2;
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typedef typename Gt::Segment_2 Segment_2;
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typedef typename Gt::Line_2 Line_2;
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typedef typename Gt::FT 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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// typedef CGAL::Line_2< Cartesian<double> > Line_2;
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private:
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typedef Algebraic_structure_traits<FT> AST;
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protected:
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// inline static
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// FT square(const FT &x)
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// {
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// return x * x;
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// }
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inline static
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FT divide(const FT& x, const FT& y, Integral_domain_without_division_tag) {
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return FT(CGAL::to_double(x) / CGAL::to_double(y));
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}
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inline static
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FT divide(const FT& x, const FT& y, Field_tag) {
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return x / y;
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}
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inline static
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FT divide(const FT& x, const FT& y) {
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return divide(x,y, typename AST::Algebraic_category());
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}
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inline static
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FT sqrt(const FT& x, Integral_domain_without_division_tag) {
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return CGAL::sqrt(CGAL::to_double(x));
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}
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inline static
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FT sqrt(const FT& x, Field_with_sqrt_tag) {
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return CGAL::sqrt(x);
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}
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inline static
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FT sqrt(const FT& x) {
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return sqrt(x, typename AST::Algebraic_category());
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}
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inline static
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FT norm2(const Point_2& p)
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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 static
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FT distance2(const Point_2& p1, const Point_2& p2)
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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 static
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FT distance(const Point_2& p1, const Point_2& p2)
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{
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return sqrt( distance2(p1, p2) );
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}
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inline static
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FT distance(const Point_2& p, const Line_2& l)
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{
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return divide( p.x() * l.a() + p.y() * l.b() + l.c(),
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sqrt( CGAL::square(l.a()) + CGAL::square(l.b()) ) );
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}
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// instance stuff
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Point_2 c;
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Line_2 l;
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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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std::vector< Point_2 > compute_points(const FT &d) const
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{
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CGAL_assertion(d >= 0);
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FT d1 = distance(o, c) + d;
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FT d2 = distance(o, l) + d;
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d2 = d1;
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d1 *= d1;
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std::vector< Point_2 > p;
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if ( l.a() == FT(0) ) {
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FT y = d2 * int(CGAL::sign(l.b())) - divide(l.c(), l.b());
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FT C = CGAL::square(y) - FT(2) * c.y() * y +
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CGAL::square(c.x()) + CGAL::square(c.y()) - d1;
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FT D = CGAL::square(c.x()) - C;
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D = CGAL::abs(D);
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FT x1 = sqrt(D) + c.x();
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FT x2 = -sqrt(D) + c.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 A = d2 * sqrt( CGAL::square(l.a()) + CGAL::square(l.b()) ) - l.c();
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FT B = CGAL::square(c.x()) + CGAL::square(c.y()) - d1;
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FT alpha = FT(1) + CGAL::square(divide(l.b(), l.a()));
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FT beta = divide(A * l.b(), CGAL::square(l.a())) + c.y()
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- divide(c.x() * l.b(), l.a());
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FT gamma = CGAL::square(divide(A, l.a())) + B
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- divide(FT(2) * c.x() * A, l.a());
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FT D = CGAL::square(beta) - alpha * gamma;
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D = CGAL::abs(D);
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FT y1 = divide((beta + sqrt(D)), alpha);
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FT y2 = divide((beta - sqrt(D)), alpha);
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FT x1 = divide(A - l.b() * y1, l.a());
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FT x2 = divide(A - l.b() * y2, l.a());
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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_positive( determinant<FT>(c.x(), c.y(), FT(1),
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o.x(), o.y(), FT(1),
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p.x(), p.y(), FT(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 = divide(t1+t2, FT(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(p, c) - distance(c, o);
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if ( right(p) ) return -tt;
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return tt;
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}
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void compute_origin()
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{
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FT d = divide(l.a() * c.x() + l.b() * c.y() + l.c(),
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FT(2) * ( CGAL::square(l.a()) + CGAL::square(l.b()) ) );
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o = Point_2(c.x() - l.a() * d, c.y() - l.b() * d);
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}
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public:
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Parabola_2() {}
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template<class ApolloniusSite>
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Parabola_2(const ApolloniusSite &p, const Line_2 &l1)
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{
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this->c = p.point();
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FT d_a = CGAL::to_double(l1.a());
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FT d_b = CGAL::to_double(l1.b());
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FT len = sqrt(CGAL::square(d_a) + CGAL::square(d_b));
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FT r = p.weight() * len;
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this->l = Line_2(-l1.a(), -l1.b(), -l1.c() + r);
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compute_origin();
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}
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Parabola_2(const Point_2 &p, const Line_2 &line)
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{
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this->c = p;
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if ( line.has_on_positive_side(p) ) {
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this->l = line;
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} else {
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this->l = line.opposite();
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}
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compute_origin();
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}
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Oriented_side
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side_of_parabola(const Point_2& p) const
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{
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Point_2 q(CGAL::to_double(p.x()), CGAL::to_double(p.y()));
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FT d = distance(q, c) - CGAL::abs(distance(q, l));
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if ( d < 0 ) return ON_NEGATIVE_SIDE;
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if ( d > 0 ) return ON_POSITIVE_SIDE;
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return ON_ORIENTED_BOUNDARY;
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}
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inline Line_2 line() const
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{
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return l;
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}
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inline Point_2 center() const
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{
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return c;
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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 > p;
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std::vector< Point_2 > pleft, pright;
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pleft.push_back(o);
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pright.push_back(o);
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const FT STEP(2);
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for (int i = 1; i <= 100; i++) {
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p = compute_points(i * i * STEP);
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W << p[0];
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W << p[1];
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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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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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W << o;
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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 Parabola_2<Gt> &P)
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{
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P.draw(s);
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return s;
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}
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} //namespace CGAL
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#endif // CGAL_PARABOLA_2_H
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