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// Copyright (c) 2003-2008 INRIA Sophia-Antipolis (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL: https://github.com/CGAL/cgal/blob/v6.1.1/Circular_kernel_2/include/CGAL/Circular_kernel_2/internal_functions_on_circle_2.h $
// $Id: include/CGAL/Circular_kernel_2/internal_functions_on_circle_2.h 08b27d3db14 $
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
// Author(s) : Monique Teillaud, Sylvain Pion, Pedro Machado
// Partially supported by the IST Programme of the EU as a Shared-cost
// RTD (FET Open) Project under Contract No IST-2000-26473
// (ECG - Effective Computational Geometry for Curves and Surfaces)
// and a STREP (FET Open) Project under Contract No IST-006413
// (ACS -- Algorithms for Complex Shapes)
#ifndef CGAL_CIRCULAR_KERNEL_INTERNAL_FUNCTIONS_ON_CIRCLE_2_H
#define CGAL_CIRCULAR_KERNEL_INTERNAL_FUNCTIONS_ON_CIRCLE_2_H
#include <CGAL/license/Circular_kernel_2.h>
#include <CGAL/Circular_kernel_2/Intersection_traits.h>
#include <vector>
namespace CGAL {
// temporary function : where to put it, if we want to keep it ?
template< class CK>
typename CK::Circular_arc_point_2
circle_intersect( const typename CK::Circle_2 & c1,
const typename CK::Circle_2 & c2,
bool b )
{
typedef std::vector<typename CK2_Intersection_traits<CK, typename CK::Circle_2,
typename CK::Circle_2>::type> solutions_container;
solutions_container solutions;
intersection( c1, c2, std::back_inserter(solutions) );
typename solutions_container::iterator it = solutions.begin();
CGAL_kernel_precondition( it != solutions.end() );
// the circles intersect
const std::pair<typename CK::Circular_arc_point_2, unsigned>*
result = Intersections::internal::intersect_get<std::pair<typename CK::Circular_arc_point_2, unsigned> > (*it);
if ( result->second == 2 ) // double solution
return result->first;
if (b)
return result->first;
++it;
result = Intersections::internal::intersect_get<std::pair<typename CK::Circular_arc_point_2, unsigned> > (*it);
return result->first;
}
namespace CircularFunctors {
template < class CK >
typename CK::Polynomial_for_circles_2_2
get_equation( const typename CK::Circle_2 & c )
{
typedef typename CK::Algebraic_kernel AK;
return AK().construct_polynomial_for_circles_2_2_object()
( c.center().x(), c.center().y(), c.squared_radius() );
}
template < class CK >
typename CK::Circle_2
construct_circle_2( const typename CK::Polynomial_for_circles_2_2 &eq )
{
return typename
CK::Circle_2( typename CK::Point_2(eq.a(), eq.b()), eq.r_sq() );
}
template < class CK >
bool
has_on(const typename CK::Circle_2 &a,
const typename CK::Circular_arc_point_2 &p)
{
typedef typename CK::Algebraic_kernel AK;
typedef typename CK::Polynomial_for_circles_2_2 Polynomial_for_circles_2_2;
Polynomial_for_circles_2_2 equation = CircularFunctors::get_equation<CK>(a);
return (AK().sign_at_object()(equation,p.coordinates()) == ZERO);
}
template < class CK >
inline bool
non_oriented_equal(const typename CK::Circle_2 & c1,
const typename CK::Circle_2 & c2) {
if(identical(c1,c2)) return true;
return (c1.squared_radius() == c2.squared_radius()) &&
(c1.center() == c2.center());
}
template < class CK >
inline
typename CK::Linear_kernel::Bounded_side
bounded_side(const typename CK::Circle_2 &c,
const typename CK::Circular_arc_point_2 &p) {
typedef typename CK::Algebraic_kernel AK;
typedef typename CK::Polynomial_for_circles_2_2 Equation;
Equation equation = get_equation<CK>(c);
Sign sign = AK().sign_at_object()(equation,p.coordinates());
if(sign == NEGATIVE) return ON_BOUNDED_SIDE;
else if(sign == POSITIVE) return ON_UNBOUNDED_SIDE;
else return ON_BOUNDARY;
}
template< class CK, class OutputIterator>
OutputIterator
intersect_2( const typename CK::Circle_2 & c1,
const typename CK::Circle_2 & c2,
OutputIterator res )
{
typedef typename CK::Algebraic_kernel AK;
typedef typename CK::Polynomial_for_circles_2_2 Equation;
typedef typename CK::Root_for_circles_2_2 Root_for_circles_2_2;
Equation e1 = CircularFunctors::get_equation<CK>(c1);
Equation e2 = CircularFunctors::get_equation<CK>(c2);
if (e1 == e2) {
*res++ = c1;
return res;
}
typedef std::vector< std::pair < Root_for_circles_2_2, unsigned > >
solutions_container;
solutions_container solutions;
AK().solve_object()(e1, e2, std::back_inserter(solutions));
// to be optimized
typedef typename CK::Circular_arc_point_2 Circular_arc_point_2;
for ( typename solutions_container::iterator it = solutions.begin();
it != solutions.end(); ++it )
{
*res++ = std::make_pair(Circular_arc_point_2(it->first), it->second );
}
return res;
}
// Should we have an iterator based interface, or both ?
template <class CK>
typename CK::Circular_arc_point_2
x_extremal_point(const typename CK::Circle_2 & c, bool i)
{
typedef typename CK::Algebraic_kernel AK;
return AK().x_critical_points_object()(typename CK::Get_equation()(c),i);
}
template <class CK,class OutputIterator>
OutputIterator
x_extremal_points(const typename CK::Circle_2 & c, OutputIterator res)
{
typedef typename CK::Algebraic_kernel AK;
return AK().x_critical_points_object()(typename CK::Get_equation()(c),res);
}
template <class CK>
typename CK::Circular_arc_point_2
y_extremal_point(const typename CK::Circle_2 & c, bool i)
{
typedef typename CK::Algebraic_kernel AK;
return AK().y_critical_points_object()(typename CK::Get_equation()(c),i);
}
template <class CK,class OutputIterator>
OutputIterator
y_extremal_points(const typename CK::Circle_2 & c, OutputIterator res)
{
typedef typename CK::Algebraic_kernel AK;
return AK().y_critical_points_object()(typename CK::Get_equation()(c),res);
}
} // namespace CircularFunctors
} //namespace CGAL
#endif // CGAL_CIRCULAR_KERNEL_INTERNAL_FUNCTIONS_ON_CIRCLE_2_H
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