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// Copyright (c) 2008 INRIA Sophia-Antipolis (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
// You can redistribute it and/or modify it under the terms of the GNU
// General Public License as published by the Free Software Foundation,
// either version 3 of the License, or (at your option) any later version.
//
// Licensees holding a valid commercial license may use this file in
// accordance with the commercial license agreement provided with the software.
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// $URL: svn+ssh://scm.gforge.inria.fr/svn/cgal/branches/next/Circular_kernel_3/include/CGAL/Circular_kernel_3/internal_functions_on_circle_3.h $
// $Id: internal_functions_on_circle_3.h 67117 2012-01-13 18:14:48Z lrineau $
//
// Author(s) : Monique Teillaud, Sylvain Pion, Pedro Machado,
// Sebastien Loriot, Julien Hazebrouck, Damien Leroy
// Partially supported by the IST Programme of the EU as a
// STREP (FET Open) Project under Contract No IST-006413
// (ACS -- Algorithms for Complex Shapes)
#ifndef CGAL_SPHERICAL_KERNEL_PREDICATES_ON_CIRCLE_3_H
#define CGAL_SPHERICAL_KERNEL_PREDICATES_ON_CIRCLE_3_H
#include <CGAL/Circle_type.h>
#include <CGAL/Circular_kernel_3/internal_functions_on_plane_3.h>
#include <CGAL/Circular_kernel_3/internal_functions_on_circular_arc_point_3.h>
#include <CGAL/Root_of_traits.h>
namespace CGAL {
namespace SphericalFunctors {
template < class SK >
typename SK::Circle_3
construct_circle_3(const typename SK::Polynomials_for_circle_3 &eq)
{
typedef typename SK::Point_3 Point_3;
typedef typename SK::Plane_3 Plane_3;
typedef typename SK::Circle_3 Circle_3;
typedef typename SK::Sphere_3 Sphere_3;
typedef typename SK::FT FT;
Sphere_3 s = construct_sphere_3<SK>(eq.first);
Plane_3 p = construct_plane_3<SK>(eq.second);
const FT d2 = CGAL::square(p.a()*s.center().x() +
p.b()*s.center().y() +
p.c()*s.center().z() + p.d()) /
(CGAL::square(p.a()) + CGAL::square(p.b()) + CGAL::square(p.c()));
// We do not accept circles with radius 0 (should we?)
CGAL_kernel_precondition(d2 < s.squared_radius());
// d2 < s.squared_radius()
Point_3 center = p.projection(s.center());
return Circle_3(center,s.squared_radius() - d2,p);
}
template < class SK >
CGAL::Circle_type
classify_circle_3(const typename SK::Circle_3& circle,const typename SK::Sphere_3& sphere)
{
typedef typename SK::Algebraic_kernel::Root_for_spheres_2_3 Root_for_spheres_2_3;
typedef typename SK::Circular_arc_point_3 Circular_arc_point_3;
CGAL_kernel_precondition(SK().has_on_3_object()(sphere,circle));
//if circle is a great circle, it can only be a bipolar or a threaded.
if (circle.center()==sphere.center()){
if (circle.supporting_plane().orthogonal_vector().z()==0)
return CGAL::BIPOLAR;
return CGAL::THREADED;
}
typename SK::Root_of_2 radius=CGAL::make_sqrt(sphere.squared_radius());
Circular_arc_point_3 north_pole( Root_for_spheres_2_3(sphere.center().x(),sphere.center().y(),sphere.center().z()+radius) );
Circular_arc_point_3 south_pole( Root_for_spheres_2_3(sphere.center().x(),sphere.center().y(),sphere.center().z()-radius) );
const typename SK::Sphere_3& supp_sphere=circle.diametral_sphere();
typename SK::Bounded_side_3 bounded_side=SK().bounded_side_3_object();
CGAL::Bounded_side side_of_north=bounded_side(supp_sphere,north_pole);
CGAL::Bounded_side side_of_south=bounded_side(supp_sphere,south_pole);
if (side_of_north==ON_BOUNDARY || side_of_south==ON_BOUNDARY)
return CGAL::POLAR;
if (side_of_north==ON_BOUNDED_SIDE || side_of_south==ON_BOUNDED_SIDE)
return CGAL::THREADED;
CGAL_kernel_precondition(side_of_north==ON_UNBOUNDED_SIDE && side_of_south==ON_UNBOUNDED_SIDE);
return CGAL::NORMAL;
}
template < class SK >
inline typename SK::FT
extremal_points_z_coordinate(const typename SK::Circle_3& circle,const typename SK::Sphere_3& sphere)
{
CGAL_kernel_precondition(SK().has_on_3_object()(sphere,circle));
CGAL_kernel_precondition(classify_circle_3<SK>(circle,sphere)==CGAL::NORMAL);
const typename SK::Point_3& circle_center=circle.center();
const typename SK::Point_3& sphere_center=sphere.center();
return
typename SK::FT(2) * (circle_center-sphere_center).z() * sphere.squared_radius()
/ ( SK().compute_squared_distance_3_object()(circle_center,sphere_center) + sphere.squared_radius()-circle.squared_radius() )
+ sphere_center.z();
}
template < class SK, class Output_iterator >
Output_iterator theta_extremal_points(const typename SK::Circle_3& circle,const typename SK::Sphere_3& sphere,Output_iterator out_it){
CGAL_kernel_precondition(classify_circle_3<SK>(circle,sphere)==NORMAL);
CGAL_kernel_precondition(SK().has_on_3_object()(sphere,circle));
typename SK::FT z_coord=extremal_points_z_coordinate<SK>(circle,sphere);
typename SK::Plane_3 plane(0,0,1,-z_coord);
std::vector<CGAL::Object> inters;
intersect_3<SK>(circle,plane,std::back_inserter(inters));
CGAL_kernel_precondition(inters.size()==2);
const std::pair<typename SK::Circular_arc_point_3,unsigned>* pt[2]={NULL,NULL};
pt[0]=object_cast<std::pair<typename SK::Circular_arc_point_3,unsigned> >(&inters[0]);
pt[1]=object_cast<std::pair<typename SK::Circular_arc_point_3,unsigned> >(&inters[1]);
CGAL_kernel_precondition(pt[0]!=NULL);
CGAL_kernel_precondition(pt[1]!=NULL);
if ( compare_theta_of_pts<SK>(pt[0]->first,pt[1]->first,sphere) == SMALLER){
*out_it++=pt[0]->first;
*out_it++=pt[1]->first;
}
else{
*out_it++=pt[1]->first;
*out_it++=pt[0]->first;
}
return out_it;
}
template < class SK >
typename SK::Circular_arc_point_3 theta_extremal_point(const typename SK::Circle_3& circle,const typename SK::Sphere_3& sphere,bool is_smallest){
typename SK::Circular_arc_point_3 pts[2];
theta_extremal_points(circle,sphere,pts);
if (is_smallest)
return pts[0];
return pts[1];
}
template < class SK,class Output_iterator>
Output_iterator make_circle_theta_monotone(const typename SK::Circle_3& circle,const typename SK::Sphere_3& sphere,Output_iterator out_it){
CGAL::Circle_type type=classify_circle_3<SK>(circle,sphere);
switch (type){
case THREADED:
{
*out_it++=typename SK::Circular_arc_3(circle);
break;
}
case POLAR:{
typename SK::Vector_3 ortho=circle.center()-sphere.center();
CGAL_kernel_precondition(ortho.z()!=0);
bool is_north_pole=ortho.z()>0;
typename SK::Root_of_2 radius = (is_north_pole?1:-1)* make_sqrt(sphere.squared_radius());
typename SK::Circular_arc_point_3 source_target(
typename SK::Algebraic_kernel::Root_for_spheres_2_3(
sphere.center().x(),
sphere.center().y(),
sphere.center().z()+radius
)
);
*out_it++=typename SK::Circular_arc_3(circle,source_target);
break;
}
case NORMAL:{
typename SK::Circular_arc_point_3 ints[2];
theta_extremal_points(circle,sphere,ints);
*out_it++=typename SK::Circular_arc_3(circle,ints[0],ints[1]);
*out_it++=typename SK::Circular_arc_3(circle,ints[1],ints[0]);
}
break;
case BIPOLAR:
CGAL_kernel_precondition(!"This function does not accept bipolar circle as input.");
}
return out_it;
}
}//SphericalFunctors
}//CGAL
#endif //CGAL_SPHERICAL_KERNEL_PREDICATES_ON_CIRCLE_3_H
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