CGAL 6.2 - 3D Spherical Geometry Kernel

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Circular_kernel_3/functor_compare_theta_3.cpp
#include <CGAL/Exact_spherical_kernel_3.h>
#include <CGAL/iterator.h>
typedef CGAL::Exact_spherical_kernel_3 SK;
int main(){
//construction of 3 spheres from their centers and squared radii
SK::Sphere_3 s1(SK::Point_3(0,0,0),2);
SK::Sphere_3 s2(SK::Point_3(0,1,0),1);
SK::Sphere_3 s3(SK::Point_3(1,0,0),3);
//construct two circles lying on sphere s1
SK::Circle_3 C1(s1,s2);
SK::Circle_3 C2(s1,s3);
SK::Intersect_3 inter;
//create a functor to compare theta-coordinates on sphere s1
SK::Compare_theta_z_3 cmp(s1);
//unsigned integer indicates multiplicity of intersection point
typedef std::pair<SK::Circular_arc_point_3,unsigned> Point_and_multiplicity;
// only recover points
std::vector< Point_and_multiplicity > intersections;
inter(C1,C2,
CGAL::dispatch_or_drop_output<Point_and_multiplicity>(std::back_inserter(intersections)));
const Point_and_multiplicity& p1=intersections[0];
const Point_and_multiplicity& p2=intersections[1];
SK::Circular_arc_point_3 t_extreme[2];
//Compute theta extremal points of circle C1 on sphere s1
CGAL::theta_extremal_points(C1,s1,t_extreme);
//The theta coordinates of theta extremal points of C1 enclose that of each intersection point.
assert(cmp(t_extreme[0],p1.first)==CGAL::SMALLER);
assert(cmp(t_extreme[0],p2.first)==CGAL::SMALLER);
assert(cmp(t_extreme[1],p1.first)==CGAL::LARGER);
assert(cmp(t_extreme[1],p2.first)==CGAL::LARGER);
return 0;
}
CGAL::Exact_spherical_kernel_3
A typedef to a spherical kernel that provides both exact geometric predicates and exact geometric con...
Definition: Exact_spherical_kernel_3.h:16
CGAL::theta_extremal_points
OutputIterator theta_extremal_points(const CGAL::Circle_3< SphericalKernel > &c, const CGAL::Sphere_3< SphericalKernel > &sphere, OutputIterator res)
Copies in the output iterator the -extremal points of the circle relatively to sphere.
CGAL::LARGER
LARGER
CGAL::SMALLER
SMALLER