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CGAL 4.3 - 3D Spherical Geometry Kernel
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Geometric Global Functions

Functions

CGAL::Circle_type CGAL::classify (const CGAL::Circle_3< SphericalKernel > &c, const CGAL::Sphere_3< SphericalKernel > &sphere)
 Classify a circle according to sphere, as defined in Section Spherical Kernel Objects. More...
 
Comparison_result CGAL::compare_theta (const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Circular_arc_point_3< SphericalKernel > &q, const CGAL::Sphere_3< SphericalKernel > &sphere)
 Compares the θ-coordinates of p and q relatively to sphere. More...
 
Comparison_result CGAL::compare_theta (const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Vector_3< SphericalKernel > &m, const CGAL::Sphere_3< SphericalKernel > &sphere)
 Compares the θ-coordinates of p and of the meridian defined by m (see Section Spherical Kernel Objects) in the cylindrical coordinate system relative to sphere. More...
 
Comparison_result CGAL::compare_theta (const CGAL::Vector_3< SphericalKernel > &m, const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Sphere_3< SphericalKernel > &sphere)
 Compares the θ-coordinates of the meridian defined by m and of p (see Section Spherical Kernel Objects) in the cylindrical coordinate system relative to sphere. More...
 
bool CGAL::compare_theta_z (const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Circular_arc_point_3< SphericalKernel > &q, const CGAL::Sphere_3< SphericalKernel > &sphere)
 Compares p and q according to the lexicographic ordering on θ and z-coordinates in the cylindrical coordinate system relative to sphere. More...
 
bool CGAL::is_theta_monotone (const CGAL::Circular_arc_3< SphericalKernel > &a, const CGAL::Sphere_3< SphericalKernel > &sphere)
 Tests whether the arc a is θ-monotone, i.e. the intersection of any meridian anchored at the poles sphere and the arc a is reduced to at most one point in general, and two points if a pole of sphere is an endpoint of the arc. More...
 
CGAL::Circular_arc_point_3
< SphericalKernel
CGAL::theta_extremal_point (const CGAL::Circle_3< SphericalKernel > &c, const CGAL::Sphere_3< SphericalKernel > sphere, bool b)
 Returns the point on the circle that is extremal in θ using the cylindrical coordinate system relative to sphere, and that has the smallest (resp. largest) θ-coordinate of the two points if b is true (resp. false). More...
 
OutputIterator CGAL::theta_extremal_points (const CGAL::Circle_3< SphericalKernel > &c, const CGAL::Sphere_3< SphericalKernel > &sphere, OutputIterator res)
 Copies in the output iterator the θ-extremal points of the circle relatively to sphere. More...
 
CGAL::Circular_arc_point_3
< SphericalKernel
CGAL::x_extremal_point (const CGAL::Sphere_3< SphericalKernel > &c, bool b)
 Returns the point on the sphere that is extremal in the x-direction, and that is the smallest (resp. largest) of the two x-extremal points for the lexicographic order if b is true (resp. false).
 
CGAL::Circular_arc_point_3
< SphericalKernel
CGAL::x_extremal_point (const CGAL::Circle_3< SphericalKernel > &c, bool b)
 Same for a circle. More...
 
OutputIterator CGAL::x_extremal_points (const CGAL::Sphere_3< SphericalKernel > &c, OutputIterator res)
 Copies in the output iterator the x-extremal points of the sphere. More...
 
OutputIterator CGAL::x_extremal_points (const CGAL::Circle_3< SphericalKernel > &c, OutputIterator res)
 Copies in the output iterator the x-extremal points of the circle. More...
 
CGAL::Circular_arc_point_3
< SphericalKernel
CGAL::y_extremal_point (const CGAL::Sphere_3< SphericalKernel > &c, bool b)
 Returns the point on the sphere that is extremal in the y-direction, and that is the smallest (resp. largest) of the two y-extremal points for the lexicographic order if b is true (resp. false).
 
CGAL::Circular_arc_point_3
< SphericalKernel
CGAL::y_extremal_point (const CGAL::Circle_3< SphericalKernel > &c, bool b)
 Same for a circle. More...
 
OutputIterator CGAL::y_extremal_points (const CGAL::Sphere_3< SphericalKernel > &c, OutputIterator res)
 Copies in the output iterator the y-extremal points of the sphere. More...
 
OutputIterator CGAL::y_extremal_points (const CGAL::Circle_3< SphericalKernel > &c, OutputIterator res)
 Copies in the output iterator the y-extremal points of the circle. More...
 
CGAL::Circular_arc_point_3
< SphericalKernel
CGAL::z_extremal_point (const CGAL::Sphere_3< SphericalKernel > &c, bool b)
 Returns the point on the sphere that is extremal in the z-direction, and that is the smallest (resp. largest) of the two z-extremal points for the lexicographic order if b is true (resp. false).
 
CGAL::Circular_arc_point_3
< SphericalKernel
CGAL::z_extremal_point (const CGAL::Circle_3< SphericalKernel > &c, bool b)
 Same for a circle. More...
 
OutputIterator CGAL::z_extremal_points (const CGAL::Sphere_3< SphericalKernel > &c, OutputIterator res)
 Copies in the output iterator the z-extremal points of the sphere. More...
 
OutputIterator CGAL::z_extremal_points (const CGAL::Circle_3< SphericalKernel > &c, OutputIterator res)
 Copies in the output iterator the z-extremal points of the circle. More...