CGAL Namespace Reference

Classes
struct	Algebraic_kernel_for_spheres_2_3
class	Circular_arc_3
class	Circular_arc_point_3
class	Exact_spherical_kernel_3
	A typedef to a spherical kernel that provides both exact geometric predicates and exact geometric constructions. More...
class	Line_arc_3
class	Polynomial_1_3
class	Polynomial_for_spheres_2_3
class	Polynomials_for_lines_3
class	Root_for_spheres_2_3
struct	Spherical_kernel_3

Enumerations
enum	Circle_type { NORMAL , THREADED , POLAR , BIPOLAR }
	The enum Circle_type is used to classify an object of type Circle_3, so as to specify its type (normal,polar,bipolar or threaded), as defined in Section Spherical Kernel Objects. More...

Functions
template<class SphericalKernel >
CGAL::Circle_type	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.
template<class SphericalKernel >
Comparison_result	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 \( \theta\)-coordinates of p and q relatively to sphere.
template<class SphericalKernel >
Comparison_result	compare_theta (const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Vector_3< SphericalKernel > &m, const CGAL::Sphere_3< SphericalKernel > &sphere)
	Compares the \( \theta\)-coordinates of p and of the meridian defined by m (see Section Spherical Kernel Objects) in the cylindrical coordinate system relative to sphere.
template<class SphericalKernel >
Comparison_result	compare_theta (const CGAL::Vector_3< SphericalKernel > &m, const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Sphere_3< SphericalKernel > &sphere)
	Compares the \( \theta\)-coordinates of the meridian defined by m and of p (see Section Spherical Kernel Objects) in the cylindrical coordinate system relative to sphere.
template<class SphericalKernel >
bool	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 \( \theta\) and \( z\)-coordinates in the cylindrical coordinate system relative to sphere.
template<class SphericalKernel >
bool	is_theta_monotone (const CGAL::Circular_arc_3< SphericalKernel > &a, const CGAL::Sphere_3< SphericalKernel > &sphere)
	Tests whether the arc a is \( \theta\)-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.
template<class SphericalKernel >
CGAL::Circular_arc_point_3< SphericalKernel >	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 \( \theta\) using the cylindrical coordinate system relative to sphere, and that has the smallest (resp. largest) \( \theta\)-coordinate of the two points if b is true (resp. false).
template<class SphericalKernel , class OutputIterator >
OutputIterator	theta_extremal_points (const CGAL::Circle_3< SphericalKernel > &c, const CGAL::Sphere_3< SphericalKernel > &sphere, OutputIterator res)
	Copies in the output iterator the \( \theta\)-extremal points of the circle relatively to sphere.
template<class SphericalKernel >
CGAL::Circular_arc_point_3< SphericalKernel >	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).
template<class SphericalKernel >
CGAL::Circular_arc_point_3< SphericalKernel >	x_extremal_point (const CGAL::Circle_3< SphericalKernel > &c, bool b)
	Same for a circle.
template<class SphericalKernel , class OutputIterator >
OutputIterator	x_extremal_points (const CGAL::Sphere_3< SphericalKernel > &c, OutputIterator res)
	Copies in the output iterator the \( x\)-extremal points of the sphere.
template<class SphericalKernel , class OutputIterator >
OutputIterator	x_extremal_points (const CGAL::Circle_3< SphericalKernel > &c, OutputIterator res)
	Copies in the output iterator the \( x\)-extremal points of the circle.
template<class SphericalKernel >
CGAL::Circular_arc_point_3< SphericalKernel >	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).
template<class SphericalKernel >
CGAL::Circular_arc_point_3< SphericalKernel >	y_extremal_point (const CGAL::Circle_3< SphericalKernel > &c, bool b)
	Same for a circle.
template<class SphericalKernel class OutputIterator>
OutputIterator	y_extremal_points (const CGAL::Sphere_3< SphericalKernel > &c, OutputIterator res)
	Copies in the output iterator the \( y\)-extremal points of the sphere.
template<class SphericalKernel , class OutputIterator >
OutputIterator	y_extremal_points (const CGAL::Circle_3< SphericalKernel > &c, OutputIterator res)
	Copies in the output iterator the \( y\)-extremal points of the circle.
template<class SphericalKernel >
CGAL::Circular_arc_point_3< SphericalKernel >	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).
template<class SphericalKernel >
CGAL::Circular_arc_point_3< SphericalKernel >	z_extremal_point (const CGAL::Circle_3< SphericalKernel > &c, bool b)
	Same for a circle.
template<class SphericalKernel , class OutputIterator >
OutputIterator	z_extremal_points (const CGAL::Sphere_3< SphericalKernel > &c, OutputIterator res)
	Copies in the output iterator the \( z\)-extremal points of the sphere.
template<class SphericalKernel , class OutputIterator >
OutputIterator	z_extremal_points (const CGAL::Circle_3< SphericalKernel > &c, OutputIterator res)
	Copies in the output iterator the \( z\)-extremal points of the circle.