CGAL::Nef_polyhedron_S2< Traits >::Sphere_circle Class Reference

#include <CGAL/Nef_polyhedron_S2.h>

Definition

template<typename Traits>
class CGAL::Nef_polyhedron_S2< Traits >::Sphere_circle

An object c of type Sphere_circle is an oriented great circle on the surface of a unit sphere.

Such circles correspond to the intersection of an oriented plane (that contains the origin) and the surface of $S_2$. The orientation of the great circle is that of a counterclockwise walk along the circle as seen from the positive halfspace of the oriented plane.

Related Functions
(Note that these are not member functions.)
bool	equal_as_sets (const Nef_polyhedron_S2< Traits >::Sphere_circle c1, const Nef_polyhedron_S2< Traits >::Sphere_circle c2)
	returns true iff c1 and c2 are equal as unoriented circles.

Types
typedef unspecified_type	RT
	ring type.
typedef unspecified_type	Plane_3
	plane a Sphere_circle lies in.

Creation
	Sphere_circle ()
	creates some great circle.
	Sphere_circle (const Sphere_point &p, const Sphere_point &q)
	If $p$ and $q$ are opposite of each other, then we create the unique great circle on $S_2$ which contains p and q.
	Sphere_circle (const Plane_3 &h)
	creates the circle corresponding to the plane h.
	Sphere_circle (const RT &x, const RT &y, const RT &z)
	creates the circle orthogonal to the vector $(x,y,z)$.
	Sphere_circle (Sphere_circle c, const Sphere_point &p)
	creates a great circle orthogonal to $c$ that contains $p$.

Operations
Sphere_circle	opposite ()
	Returns a sphere circle in the opposite direction of c.
bool	has_on (const Sphere_point &p)
	returns true iff c contains p.
Plane_3	plane ()
	returns the plane supporting c.
Sphere_point	orthogonal_pole ()
	returns the point that is the pole of the hemisphere left of c.

Constructor & Destructor Documentation

Sphere_circle() [1/3]

template<typename Traits >

CGAL::Nef_polyhedron_S2< Traits >::Sphere_circle::Sphere_circle	(	const Sphere_point &	p,
		const Sphere_point &	q
	)

If $p$ and $q$ are opposite of each other, then we create the unique great circle on $S_2$ which contains p and q.

This circle is oriented such that a walk along c meets $p$ just before the shorter segment between $p$ and $q$. If $p$ and $q$ are opposite of each other then we create any great circle that contains $p$ and $q$.

Sphere_circle() [2/3]

template<typename Traits >

CGAL::Nef_polyhedron_S2< Traits >::Sphere_circle::Sphere_circle

(

const Plane_3 &

h

)

creates the circle corresponding to the plane h.

Precondition

h contains the origin.

Sphere_circle() [3/3]

template<typename Traits >

CGAL::Nef_polyhedron_S2< Traits >::Sphere_circle::Sphere_circle	(	Sphere_circle	c,
		const Sphere_point &	p
	)

creates a great circle orthogonal to $c$ that contains $p$.

Precondition

$p$ is not part of $c$.