CGAL 4.9 - 2D Boolean Operations on Nef Polygons Embedded on the Sphere
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CGAL::Nef_polyhedron_S2< Traits >::Sphere_segment Class Reference
2D Boolean Operations on Nef Polygons Embedded on the Sphere Reference

#include <CGAL/Nef_polyhedron_S2.h>

Definition

An object s of type Sphere_segment is a segment in the surface of a unit sphere that is part of a great circle trough the origin.

Sphere segments are represented by two sphere points p and q plus an oriented plane h that contains p and q. The plane determines the sphere segment as follows. Let c be the circle in the intersection of h and S2. Then s is that part of c that is swept, when we rotate p into q in counterclockwise rotation around the normal vector of h as seen from the positive halfspace.

Creation

 Sphere_segment ()
 creates some sphere segment.
 
 Sphere_segment (const Sphere_point &p1, const Sphere_point &p2, bool shorter_arc=true)
 creates a spherical segment spanning the shorter arc from p1 to p2 if shorter_arc == true. More...
 
 Sphere_segment (const Sphere_point &p1, const Sphere_point &p2, const Sphere_circle &c)
 creates a spherical segment spanning the arc from p1 to p2 as part of the oriented circle c (p1 == p2 or p1 == p2.opposite() are possible.) More...
 
 Sphere_segment (const Sphere_circle &c1, const Sphere_circle &c2)
 creates the spherical segment as part of c1 that is part of the halfsphere left of the oriented circle c2. More...
 

Operations

const Sphere_point & source ()
 the source point of s.
 
const Sphere_point & target ()
 the target point of s.
 
const Sphere_circle & sphere_circle ()
 the great circle supporting s.
 
Sphere_segment opposite ()
 returns the sperical segment oriented from target() to source() with the same point set as s.
 
Sphere_segment complement ()
 returns the sperical segment oriented from target() to source() with the point set completing s to a full circle.
 
bool is_short ()
 a segment is short iff it is shorter than a half-circle.
 
bool is_long ()
 a segment is long iff it is longer than a half-circle.
 
bool is_degenerate ()
 return true iff s is degenerate, i.e. source and target are the same.
 
bool is_halfcircle ()
 return true iff s is a perfect half-circle, i.e. source().antipode == target().
 
bool has_on (const Sphere_point &p)
 return true iff s contains p.
 
bool has_in_relative_interior (const Sphere_point &p)
 return true iff s contains p in its relative interior.
 

Constructor & Destructor Documentation

template<typename Traits >
CGAL::Nef_polyhedron_S2< Traits >::Sphere_segment::Sphere_segment ( const Sphere_point &  p1,
const Sphere_point &  p2,
bool  shorter_arc = true 
)

creates a spherical segment spanning the shorter arc from p1 to p2 if shorter_arc == true.

Otherwise the longer arc is created.

Precondition
p1 != p2 and p1 != p2.opposite().
template<typename Traits >
CGAL::Nef_polyhedron_S2< Traits >::Sphere_segment::Sphere_segment ( const Sphere_point &  p1,
const Sphere_point &  p2,
const Sphere_circle &  c 
)

creates a spherical segment spanning the arc from p1 to p2 as part of the oriented circle c (p1 == p2 or p1 == p2.opposite() are possible.)

Precondition
p1 and p2 are contained in c.
template<typename Traits >
CGAL::Nef_polyhedron_S2< Traits >::Sphere_segment::Sphere_segment ( const Sphere_circle &  c1,
const Sphere_circle &  c2 
)

creates the spherical segment as part of c1 that is part of the halfsphere left of the oriented circle c2.

Precondition
c1 != c2 as unoriented circles.