CGAL::Nef_polyhedron_S2<Traits>::Sphere_segment

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

Nef_polyhedron_S2<Traits>::Sphere_segment s;
	creates some sphere segment.
Nef_polyhedron_S2<Traits>::Sphere_segment s ( Sphere_point p1, 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().
Nef_polyhedron_S2<Traits>::Sphere_segment s ( Sphere_point p1, Sphere_point p2, 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.
Nef_polyhedron_S2<Traits>::Sphere_segment s ( Sphere_circle c1, 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.

Operations

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