Nef_polyhedron_S2<Traits>::Sphere

Navigation: Up, Table of Contents, Package Overview, Bibliography, Index, Title Page , Acknowledging CGAL

CGAL::Nef_polyhedron_S2<Traits>::Sphere_circle

Definition

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 S₂. 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.

Types

Nef_polyhedron_S2<Traits>::Sphere_circle::RT
	ring type.

Nef_polyhedron_S2<Traits>::Sphere_circle::Plane_3
	plane a Sphere_circle lies in.

Creation

Nef_polyhedron_S2<Traits>::Sphere_circle c;

creates some great circle.

Nef_polyhedron_S2<Traits>::Sphere_circle c ( Sphere_point p, Sphere_point q);

p and

q are opposite of each other, then we create the unique great circle on

S₂ 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

Nef_polyhedron_S2<Traits>::Sphere_circle c ( Plane_3 h);

creates the circle corresponding to the plane h.

Precondition:

h contains the origin.

Nef_polyhedron_S2<Traits>::Sphere_circle c ( RT x, RT y, RT z);

creates the circle orthogonal to the vector

(x,y,z).

Nef_polyhedron_S2<Traits>::Sphere_circle c ( Sphere_circle c, Sphere_point p);

creates a great circle orthogonal to

c that contains

Precondition:

p is not part of

Operations

Sphere_circle	c.opposite ()	Returns a sphere circle in the oppostie direction of c.

bool	c.has_on ( Sphere_point p)	returns true iff c contains p.

Plane_3	c.plane ()	returns the plane supporting c.

Sphere_point	c.orthogonal_pole ()	returns the point that is the pole of the hemisphere left of c.

Global functions

bool	equal_as_sets ( const c1, const c2)
		returns true iff c1 and c2 are equal as unoriented circles.

Next: Nef_polyhedron_S2<Traits>::SVertex

Navigation: Up, Table of Contents, Package Overview, Bibliography, Index, Title Page , Acknowledging CGAL

CGAL Open Source Project. Release 3.3.1. 25 August 2007.