Kernel::SideOfOrientedSphere_3 Concept Reference

Definition

Refines

AdaptableQuinaryFunction

See also

CGAL::side_of_oriented_sphere()

Operations
A model of this concept must provide:
Oriented_side	operator() (const Kernel::Point_3 &p, const Kernel::Point_3 &q, const Kernel::Point_3 &r, const Kernel::Point_3 &s, const Kernel::Point_3 &t)
	returns the relative position of point t to the oriented sphere defined by p, q, r and s. More...

Member Function Documentation

operator()()

Oriented_side Kernel::SideOfOrientedSphere_3::operator()	(	const Kernel::Point_3 &	p,
		const Kernel::Point_3 &	q,
		const Kernel::Point_3 &	r,
		const Kernel::Point_3 &	s,
		const Kernel::Point_3 &	t
	)

returns the relative position of point t to the oriented sphere defined by p, q, r and s.

The order of the points p, q, r, and s is important, since it determines the orientation of the implicitly constructed sphere. If the points p, q, r and s are positive oriented, positive side is the bounded interior of the sphere.

In case of degeneracies, CGAL::ON_ORIENTED_BOUNDARY is returned if all points are coplanar. Otherwise, there is a cyclic permutation of the five points that puts four non coplanar points first, it is used to answer the predicate: e.g. side_of_oriented_sphere(q, r, s, t, p) is returned if q, r, s, and t are non coplanar.