CGAL 4.12.1 - 2D and 3D Linear Geometry Kernel
Kernel::SideOfOrientedSphere_3 Concept Reference

## Definition

Refines:
AdaptableFunctor (with five arguments)
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...

## ◆ 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.