CGAL 6.1.2 - 2D and 3D Linear Geometry Kernel: Kernel::SideOfOrientedSphere_3 Concept Reference

CGAL 6.1.2 - 2D and 3D Linear Geometry Kernel

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Kernel::SideOfOrientedSphere_3 Concept Reference
Reference Manual » Concepts » Kernel Function Object Concepts

## 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`.

## 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.