CGAL 6.2 - 2D and 3D Linear Geometry Kernel: CGAL::side_of_oriented_sphere()

CGAL 6.2 - 2D and 3D Linear Geometry Kernel

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Functions
CGAL::side_of_oriented_sphere()
Reference Manual » Global Kernel Functions

##

See also
  `CGAL::side_of_bounded_sphere()`

## Functions
template<typename Kernel >
Oriented_side | CGAL::side_of_oriented_sphere (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s, const CGAL::Point_3< Kernel > &test)
| returns the relative position of point `test` to the oriented sphere defined by `p`, `q`, `r` and `s`.

## Function Documentation

## ◆ side_of_oriented_sphere()

template<typename Kernel >

Oriented_side CGAL::side_of_oriented_sphere | ( | const CGAL::Point_3< Kernel > & | p,
|  | const CGAL::Point_3< Kernel > & | q,
|  | const CGAL::Point_3< Kernel > & | r,
|  | const CGAL::Point_3< Kernel > & | s,
|  | const CGAL::Point_3< Kernel > & | test
| ) |  |

`#include <CGAL/Kernel/global_functions.h>`

returns the relative position of point `test` 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. `CGAL::side_of_oriented_sphere(q, r, s, test, p)` is returned if `q`, `r`, `s`, and `test` are non coplanar.