\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.14.3 - 2D and 3D Linear Geometry Kernel
Functions
CGAL::side_of_oriented_sphere()
2D and 3D Linear Geometry Kernel Reference » 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. More...
 

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.