\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.4 - 2D and 3D Linear Geometry Kernel
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Kernel::SideOfOrientedSphere_3 Concept Reference
Kernel Function Object Concepts

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...
 

Member Function Documentation

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.