\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.10 - 2D and 3D Linear Geometry Kernel
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Kernel::ConstructCircumcenter_3 Concept Reference

Definition

Refines:
AdaptableFunctor (with four arguments)
See Also
CGAL::circumcenter()

Operations

A model of this concept must provide:

Kernel::Point_3 operator() (const Kernel::Point_3 &p, const Kernel::Point_3 &q)
 compute the center of the smallest circle passing through the points p and q. More...
 
Kernel::Point_3 operator() (const Kernel::Point_3 &p, const Kernel::Point_3 &q, const Kernel::Point_3 &r, const Kernel::Point_3 &s)
 compute the center of the sphere passing through the points p, q, r, and s. More...
 
Kernel::Point_3 operator() (const Kernel::Tetrahedron_3 &t)
 compute the center of the sphere passing through the vertices of t. More...
 
Kernel::Point_3 operator() (const Kernel::Point_3 &p, const Kernel::Point_3 &q, const Kernel::Point_3 &r)
 compute the center of the circle passing through the points p, q and r. More...
 
Kernel::Point_3 operator() (const Kernel::Triangle_3 &t)
 compute the center of the circle passing through the vertices of t. More...
 

Member Function Documentation

Kernel::Point_3 Kernel::ConstructCircumcenter_3::operator() ( const Kernel::Point_3 p,
const Kernel::Point_3 q 
)

compute the center of the smallest circle passing through the points p and q.

Note : this is the same as Kernel::ConstructMidpoint_3.

Kernel::Point_3 Kernel::ConstructCircumcenter_3::operator() ( const Kernel::Point_3 p,
const Kernel::Point_3 q,
const Kernel::Point_3 r,
const Kernel::Point_3 s 
)

compute the center of the sphere passing through the points p, q, r, and s.

Precondition
p, q, r, and s are not coplanar.
Kernel::Point_3 Kernel::ConstructCircumcenter_3::operator() ( const Kernel::Tetrahedron_3 t)

compute the center of the sphere passing through the vertices of t.

Precondition
t is not degenerate.
Kernel::Point_3 Kernel::ConstructCircumcenter_3::operator() ( const Kernel::Point_3 p,
const Kernel::Point_3 q,
const Kernel::Point_3 r 
)

compute the center of the circle passing through the points p, q and r.

Precondition
p, q and r are not collinear.
Kernel::Point_3 Kernel::ConstructCircumcenter_3::operator() ( const Kernel::Triangle_3 t)

compute the center of the circle passing through the vertices of t.

Precondition
t is not degenerate.