CGAL 4.7 - 2D and 3D Linear Geometry Kernel: CGAL::squared_radius()

\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.7 - 2D and 3D Linear Geometry Kernel

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Functions
CGAL::squared_radius()
Global Kernel Functions

##

See Also
  `Circle_2<Kernel>_grp`
  `Circle_3<Kernel>_grp`
  `Sphere_3<Kernel>_grp`

## Functions

template<typename Kernel >
FT | CGAL::squared_radius (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r)
| compute the squared radius of the circle passing through the points `p`, `q`, and `r`. More...
template<typename Kernel >
FT | CGAL::squared_radius (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q)
| compute the squared radius of the smallest circle passing through `p`, and `q`, i.e. one fourth of the squared distance between `p` and `q`.
template<typename Kernel >
FT | CGAL::squared_radius (const CGAL::Point_2< Kernel > &p)
| compute the squared radius of the smallest circle passing through `p`, i.e. \( 0\).
template<typename Kernel >
FT | CGAL::squared_radius (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s)
| compute the squared radius of the sphere passing through the points `p`, `q`, `r` and `s`. More...
template<typename Kernel >
FT | CGAL::squared_radius (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r)
| compute the squared radius of the sphere passing through the points `p`, `q`, and `r` and whose center is in the same plane as those three points.
template<typename Kernel >
FT | CGAL::squared_radius (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q)
| compute the squared radius of the smallest circle passing through `p`, and `q`, i.e. one fourth of the squared distance between `p` and `q`.
template<typename Kernel >
FT | CGAL::squared_radius (const CGAL::Point_3< Kernel > &p)
| compute the squared radius of the smallest circle passing through `p`, i.e. \( 0\).

## Function Documentation

template<typename Kernel >

FT CGAL::squared_radius | ( | const CGAL::Point_2< Kernel > & | p,
|  | const CGAL::Point_2< Kernel > & | q,
|  | const CGAL::Point_2< Kernel > & | r
| ) |  |

compute the squared radius of the circle passing through the points `p`, `q`, and `r`.

Precondition
  `p`, `q`, and `r` are not collinear.

`#include <CGAL/global_functions.h>`

template<typename Kernel >

FT CGAL::squared_radius | ( | const CGAL::Point_3< Kernel > & | p,
|  | const CGAL::Point_3< Kernel > & | q,
|  | const CGAL::Point_3< Kernel > & | r,
|  | const CGAL::Point_3< Kernel > & | s
| ) |  |

compute the squared radius of the sphere passing through the points `p`, `q`, `r` and `s`.

Precondition
  `p`, `q`, `r` and `s` are not coplanar.

`#include <CGAL/global_functions.h>`