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

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

CGAL 4.7 - 2D and 3D Linear Geometry Kernel

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Functions
CGAL::circumcenter()
Global Kernel Functions

##

## Functions

template<typename Kernel >
CGAL::Point_2< Kernel > | CGAL::circumcenter (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q)
| compute the center of the smallest circle passing through the points `p` and `q`. More...
template<typename Kernel >
CGAL::Point_2< Kernel > | CGAL::circumcenter (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r)
| compute the center of the circle passing through the points `p`, `q`, and `r`. More...
template<typename Kernel >
CGAL::Point_2< Kernel > | CGAL::circumcenter (const CGAL::Triangle_2< Kernel > &t)
| compute the center of the circle passing through the vertices of `t`. More...
template<typename Kernel >
CGAL::Point_3< Kernel > | CGAL::circumcenter (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q)
| compute the center of the smallest sphere passing through the points `p` and `q`. More...
template<typename Kernel >
CGAL::Point_3< Kernel > | CGAL::circumcenter (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r)
| compute the center of the circle passing through the points `p`, `q`, and `r`. More...
template<typename Kernel >
CGAL::Point_3< Kernel > | CGAL::circumcenter (const CGAL::Triangle_3< Kernel > &t)
| compute the center of the circle passing through the vertices of `t`. More...
template<typename Kernel >
CGAL::Point_3< Kernel > | CGAL::circumcenter (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 center of the sphere passing through the points `p`, `q`, `r`, and `s`. More...
template<typename Kernel >
CGAL::Point_3< Kernel > | CGAL::circumcenter (const CGAL::Tetrahedron_3< Kernel > &t)
| compute the center of the sphere passing through the vertices of `t`. More...

## Function Documentation

template<typename Kernel >

CGAL::Point_2<Kernel> CGAL::circumcenter | ( | const CGAL::Point_2< Kernel > & | p,
|  | const CGAL::Point_2< Kernel > & | q
| ) |  |

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

Note: this is the same as `CGAL::midpoint(p, q)` but is provided for homogeneity.

`#include <CGAL/global_functions.h>`

template<typename Kernel >

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

compute the center 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 >

CGAL::Point_2<Kernel> CGAL::circumcenter | ( | const CGAL::Triangle_2< Kernel > & | t) |  |

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

Precondition
  `t` is not degenerate.

`#include <CGAL/global_functions.h>`

template<typename Kernel >

CGAL::Point_3<Kernel> CGAL::circumcenter | ( | const CGAL::Point_3< Kernel > & | p,
|  | const CGAL::Point_3< Kernel > & | q
| ) |  |

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

Note: this is the same as `CGAL::midpoint(p, q)` but is provided for homogeneity.

`#include <CGAL/global_functions.h>`

template<typename Kernel >

CGAL::Point_3<Kernel> CGAL::circumcenter | ( | const CGAL::Point_3< Kernel > & | p,
|  | const CGAL::Point_3< Kernel > & | q,
|  | const CGAL::Point_3< Kernel > & | r
| ) |  |

compute the center 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 >

CGAL::Point_3<Kernel> CGAL::circumcenter | ( | const CGAL::Triangle_3< Kernel > & | t) |  |

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

Precondition
  `t` is not degenerate.

`#include <CGAL/global_functions.h>`

template<typename Kernel >

CGAL::Point_3<Kernel> CGAL::circumcenter | ( | 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 center 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>`

template<typename Kernel >

CGAL::Point_3<Kernel> CGAL::circumcenter | ( | const CGAL::Tetrahedron_3< Kernel > & | t) |  |

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

Precondition
  `t` is not degenerate.

`#include <CGAL/global_functions.h>`