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

CGAL 4.8 - 2D and 3D Linear Geometry Kernel

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Kernel::ConstructCircle_2 Concept Reference
Kernel Function Object Concepts

## Definition

Refines:
  `AdaptableFunctor` (with three arguments)

See Also
  `CGAL::Circle_2<Kernel>`

## Operations
A model of this concept must provide:
Kernel::Circle_2 | operator() (Kernel::Point_2 const &center, Kernel::FT const &squared_radius, Orientation const &orientation=COUNTERCLOCKWISE)
| introduces a variable of type `Kernel::Circle_2`. More...
Kernel::Circle_2 | operator() (Kernel::Point_2 const &p, Kernel::Point_2 const &q, Kernel::Point_2 const &r)
| introduces a variable of type `Kernel::Circle_2`. More...
Kernel::Circle_2 | operator() (Kernel::Point_2 const &p, Kernel::Point_2 const &q, Orientation const &orientation=COUNTERCLOCKWISE)
| introduces a variable of type `Kernel::Circle_2`. More...
Kernel::Circle_2 | operator() (Kernel::Point_2 const &center, Orientation const &orientation=COUNTERCLOCKWISE)
| introduces a variable of type `Kernel::Circle_2`. More...

## Member Function Documentation

Kernel::Circle_2 Kernel::ConstructCircle_2::operator() | ( | Kernel::Point_2 const & | center,
|  | Kernel::FT const & | squared_radius,
|  | Orientation const & | orientation = `COUNTERCLOCKWISE`
| ) |  |

introduces a variable of type `Kernel::Circle_2`.

It is initialized to the circle with center `center`, squared radius `squared_radius` and orientation `orientation`.

Precondition
  `orientation` \( \neq\) CGAL::COLLINEAR, and further, `squared_radius` \( \geq\) 0.

Kernel::Circle_2 Kernel::ConstructCircle_2::operator() | ( | Kernel::Point_2 const & | p,
|  | Kernel::Point_2 const & | q,
|  | Kernel::Point_2 const & | r
| ) |  |

introduces a variable of type `Kernel::Circle_2`.

It is initialized to the unique circle which passes through the points `p`, `q` and `r`. The orientation of the circle is the orientation of the point triple `p`, `q`, `r`.

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

Kernel::Circle_2 Kernel::ConstructCircle_2::operator() | ( | Kernel::Point_2 const & | p,
|  | Kernel::Point_2 const & | q,
|  | Orientation const & | orientation = `COUNTERCLOCKWISE`
| ) |  |

introduces a variable of type `Kernel::Circle_2`.

It is initialized to the circle with diameter `pq` and orientation `orientation`.

Precondition
  `orientation` \( \neq\) CGAL::COLLINEAR.

Kernel::Circle_2 Kernel::ConstructCircle_2::operator() | ( | Kernel::Point_2 const & | center,
|  | Orientation const & | orientation = `COUNTERCLOCKWISE`
| ) |  |

introduces a variable of type `Kernel::Circle_2`.

It is initialized to the circle with center `center`, squared radius zero and orientation `orientation`.

Precondition
  `orientation` \( \neq\) CGAL::COLLINEAR.

Postcondition
  .`is_degenerate()` = `true`.