CGAL 4.7 - 2D and 3D Linear Geometry Kernel: Kernel::ConstructSphere_3 Concept Reference

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CGAL 4.7 - 2D and 3D Linear Geometry Kernel

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Kernel::ConstructSphere_3 Concept Reference
Kernel Function Object Concepts

## Definition

Refines:
  `AdaptableFunctor` (with four arguments)

See Also
  `CGAL::Sphere_3<Kernel>`

## Operations

A model of this concept must provide:
Kernel::Sphere_3 | operator() (const Kernel::Point_3 &center, const Kernel::FT &squared_radius, const Orientation &orientation=COUNTERCLOCKWISE)
| introduces a sphere initialized to the sphere with center `center`, squared radius `squared_radius` and orientation `orientation`. More...
Kernel::Sphere_3 | operator() (const Kernel::Point_3 &p, const Kernel::Point_3 &q, const Kernel::Point_3 &r, const Kernel::Point_3 &s)
| introduces a sphere initialized to the unique sphere which passes through the points `p`, `q`, `r` and `s`. More...
Kernel::Sphere_3 | operator() (const Kernel::Point_3 &p, const Kernel::Point_3 &q, const Kernel::Point_3 &r, const Orientation &o=COUNTERCLOCKWISE)
| introduces a sphere initialized to the smallest sphere which passes through the points `p`, `q`, and `r`. More...
Kernel::Sphere_3 | operator() (const Kernel::Point_3 &p, const Kernel::Point_3 &q, const Orientation &o=COUNTERCLOCKWISE)
| introduces a sphere initialized to the smallest sphere which passes through the points `p` and `q`. More...
Kernel::Sphere_3 | operator() (const Kernel::Point_3 &center, const Orientation &orientation=COUNTERCLOCKWISE)
| introduces a sphere `s` initialized to the sphere with center `center`, squared radius zero and orientation `orientation`. More...
Kernel::Sphere_3 | operator() (const Kernel::Circle_3 &c)
| introduces a sphere initialized to the diametral sphere of the circle.

## Member Function Documentation

Kernel::Sphere_3 Kernel::ConstructSphere_3::operator() | ( | const Kernel::Point_3 & | center,
|  | const Kernel::FT & | squared_radius,
|  | const Orientation & | orientation = `COUNTERCLOCKWISE`
| ) |  |

introduces a sphere initialized to the sphere with center `center`, squared radius `squared_radius` and orientation `orientation`.

Precondition
  `orientation` \( \neq\) CGAL::COPLANAR, and furthermore, `squared_radius` \( \geq\) 0.

Kernel::Sphere_3 Kernel::ConstructSphere_3::operator() | ( | const Kernel::Point_3 & | p,
|  | const Kernel::Point_3 & | q,
|  | const Kernel::Point_3 & | r,
|  | const Kernel::Point_3 & | s
| ) |  |

introduces a sphere initialized to the unique sphere which passes through the points `p`, `q`, `r` and `s`.

The orientation of the sphere is the orientation of the point quadruple `p`, `q`, `r`, `s`.

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

Kernel::Sphere_3 Kernel::ConstructSphere_3::operator() | ( | const Kernel::Point_3 & | p,
|  | const Kernel::Point_3 & | q,
|  | const Kernel::Point_3 & | r,
|  | const Orientation & | o = `COUNTERCLOCKWISE`
| ) |  |

introduces a sphere initialized to the smallest sphere which passes through the points `p`, `q`, and `r`.

The orientation of the sphere is `o`.

Precondition
  `o` is not CGAL::COPLANAR.

Kernel::Sphere_3 Kernel::ConstructSphere_3::operator() | ( | const Kernel::Point_3 & | p,
|  | const Kernel::Point_3 & | q,
|  | const Orientation & | o = `COUNTERCLOCKWISE`
| ) |  |

introduces a sphere initialized to the smallest sphere which passes through the points `p` and `q`.

The orientation of the sphere is `o`.

Precondition
  `o` is not CGAL::COPLANAR.

Kernel::Sphere_3 Kernel::ConstructSphere_3::operator() | ( | const Kernel::Point_3 & | center,
|  | const Orientation & | orientation = `COUNTERCLOCKWISE`
| ) |  |

introduces a sphere `s` initialized to the sphere with center `center`, squared radius zero and orientation `orientation`.

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

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