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 CGAL 5.0 - 2D and 3D Linear Geometry Kernel
Kernel::ConstructSphere_3 Concept Reference

## Definition

Refines:
AdaptableFunctor (with four arguments)
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.

## ◆ operator()() [1/5]

 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.

## ◆ operator()() [2/5]

 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.

## ◆ operator()() [3/5]

 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.

## ◆ operator()() [4/5]

 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.

## ◆ operator()() [5/5]

 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.