CGAL 5.1.3 - 2D and 3D Linear Geometry Kernel
Kernel::ConstructCircle_3 Concept Reference

## Definition

Refines:
CGAL::Circle_3<Kernel>

## Operations

A model of this concept must provide:

Kernel::Circle_3 operator() (Kernel::Point_3 const &center, Kernel::FT const &sq_r, Kernel::Plane_3 const &plane)
introduces a variable of type Kernel::Circle_3. More...

Kernel::Circle_3 operator() (Kernel::Point_3 const &center, Kernel::FT const &sq_r, Kernel::Vector_3 const &n)
introduces a variable of type Kernel::Circle_3. More...

Kernel::Circle_3 operator() (Kernel::Point_3 const &p, Kernel::Point_3 const &q, Kernel::Point_3 const &r)
introduces a variable of type Kernel::Point_3. More...

Kernel::Circle_3 operator() (Kernel::Sphere_3 const &sphere1, Kernel::Sphere_3 const &sphere2)
introduces a variable of type Kernel::Circle_3. More...

Kernel::Circle_3 operator() (Kernel::Sphere_3 const &sphere, Kernel::Plane_3 const &plane)
introduces a variable of type Kernel::Circle_3. More...

Kernel::Circle_3 operator() (Kernel::Plane_3 const &plane, Kernel::Sphere_3 const &sphere)
introduces a variable of type Kernel::Circle_3. More...

## ◆ operator()() [1/6]

 Kernel::Circle_3 Kernel::ConstructCircle_3::operator() ( Kernel::Point_3 const & center, Kernel::FT const & sq_r, Kernel::Plane_3 const & plane )

introduces a variable of type Kernel::Circle_3.

It is initialized to the circle with center center, and squared radius sq_r in the plane plane.

Precondition
center lies in plane and sq_r $$\geq$$ 0.

## ◆ operator()() [2/6]

 Kernel::Circle_3 Kernel::ConstructCircle_3::operator() ( Kernel::Point_3 const & center, Kernel::FT const & sq_r, Kernel::Vector_3 const & n )

introduces a variable of type Kernel::Circle_3.

It is initialized to the circle with center center, and squared radius sq_r in the plane containing center and normal to n.

Precondition
sq_r $$\geq$$ 0.

## ◆ operator()() [3/6]

 Kernel::Circle_3 Kernel::ConstructCircle_3::operator() ( Kernel::Point_3 const & p, Kernel::Point_3 const & q, Kernel::Point_3 const & r )

introduces a variable of type Kernel::Point_3.

It is initialized to the circle passing through the three points.

Precondition
The three points are not collinear.

## ◆ operator()() [4/6]

 Kernel::Circle_3 Kernel::ConstructCircle_3::operator() ( Kernel::Sphere_3 const & sphere1, Kernel::Sphere_3 const & sphere2 )

introduces a variable of type Kernel::Circle_3.

It is initialized to the circle along which the two spheres intersect.

Precondition
The two spheres intersect along a circle.

## ◆ operator()() [5/6]

 Kernel::Circle_3 Kernel::ConstructCircle_3::operator() ( Kernel::Sphere_3 const & sphere, Kernel::Plane_3 const & plane )

introduces a variable of type Kernel::Circle_3.

It is initialized to the circle along which the sphere and the plane intersect.

Precondition
The sphere and the plane intersect along a circle.

## ◆ operator()() [6/6]

 Kernel::Circle_3 Kernel::ConstructCircle_3::operator() ( Kernel::Plane_3 const & plane, Kernel::Sphere_3 const & sphere )

introduces a variable of type Kernel::Circle_3.

It is initialized to the circle along which the sphere and the plane intersect.

Precondition
The sphere and the plane intersect along a circle.