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CGAL 4.4 - 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.