Kernel::ConstructSphere_3 Concept Reference

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

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.