Kernel::ConstructSphere_3 Concept Reference Definition Refines AdaptableQuaternaryFunction See alsoCGAL::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. 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. 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. 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. 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. 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. Preconditionorientation != CGAL::COPLANAR and squared_radius >= 0. operator()() [2/5] 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. Preconditionorientation != CGAL::COPLANAR. Postconditions.is_degenerate() = true. 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 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. Preconditionp, q, r, and s are not coplanar. operator()() [4/5] 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. Preconditiono != CGAL::COPLANAR. operator()() [5/5] 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. Preconditiono != CGAL::COPLANAR. KernelConstructSphere_3 Generated by 1.17.0

Definition

Refines

AdaptableQuaternaryFunction

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.
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.
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.
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.
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.
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 != CGAL::COPLANAR and squared_radius >= 0.

operator()() [2/5]

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 != CGAL::COPLANAR.

Postcondition

s.is_degenerate() = true.

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 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()() [4/5]

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 != CGAL::COPLANAR.

operator()() [5/5]

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 != CGAL::COPLANAR.