Kernel::ConstructPlane_3 Concept Reference

Definition

Refines

AdaptableBinaryFunction

See also

CGAL::Plane_3<Kernel>

Operations
A model of this concept must provide:
Kernel::Plane_3	operator() (const Kernel::RT &a, const Kernel::RT &b, const Kernel::RT &c, const Kernel::RT &d)
	creates a plane defined by the equation \( a\, x +b\, y +c\, z + d = 0\). More...
Kernel::Plane_3	operator() (const Kernel::Point_3 &p, const Kernel::Point_3 &q, const Kernel::Point_3 &r)
	creates a plane passing through the points p, q and r. More...
Kernel::Plane_3	operator() (const Kernel::Point_3 &p, const Kernel::Direction_3 &d)
	introduces a plane that passes through point p and that has as an orthogonal direction equal to d.
Kernel::Plane_3	operator() (const Kernel::Point_3 &p, const Kernel::Vector_3 &v)
	introduces a plane that passes through point p and that is orthogonal to v.
Kernel::Plane_3	operator() (const Kernel::Line_3 &l, const Kernel::Point_3 &p)
	introduces a plane that is defined through the three points l.point(0), l.point(1) and p.
Kernel::Plane_3	operator() (const Kernel::Ray_3 &r, const Kernel::Point_3 &p)
	introduces a plane that is defined through the three points r.point(0), r.point(1) and p.
Kernel::Plane_3	operator() (const Kernel::Segment_3 &s, const Kernel::Point_3 &p)
	introduces a plane that is defined through the three points s.source(), s.target() and p.
Kernel::Plane_3	operator() (const Kernel::Circle_3 &c)
	introduces a plane that is defined as the plane containing the circle.

Member Function Documentation

operator()() [1/2]

Kernel::Plane_3 Kernel::ConstructPlane_3::operator()	(	const Kernel::RT &	a,
		const Kernel::RT &	b,
		const Kernel::RT &	c,
		const Kernel::RT &	d
	)

creates a plane defined by the equation \( a\, x +b\, y +c\, z + d = 0\).

Notice that it is degenerate if \( a = b = c = 0\).

operator()() [2/2]

Kernel::Plane_3 Kernel::ConstructPlane_3::operator()	(	const Kernel::Point_3 &	p,
		const Kernel::Point_3 &	q,
		const Kernel::Point_3 &	r
	)

creates a plane passing through the points p, q and r.

The plane is oriented such that p, q and r are oriented in a positive sense (that is counterclockwise) when seen from the positive side of the plane. Notice that it is degenerate if the points are collinear.