 CGAL 4.14.3 - 2D and 3D Linear Geometry Kernel
Kernel::ConstructPlane_3 Concept Reference

## Definition

Refines:
AdaptableFunctor (with two arguments)
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.

## ◆ 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.