CGAL 5.4.4  2D and 3D Linear Geometry Kernel

AdaptableFunctor
(with two arguments)CGAL::Plane_3<Kernel>
Operations  
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.  
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 \( a = b = c = 0\).
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.