CGAL::Tetrahedron_3<Kernel>

Definition

³

It is defined by four vertices $$p₀, $$p₁, $$p₂ and $$p₃. The orientation of a tetrahedron is the orientation of its four vertices. That means it is positive when $$p₃ is on the positive side of the plane defined by $$p₀, $$p₁ and $$p₂.

The tetrahedron itself splits the space $$ ₃ in a positive and a negative side.

The boundary of a tetrahedron splits the space in two open regions, a bounded one and an unbounded one.

Creation

Tetrahedron_3<Kernel> t ( Point_3<Kernel> p0, Point_3<Kernel> p1, Point_3<Kernel> p2, Point_3<Kernel> p3);
	introduces a tetrahedron t with vertices $$p0, $$p1, $$p2 and $$p3.

Operations

bool	t.operator== ( t2)
		Test for equality: two tetrahedra t and t2 are equal, iff t and t2 have the same orientation and their sets (not sequences) of vertices are equal.
bool	t.operator!= ( t2)
		Test for inequality.
Point_3<Kernel>	t.vertex ( int i)	returns the i'th vertex modulo 4 of t.
Point_3<Kernel>	t.operator[] ( int i)
		returns vertex(int i).

Predicates

bool	t.is_degenerate ()	Tetrahedron t is degenerate, if the vertices are coplanar.
Orientation	t.orientation ()
Oriented_side	t.oriented_side ( Point_3<Kernel> p)
		Precondition: : t is not degenerate.
Bounded_side	t.bounded_side ( Point_3<Kernel> p)
		Precondition: : t is not degenerate.

For convenience we provide the following boolean functions:

bool	t.has_on_positive_side ( Point_3<Kernel> p)
bool	t.has_on_negative_side ( Point_3<Kernel> p)
bool	t.has_on_boundary ( Point_3<Kernel> p)
bool	t.has_on_bounded_side ( Point_3<Kernel> p)
bool	t.has_on_unbounded_side ( Point_3<Kernel> p)

Miscellaneous

Kernel::FT	t.volume ()	returns the signed volume of t.
Bbox_3	t.bbox ()	returns a bounding box containing t.
Tetrahedron_3<Kernel>
	t.transform ( Aff_transformation_3<Kernel> at)
		returns the tetrahedron obtained by applying $$at on the three vertices of t.

See Also