Tetrahedron_3<Kernel>

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CGAL::Tetrahedron_3<Kernel>

Definition

An object

t of the class Tetrahedron_3<Kernel> is an oriented tetrahedron in the three-dimensional Euclidean space

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)