3D Tetrahedron (CGAL_Tetrahedron_3)

Definition

It is defined by four vertices $p$₀, $p$₁, $p$₂ and $p$₃. The orientation of a tetrahedron is the orientation of its four vertices. That means it is positive when $p$₃ is on the positive side of the plane defined by $p$₀, $p$₁ and $p$₂.

The tetrahedron itself splits the space $$E₃ 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.

#include <CGAL/Tetrahedron_3.h>

Creation

CGAL_Tetrahedron_3<R> t ( CGAL_Point_3<R> p0, CGAL_Point_3<R> p1, CGAL_Point_3<R> p2, CGAL_Point_3<R> p3);
	introduces a tetrahedron t with vertices $p$0, $p$1, $p$2 and $p$3.

Operations

bool	t == t2	Test for equality: two tetrahedra are equal, iff there exists a cyclic permutation of the vertices of $t2$, such that they are equal to the vertices of t.
bool	t != t2	Test for inequality.
CGAL_Point_3<R>	t.vertex ( int i)	returns the i'th vertex modulo 4 of t.
CGAL_Point_3<R>	t [ int i]	returns vertex(int i).

Predicates

bool	t.is_degenerate ()	Tetrahedron t is degenerate, if the vertices are coplanar.
CGAL_Orientation	t.orientation ()
CGAL_Oriented_side	t.oriented_side ( CGAL_Point_3<R> p)
CGAL_Bounded_side	t.bounded_side ( CGAL_Point_3<R> p)

For convenience we provide the following boolean functions:

bool	t.has_on_positive_side ( CGAL_Point_3<R> p)
bool	t.has_on_negative_side ( CGAL_Point_3<R> p)
bool	t.has_on_boundary ( CGAL_Point_3<R> p)
bool	t.has_on_bounded_side ( CGAL_Point_3<R> p)
bool	t.has_on_unbounded_side ( CGAL_Point_3<R> p)

Miscellaneous

CGAL_Bbox_3	t.bbox ()	returns a bounding box containing t.
CGAL_Tetrahedron_3<R>
	t.transform ( CGAL_Aff_transformation_3<R> at)
		returns the tetrahedron obtained by applying $at$ on the three vertices of t.

Footnotes

1. See Chapter [ref:Utilities] for the definition of CGAL_Oriented_side.