CGAL::Tetrahedron_3< Kernel > Class Template Reference

#include <CGAL/Tetrahedron_3.h>

Definition

template<typename Kernel>
class CGAL::Tetrahedron_3< Kernel >

An object t of the class Tetrahedron_3 is an oriented tetrahedron in the three-dimensional Euclidean space \( \E^3\).

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 \( \E^3\) 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.

Is model of

Kernel::Tetrahedron_3

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

Operations
bool	operator== (const Tetrahedron_3< Kernel > &t2) const
	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	operator!= (const Tetrahedron_3< Kernel > &t2) const
	Test for inequality.
Point_3< Kernel >	vertex (int i) const
	returns the i'th vertex modulo 4 of t.
Point_3< Kernel >	operator[] (int i) const
	returns vertex(int i).

Predicates
bool	is_degenerate () const
	Tetrahedron t is degenerate, if the vertices are coplanar.
Orientation	orientation () const
Oriented_side	oriented_side (const Point_3< Kernel > &p) const
Bounded_side	bounded_side (const Point_3< Kernel > &p) const

Convenience Boolean Functions
bool	has_on_positive_side (const Point_3< Kernel > &p) const
bool	has_on_negative_side (const Point_3< Kernel > &p) const
bool	has_on_boundary (const Point_3< Kernel > &p) const
bool	has_on_bounded_side (const Point_3< Kernel > &p) const
bool	has_on_unbounded_side (const Point_3< Kernel > &p) const

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

Constructor & Destructor Documentation

Tetrahedron_3()

template<typename Kernel >

CGAL::Tetrahedron_3< Kernel >::Tetrahedron_3	(	const Point_3< Kernel > &	p0,
		const Point_3< Kernel > &	p1,
		const Point_3< Kernel > &	p2,
		const Point_3< Kernel > &	p3
	)

introduces a tetrahedron t with vertices p0, p1, p2 and p3.

Exactness

This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

Member Function Documentation

bbox()

template<typename Kernel >

Bbox_3 CGAL::Tetrahedron_3< Kernel >::bbox

(

)

const

returns a bounding box containing t.

Exactness

This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

bounded_side()

template<typename Kernel >

Bounded_side CGAL::Tetrahedron_3< Kernel >::bounded_side

(

const Point_3< Kernel > &

p

)

const

Precondition

t is not degenerate.

operator[]()

template<typename Kernel >

Point_3< Kernel > CGAL::Tetrahedron_3< Kernel >::operator[]

(

int

i

)

const

returns vertex(int i).

Exactness

This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

oriented_side()

template<typename Kernel >

Oriented_side CGAL::Tetrahedron_3< Kernel >::oriented_side

(

const Point_3< Kernel > &

p

)

const

Precondition

t is not degenerate.

vertex()

template<typename Kernel >

Point_3< Kernel > CGAL::Tetrahedron_3< Kernel >::vertex

(

int

i

)

const

returns the i'th vertex modulo 4 of t.

Exactness

This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.