#include <CGAL/Tetrahedron_3.h>

Definition

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

Convencience 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`.

Member Function Documentation

◆ bounded_side()

template<typename Kernel >

Bounded_side CGAL::Tetrahedron_3< Kernel >::bounded_side ( const Point_3< Kernel > & p ) const

Precondition: t is not degenerate.

◆ oriented_side()

template<typename Kernel >

Oriented_side CGAL::Tetrahedron_3< Kernel >::oriented_side ( const Point_3< Kernel > & p ) const

Precondition: t is not degenerate.

Definition

Creation

Operations

Predicates

Convencience Boolean Functions

Miscellaneous

Member Function Documentation

◆ bounded_side()

◆ oriented_side()