CGAL::Triangle_3< Kernel > Class Template Reference

#include <CGAL/Triangle_3.h>

Definition

template<typename Kernel>
class CGAL::Triangle_3< Kernel >

An object t of the class Triangle_3 is a triangle in the three-dimensional Euclidean space \( \E^3\). As the triangle is not a full-dimensional object there is only a test whether a point lies on the triangle or not.

Is Model Of:

Kernel::Triangle_3

Creation
	Triangle_3 (const Point_3< Kernel > &p, const Point_3< Kernel > &q, const Point_3< Kernel > &r)
	introduces a triangle t with vertices p, q and r. More...

Operations
bool	operator== (const Triangle_3< Kernel > &t2) const
	Test for equality: two triangles t1 and t2 are equal, iff there exists a cyclic permutation of the vertices of t2, such that they are equal to the vertices oft1`. More...
bool	operator!= (const Triangle_3< Kernel > &t2) const
	Test for inequality. More...
Point_3< Kernel >	vertex (int i) const
	returns the i'th vertex modulo 3 of t. More...
Point_3< Kernel >	operator[] (int i) const
	returns vertex(int i). More...
Plane_3< Kernel >	supporting_plane ()
	returns the supporting plane of t, with same orientation. More...

Predicates
bool	is_degenerate () const
	t is degenerate if its vertices are collinear. More...
bool	has_on (const Point_3< Kernel > &p) const
	A point is on t, if it is on a vertex, an edge or the face of t. More...

Miscellaneous
Kernel::FT	squared_area () const
	returns a square of the area of t. More...
Bbox_3	bbox () const
	returns a bounding box containing t. More...
Triangle_3< Kernel >	transform (const Aff_transformation_3< Kernel > &at) const
	returns the triangle obtained by applying at on the three vertices of t. More...

Constructor & Destructor Documentation

Triangle_3()

template<typename Kernel >

CGAL::Triangle_3< Kernel >::Triangle_3	(	const Point_3< Kernel > &	p,
		const Point_3< Kernel > &	q,
		const Point_3< Kernel > &	r
	)

introduces a triangle t with vertices p, q and r.

Member Function Documentation

bbox()

template<typename Kernel >

Bbox_3 CGAL::Triangle_3< Kernel >::bbox

(

)

const

returns a bounding box containing t.

has_on()

template<typename Kernel >

bool CGAL::Triangle_3< Kernel >::has_on

(

const Point_3< Kernel > &

p

)

const

A point is on t, if it is on a vertex, an edge or the face of t.

is_degenerate()

template<typename Kernel >

bool CGAL::Triangle_3< Kernel >::is_degenerate

(

)

const

t is degenerate if its vertices are collinear.

operator!=()

template<typename Kernel >

bool CGAL::Triangle_3< Kernel >::operator!=

(

const Triangle_3< Kernel > &

t2

)

const

Test for inequality.

operator==()

template<typename Kernel >

bool CGAL::Triangle_3< Kernel >::operator==

(

const Triangle_3< Kernel > &

t2

)

const

Test for equality: two triangles t1 and t2 are equal, iff there exists a cyclic permutation of the vertices of t2, such that they are equal to the vertices oft1`.

operator[]()

template<typename Kernel >

Point_3<Kernel> CGAL::Triangle_3< Kernel >::operator[]

(

int

i

)

const

returns vertex(int i).

squared_area()

template<typename Kernel >

Kernel::FT CGAL::Triangle_3< Kernel >::squared_area

(

)

const

returns a square of the area of t.

supporting_plane()

template<typename Kernel >

Plane_3<Kernel> CGAL::Triangle_3< Kernel >::supporting_plane

(

)

returns the supporting plane of t, with same orientation.

transform()

template<typename Kernel >

Triangle_3<Kernel> CGAL::Triangle_3< Kernel >::transform

(

const Aff_transformation_3< Kernel > &

at

)

const

returns the triangle obtained by applying at on the three vertices of t.

vertex()

template<typename Kernel >

Point_3<Kernel> CGAL::Triangle_3< Kernel >::vertex

(

int

i

)

const

returns the i'th vertex modulo 3 of t.