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.

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 of t1.
bool	operator!= (const Triangle_3< Kernel > &t2) const
	Test for inequality.
Point_3< Kernel >	vertex (int i) const
	returns the i'th vertex modulo 3 of t.
Point_3< Kernel >	operator[] (int i) const
	returns vertex(int i).
Plane_3< Kernel >	supporting_plane ()
	returns the supporting plane of t, with same orientation.

Predicates
bool	is_degenerate () const
	t is degenerate if its vertices are collinear.
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.

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

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.

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::Triangle_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.

operator[]()

template<typename Kernel >

Point_3< Kernel > CGAL::Triangle_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.

vertex()

template<typename Kernel >

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

(

int

i

)

const

returns the i'th vertex modulo 3 of t.

Exactness

This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.