CGAL 6.0 - 2D and 3D Linear Geometry Kernel
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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< Kernelvertex (int i) const
 returns the i'th vertex modulo 3 of t.
 
Point_3< Kerneloperator[] (int i) const
 returns vertex(int i).
 
Plane_3< Kernelsupporting_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< Kerneltransform (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.