\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.8.1 - 2D and 3D Linear Geometry Kernel
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CGAL::Triangle_3< Kernel > Class Template Reference
3D Kernel Objects

#include <CGAL/Triangle_3.h>

Definition

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.

See Also
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 oft1`.
 
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.