\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.3 - 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 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`.