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## CGAL::Triangle_3<Kernel>

### Definition

An object t of the class Triangle_3<Kernel> is a triangle in the three-dimensional Euclidean space 3. As the triangle is not a full-dimensional object there is only a test whether a point lies on the triangle or not.

### Creation

Triangle_3<Kernel> t ( | Point_3<Kernel> p, Point_3<Kernel> q, Point_3<Kernel> r);
| introduces a triangle t with vertices p, q and r.

### Operations

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

### Predicates

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

### Miscellaneous

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

### See Also

Kernel::Triangle_3

Next: Vector_3<Kernel>

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The CGAL Project . Tue, December 21, 2004 .