2D Triangle (CGAL_Triangle_2)

Definition

As any Jordan curve the boundary of a triangle splits the plane in two open regions, a bounded one and an unbounded one.

#include <CGAL/Triangle_2.h>

Creation

CGAL_Triangle_2<R> t ( CGAL_Point_2<R> p, CGAL_Point_2<R> q, CGAL_Point_2<R> r);
	introduces a triangle t with vertices $p$, $q$ and $r$.

Operations

bool	t == t2	Test for equality: two triangles 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 != t2	Test for inequality.
CGAL_Point_2<R>	t.vertex ( int i)	returns the i'th vertex modulo 3 of t.
CGAL_Point_2<R>	t [ int i]	returns vertex(i).

Predicates

bool	t.is_degenerate ()	triangle t is degenerate, if the vertices are collinear.
CGAL_Orientation	t.orientation ()	returns the orientation of t.
CGAL_Oriented_side	t.oriented_side ( CGAL_Point_2<R> p)
		returns CGAL_ON_ORIENTED_BOUNDARY, or CGAL_POSITIVE_SIDE, or the constant CGAL_ON_NEGATIVE_SIDE, determined by the position of point $p$.
CGAL_Bounded_side	t.bounded_side ( CGAL_Point_2<R> p)
		returns the constant CGAL_ON_BOUNDARY, CGAL_ON_BOUNDED_SIDE, or else CGAL_ON_UNBOUNDED_SIDE, depending on where point $p$ is.

For convenience we provide the following boolean functions:

bool	t.has_on_positive_side ( CGAL_Point_2<R> p)
bool	t.has_on_negative_side ( CGAL_Point_2<R> p)
bool	t.has_on_boundary ( CGAL_Point_2<R> p)
bool	t.has_on_bounded_side ( CGAL_Point_2<R> p)
bool	t.has_on_unbounded_side ( CGAL_Point_2<R> p)

Miscellaneous

CGAL_Triangle_2<R>	t.opposite ()	returns a triangle where the boundary is oriented the other way round (this flips the positive and the negative side, but not the bounded and unbounded side).
CGAL_Bbox_2	t.bbox ()	returns a bounding box containing t.
CGAL_Triangle_2<R>	t.transform ( CGAL_Aff_transformation_2<R> at)
		returns the triangle obtained by applying $at$ on the three vertices of t.