CGAL::Triangle_2< Kernel > Class Template Reference

#include <CGAL/Triangle_2.h>

Definition

template<typename Kernel>
class CGAL::Triangle_2< Kernel >

An object t of the class Triangle_2 is a triangle in the two-dimensional Euclidean plane \( \E^2\). Triangle t is oriented, i.e., its boundary has clockwise or counterclockwise orientation. We call the side to the left of the boundary the positive side and the side to the right of the boundary the negative side.

The boundary of a triangle splits the plane in two open regions, a bounded one and an unbounded one.

Is Model Of:

Kernel::Triangle_2

Creation
	Triangle_2 (const Point_2< Kernel > &p, const Point_2< Kernel > &q, const Point_2< Kernel > &r)
	introduces a triangle t with vertices p, q and r. More...

Operations
bool	operator== (const Triangle_2< Kernel > &t2) const
	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. More...
bool	operator!= (const Triangle_2< Kernel > &t2) const
	Test for inequality. More...
Point_2< Kernel >	vertex (int i) const
	returns the i'th vertex modulo 3 of t. More...
Point_2< Kernel >	operator[] (int i) const
	returns vertex(i). More...

Predicates
For convenience we provide the following Boolean functions:
bool	is_degenerate () const
	triangle t is degenerate, if the vertices are collinear. More...
Orientation	orientation () const
	returns the orientation of t. More...
Oriented_side	oriented_side (const Point_2< Kernel > &p) const
	returns ON_ORIENTED_BOUNDARY, or POSITIVE_SIDE, or the constant ON_NEGATIVE_SIDE, determined by the position of point p. More...
Bounded_side	bounded_side (const Point_2< Kernel > &p) const
	returns the constant ON_BOUNDARY, ON_BOUNDED_SIDE, or else ON_UNBOUNDED_SIDE, depending on where point p is. More...
bool	has_on_positive_side (const Point_2< Kernel > &p) const
bool	has_on_negative_side (const Point_2< Kernel > &p) const
bool	has_on_boundary (const Point_2< Kernel > &p) const
bool	has_on_bounded_side (const Point_2< Kernel > &p) const
bool	has_on_unbounded_side (const Point_2< Kernel > &p) const

Miscellaneous
Triangle_2< Kernel >	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). More...
Kernel::FT	area () const
	returns the signed area of t. More...
Bbox_2	bbox () const
	returns a bounding box containing t. More...
Triangle_2< Kernel >	transform (const Aff_transformation_2< Kernel > &at) const
	returns the triangle obtained by applying \( at\) on the three vertices of t. More...

Constructor & Destructor Documentation

Triangle_2()

template<typename Kernel >

CGAL::Triangle_2< Kernel >::Triangle_2	(	const Point_2< Kernel > &	p,
		const Point_2< Kernel > &	q,
		const Point_2< Kernel > &	r
	)

introduces a triangle t with vertices p, q and r.

Member Function Documentation

area()

template<typename Kernel >

Kernel::FT CGAL::Triangle_2< Kernel >::area

(

)

const

returns the signed area of t.

bbox()

template<typename Kernel >

Bbox_2 CGAL::Triangle_2< Kernel >::bbox

(

)

const

returns a bounding box containing t.

bounded_side()

template<typename Kernel >

Bounded_side CGAL::Triangle_2< Kernel >::bounded_side

(

const Point_2< Kernel > &

p

)

const

returns the constant ON_BOUNDARY, ON_BOUNDED_SIDE, or else ON_UNBOUNDED_SIDE, depending on where point p is.

Precondition

t is not degenerate.

has_on_boundary()

template<typename Kernel >

bool CGAL::Triangle_2< Kernel >::has_on_boundary

(

const Point_2< Kernel > &

p

)

const

has_on_bounded_side()

template<typename Kernel >

bool CGAL::Triangle_2< Kernel >::has_on_bounded_side

(

const Point_2< Kernel > &

p

)

const

has_on_negative_side()

template<typename Kernel >

bool CGAL::Triangle_2< Kernel >::has_on_negative_side

(

const Point_2< Kernel > &

p

)

const

has_on_positive_side()

template<typename Kernel >

bool CGAL::Triangle_2< Kernel >::has_on_positive_side

(

const Point_2< Kernel > &

p

)

const

has_on_unbounded_side()

template<typename Kernel >

bool CGAL::Triangle_2< Kernel >::has_on_unbounded_side

(

const Point_2< Kernel > &

p

)

const

Precondition

t is not degenerate.

is_degenerate()

template<typename Kernel >

bool CGAL::Triangle_2< Kernel >::is_degenerate

(

)

const

triangle t is degenerate, if the vertices are collinear.

operator!=()

template<typename Kernel >

bool CGAL::Triangle_2< Kernel >::operator!=

(

const Triangle_2< Kernel > &

t2

)

const

Test for inequality.

operator==()

template<typename Kernel >

bool CGAL::Triangle_2< Kernel >::operator==

(

const Triangle_2< Kernel > &

t2

)

const

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.

operator[]()

template<typename Kernel >

Point_2<Kernel> CGAL::Triangle_2< Kernel >::operator[]

(

int

i

)

const

returns vertex(i).

opposite()

template<typename Kernel >

Triangle_2<Kernel> CGAL::Triangle_2< Kernel >::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).

orientation()

template<typename Kernel >

Orientation CGAL::Triangle_2< Kernel >::orientation

(

)

const

returns the orientation of t.

oriented_side()

template<typename Kernel >

Oriented_side CGAL::Triangle_2< Kernel >::oriented_side

(

const Point_2< Kernel > &

p

)

const

returns ON_ORIENTED_BOUNDARY, or POSITIVE_SIDE, or the constant ON_NEGATIVE_SIDE, determined by the position of point p.

Precondition

t is not degenerate.

transform()

template<typename Kernel >

Triangle_2<Kernel> CGAL::Triangle_2< Kernel >::transform

(

const Aff_transformation_2< Kernel > &

at

)

const

returns the triangle obtained by applying \( at\) on the three vertices of t.

vertex()

template<typename Kernel >

Point_2<Kernel> CGAL::Triangle_2< Kernel >::vertex

(

int

i

)

const

returns the i'th vertex modulo 3 of t.