#include <CGAL/Point_2.h>

Definition

An object p of the class Point_2 is a point in the two-dimensional Euclidean plane \( \E^2\).

Remember that Kernel::RT and Kernel::FT denote a RingNumberType and a FieldNumberType, respectively. For the kernel model Cartesian<T>, the two types are the same. For the kernel model Homogeneous<T>, Kernel::RT is equal to T, and Kernel::FT is equal to Quotient<T>.

Operators

The following operations can be applied on points:

Example

The following declaration creates two points with Cartesian double coordinates.

Point_2< Cartesian<double> > p, q(1.0, 2.0);

The variable p is uninitialized and should first be used on the left hand side of an assignment.

p = q; 
std::cout << p.x() << " " << p.y() << std::endl; 

See also: Kernel::Point_2

Related Functions
(Note that these are not member functions.)
bool	operator< (const Point_2< Kernel > &p, const Point_2< Kernel > &q)
	returns true iff `p` is lexicographically smaller than `q`, i.e. either if `p.x() < q.x()` or if `p.x() == q.x()` and `p.y() < q.y()`. More...

bool	operator> (const Point_2< Kernel > &p, const Point_2< Kernel > &q)
	returns true iff `p` is lexicographically greater than `q`. More...

bool	operator<= (const Point_2< Kernel > &p, const Point_2< Kernel > &q)
	returns true iff `p` is lexicographically smaller or equal to `q`. More...

bool	operator>= (const Point_2< Kernel > &p, const Point_2< Kernel > &q)
	returns true iff `p` is lexicographically greater or equal to `q`. More...

Vector_2< Kernel >	operator- (const Point_2< Kernel > &p, const Point_2< Kernel > &q)
	returns the difference vector between `q` and `p`. More...

Point_2< Kernel >	operator+ (const Point_2< Kernel > &p, const Vector_2< Kernel > &v)
	returns the point obtained by translating `p` by the vector `v`. More...

Point_2< Kernel >	operator- (const Point_2< Kernel > &p, const Vector_2< Kernel > &v)
	returns the point obtained by translating `p` by the vector -`v`. More...

Types
typedef unspecified_type	Cartesian_const_iterator
	An iterator for enumerating the Cartesian coordinates of a point. More...

Creation
	Point_2 (const Origin &ORIGIN)
	introduces a variable `p` with Cartesian coordinates \( (0,0)\). More...

	Point_2 (int x, int y)
	introduces a point `p` initialized to `(x,y)`. More...

	Point_2 (double x, double y)
	introduces a point `p` initialized to `(x,y)` provided `RT` supports construction from `double`. More...

	Point_2 (const Kernel::RT &hx, const Kernel::RT &hy, const Kernel::RT &hw=RT(1))
	introduces a point `p` initialized to `(hx/hw,hy/hw)`. More...

	Point_2 (const Kernel::FT &x, const Kernel::FT &y)
	introduces a point `p` initialized to `(x,y)`. More...

Operations
bool	operator== (const Point_2< Kernel > &q) const
	Test for equality. More...

bool	operator!= (const Point_2< Kernel > &q) const
	Test for inequality. More...

Coordinate Access
There are two sets of coordinate access functions, namely to the homogeneous and to the Cartesian coordinates. They can be used independently from the chosen kernel model. Note that you do not loose information with the homogeneous representation, because the `FieldNumberType` is a quotient.
Kernel::RT	hx () const
	returns the homogeneous \( x\) coordinate. More...

Kernel::RT	hy () const
	returns the homogeneous \( y\) coordinate. More...

Kernel::RT	hw () const
	returns the homogenizing coordinate. More...

Kernel::FT	x () const
	returns the Cartesian \( x\) coordinate, that is `hx()`/`hw()`. More...

Kernel::FT	y () const
	returns the Cartesian \( y\) coordinate, that is `hy()`/`hw()`. More...

Convenience Operations
The following operations are for convenience and for compatibility with higher dimensional points. Again they come in a Cartesian and in a homogeneous flavor.
Kernel::RT	homogeneous (int i) const
	returns the i'th homogeneous coordinate of `p`, starting with 0. More...

Kernel::FT	cartesian (int i) const
	returns the i'th Cartesian coordinate of `p`, starting with 0. More...

Kernel::FT	operator[] (int i) const
	returns `cartesian(i)`. More...

Cartesian_const_iterator	cartesian_begin () const
	returns an iterator to the Cartesian coordinates of `p`, starting with the 0th coordinate. More...

Cartesian_const_iterator	cartesian_end () const
	returns an off the end iterator to the Cartesian coordinates of `p`. More...

int	dimension () const
	returns the dimension (the constant 2). More...

Bbox_2	bbox () const
	returns a bounding box containing `p`. More...

Point_2< Kernel >	transform (const Aff_transformation_2< Kernel > &t) const
	returns the point obtained by applying `t` on `p`. More...

Member Typedef Documentation

template<typename Kernel >

typedef unspecified_type CGAL::Point_2< Kernel >::Cartesian_const_iterator

An iterator for enumerating the Cartesian coordinates of a point.

Constructor & Destructor Documentation

template<typename Kernel >

CGAL::Point_2< Kernel >::Point_2 ( const Origin & ORIGIN )

introduces a variable p with Cartesian coordinates \( (0,0)\).

template<typename Kernel >

CGAL::Point_2< Kernel >::Point_2	(	int	x,
		int	y
	)

introduces a point p initialized to (x,y).

template<typename Kernel >

CGAL::Point_2< Kernel >::Point_2	(	double	x,
		double	y
	)

introduces a point p initialized to (x,y) provided RT supports construction from double.

template<typename Kernel >

CGAL::Point_2< Kernel >::Point_2	(	const Kernel::RT &	hx,
		const Kernel::RT &	hy,
		const Kernel::RT &	hw = `RT(1)`
	)

introduces a point p initialized to (hx/hw,hy/hw).

Precondition: hw \( \neq\) Kernel::RT(0).

template<typename Kernel >

CGAL::Point_2< Kernel >::Point_2	(	const Kernel::FT &	x,
		const Kernel::FT &	y
	)

introduces a point p initialized to (x,y).

Member Function Documentation

template<typename Kernel >

Bbox_2 CGAL::Point_2< Kernel >::bbox ( ) const

returns a bounding box containing p.

Note that bounding boxes are not parameterized with whatsoever.

template<typename Kernel >

Kernel::FT CGAL::Point_2< Kernel >::cartesian ( int i ) const

returns the i'th Cartesian coordinate of p, starting with 0.

Precondition: \( 0\leq i \leq1\).

template<typename Kernel >

Cartesian_const_iterator CGAL::Point_2< Kernel >::cartesian_begin ( ) const

returns an iterator to the Cartesian coordinates of p, starting with the 0th coordinate.

template<typename Kernel >

Cartesian_const_iterator CGAL::Point_2< Kernel >::cartesian_end ( ) const

returns an off the end iterator to the Cartesian coordinates of p.

template<typename Kernel >

int CGAL::Point_2< Kernel >::dimension ( ) const

returns the dimension (the constant 2).

template<typename Kernel >

Kernel::RT CGAL::Point_2< Kernel >::homogeneous ( int i ) const

returns the i'th homogeneous coordinate of p, starting with 0.

Precondition: \( 0\leq i \leq2\).

template<typename Kernel >

Kernel::RT CGAL::Point_2< Kernel >::hw ( ) const

returns the homogenizing coordinate.

template<typename Kernel >

Kernel::RT CGAL::Point_2< Kernel >::hx ( ) const

returns the homogeneous \( x\) coordinate.

template<typename Kernel >

Kernel::RT CGAL::Point_2< Kernel >::hy ( ) const

returns the homogeneous \( y\) coordinate.

template<typename Kernel >

bool CGAL::Point_2< Kernel >::operator!= ( const Point_2< Kernel > & q ) const

Test for inequality.

The point can be compared with ORIGIN.

template<typename Kernel >

bool CGAL::Point_2< Kernel >::operator== ( const Point_2< Kernel > & q ) const

Test for equality.

Two points are equal, iff their \( x\) and \( y\) coordinates are equal. The point can be compared with ORIGIN.

template<typename Kernel >

Kernel::FT CGAL::Point_2< Kernel >::operator[] ( int i ) const

returns cartesian(i).

Precondition: \( 0\leq i \leq1\).

template<typename Kernel >

Point_2<Kernel> CGAL::Point_2< Kernel >::transform ( const Aff_transformation_2< Kernel > & t ) const

returns the point obtained by applying t on p.

template<typename Kernel >

Kernel::FT CGAL::Point_2< Kernel >::x ( ) const

returns the Cartesian \( x\) coordinate, that is hx()/hw().

template<typename Kernel >

Kernel::FT CGAL::Point_2< Kernel >::y ( ) const

returns the Cartesian \( y\) coordinate, that is hy()/hw().

Friends And Related Function Documentation

template<typename Kernel >

Vector_2< Kernel > operator-	(	const Point_2< Kernel > &	p,
		const Point_2< Kernel > &	q
	)

You can substitute ORIGIN for either p or q, but not for both.

template<typename Kernel >

bool operator<	(	const Point_2< Kernel > &	p,
		const Point_2< Kernel > &	q
	)

template<typename Kernel >

bool operator<=	(	const Point_2< Kernel > &	p,
		const Point_2< Kernel > &	q
	)

template<typename Kernel >

bool operator>	(	const Point_2< Kernel > &	p,
		const Point_2< Kernel > &	q
	)

template<typename Kernel >

bool operator>=	(	const Point_2< Kernel > &	p,
		const Point_2< Kernel > &	q
	)

Definition

Related Functions

Types

Creation

Operations

Coordinate Access

Convenience Operations

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation