2D Point (CGAL_Point_2)

Definition

Remember that R::RT and R::FT denote a ring type and a field type. For the representation class CGAL_Cartesian<T> the two types are the same. For the representation class CGAL_Homogeneous<T> the ring type R::RT is equal to T, and the field type R::FT is equal to CGAL_Quotient<T>.

#include <CGAL/Point_2.h>

Creation

CGAL_Point_2<R> p ( CGAL_Origin CGAL_ORIGIN);
	introduces a variable p with Cartesian coordinates $(0,0)$.
CGAL_Point_2<R> p ( R::RT hx, R::RT hy, R::RT hw = R::RT(1));
	introduces a point p initialized to $(hx/hw,hy/hw)$. If the third argument is not explicitly given, it defaults to R::RT(1). Precondition: hw is not R::RT(0)

Operations

bool	p == q	Test for equality. Two points are equal, iff their $x$ and $y$ coordinates are equal. The point can be compared with CGAL_ORIGIN.
bool	p != q	Test for inequality. The point can be compared with CGAL_ORIGIN.

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 representation type R.

R::RT	p.hx ()	returns the homogeneous $x$ coordinate.
R::RT	p.hy ()	returns the homogeneous $y$ coordinate.
R::RT	p.hw ()	returns the homogenizing coordinate.

Here come the Cartesian access functions. Note that you do not loose information with the homogeneous representation, because then the field type is a quotient.

R::FT	p.x ()	returns the Cartesian $x$ coordinate, that is $hx/hw$.
R::FT	p.y ()	returns the Cartesian $y$ coordinate, that is $hy/hw$.

The following operations are for convenience and for making this point class compatible with code for higher dimensional points. Again they come in a Cartesian and homogeneous flavor.

R::RT	p.homogeneous ( int i)
		returns the i'th homogeneous coordinate of p, starting with 0. Precondition: .
R::FT	p.cartesian ( int i)
		returns the i'th Cartesian coordinate of p, starting with 0. Precondition: .
R::FT	p [ int i]	returns cartesian(i). Precondition: .
int	p.dimension ()	returns the dimension (the constant 2).

Miscellaneous

CGAL_Bbox_2	p.bbox ()	returns a bounding box containing p. Note that bounding boxes are not parameterized with whatsoever.
CGAL_Point_2<R>	p.transform ( CGAL_Aff_transformation_2<R> t)
		returns the point obtained by applying $t$ on p.

Operations

CGAL_Vector_2<R>	p - q	returns the difference vector between q and p. You can substitute CGAL_ORIGIN for either p or q ,but not for both.
CGAL_Point_2<R>	p + CGAL_Vector_2<R> v
		returns the point obtained by translating p by the vector v.
CGAL_Point_2<R>	p - CGAL_Vector_2<R> v
		returns the point obtained by translating p by the vector - v.

See Also

Example

  CGAL_Point_2< CGAL_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;

  cout << p.x() << "  " << p.y() << endl;