CGAL 6.0 - 2D and 3D Linear Geometry Kernel
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CGAL::Weighted_point_2< Kernel > Class Template Reference

#include <CGAL/Weighted_point_2.h>

## Definition

template<typename Kernel>
class CGAL::Weighted_point_2< Kernel >

An object of the class Weighted_point_2 is a tuple of a two-dimensional point and a scalar weight.

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

Point_2<Kernel>
Is model of
Kernel::WeightedPoint_2
Hashable if Kernel is a cartesian kernel and if Kernel::FT is Hashable

## Types

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

## Creation

Constructors from coordinates are provided for convenience, except that they are only from Cartesian coordinates, and with no weight, so as to avoid any potential ambiguity between the homogeneous weight and the power weight (it should be easy enough to pass a Point_2 explicitly in those cases).

Weighted_point_2 (const Origin &ORIGIN)
introduces a weighted point with Cartesian coordinates (0,0) and weight 0.

Weighted_point_2 (const Point_2< Kernel > &p)
introduces a weighted point from point p and weight 0.

Weighted_point_2 (const Point_2< Kernel > &p, Kernel::FT &w)
introduces a weighted point from point p and weight w.

Weighted_point_2 (const Kernel::FT &x, const Kernel::FT &y)
introduces a weighted point with coordinates x, y, and weight 0.

## Bare point and weight accessors

Point_2< Kernelpoint () const
returns the point of the weighted point.

Kernel::FT weight () const
returns the weight of the weighted point.

## Operations

Warning
Comparison and equality operators (==, !=, <, etc.) currently operate directly on the underlying bare point. Consequently:
Weighted_point_2< Cartesian<double> > wp(p, 1.0), wq(p, 2.0); // same bare point, but different weights
wp == wq; // is equal to true
An object p of the class Point_2 is a point in the two-dimensional Euclidean plane .
Definition: Point_2.h:37
An object of the class Weighted_point_2 is a tuple of a two-dimensional point and a scalar weight.
Definition: Weighted_point_2.h:21
bool operator== (const Weighted_point_2< Kernel > &q) const
Test for equality.

bool operator!= (const Weighted_point_2< Kernel > &q) const
Test for inequality.

## 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 lose information with the homogeneous representation, because the FieldNumberType is a quotient.

Kernel::RT hx () const
returns the homogeneous $$x$$ coordinate.

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

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

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

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

## 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.

Kernel::FT cartesian (int i) const
returns the i'th Cartesian coordinate of p.

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

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

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

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

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

Weighted_point_2< Kerneltransform (const Aff_transformation_2< Kernel > &t) const
returns the weighted point obtained by applying t on p.

## ◆ Weighted_point_2() [1/4]

template<typename Kernel >
 CGAL::Weighted_point_2< Kernel >::Weighted_point_2 ( const Origin & ORIGIN )

introduces a weighted point with Cartesian coordinates (0,0) and weight 0.

Exactness
This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

## ◆ Weighted_point_2() [2/4]

template<typename Kernel >
 CGAL::Weighted_point_2< Kernel >::Weighted_point_2 ( const Point_2< Kernel > & p )
explicit

introduces a weighted point from point p and weight 0.

Exactness
This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.
Warning
The explicit keyword is used to avoid accidental implicit conversions between Point_2 and Weighted_point_2.

## ◆ Weighted_point_2() [3/4]

template<typename Kernel >
 CGAL::Weighted_point_2< Kernel >::Weighted_point_2 ( const Point_2< Kernel > & p, Kernel::FT & w )

introduces a weighted point from point p and weight w.

Exactness
This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

## ◆ Weighted_point_2() [4/4]

template<typename Kernel >
 CGAL::Weighted_point_2< Kernel >::Weighted_point_2 ( const Kernel::FT & x, const Kernel::FT & y )

introduces a weighted point with coordinates x, y, and weight 0.

Exactness
This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

## ◆ bbox()

template<typename Kernel >
 Bbox_2 CGAL::Weighted_point_2< Kernel >::bbox ( ) const

returns a bounding box containing p.

Exactness
This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

## ◆ cartesian()

template<typename Kernel >
 Kernel::FT CGAL::Weighted_point_2< Kernel >::cartesian ( int i ) const

returns the i'th Cartesian coordinate of p.

Precondition
0 <= i <= 1
Exactness
This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

## ◆ homogeneous()

template<typename Kernel >
 Kernel::RT CGAL::Weighted_point_2< Kernel >::homogeneous ( int i ) const

returns the i'th homogeneous coordinate of p.

Precondition
0 <= i <= 2

## ◆ operator!=()

template<typename Kernel >
 bool CGAL::Weighted_point_2< Kernel >::operator!= ( const Weighted_point_2< Kernel > & q ) const

Test for inequality.

The point can be compared with ORIGIN.

## ◆ operator==()

template<typename Kernel >
 bool CGAL::Weighted_point_2< Kernel >::operator== ( const Weighted_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.

## ◆ operator[]()

template<typename Kernel >
 Kernel::FT CGAL::Weighted_point_2< Kernel >::operator[] ( int i ) const

returns cartesian(i).

Precondition
0 <= i <= 1
Exactness
This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

## ◆ point()

template<typename Kernel >
 Point_2< Kernel > CGAL::Weighted_point_2< Kernel >::point ( ) const

returns the point of the weighted point.

Exactness
This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

## ◆ weight()

template<typename Kernel >
 Kernel::FT CGAL::Weighted_point_2< Kernel >::weight ( ) const

returns the weight of the weighted point.

Exactness
This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

## ◆ x()

template<typename Kernel >
 Kernel::FT CGAL::Weighted_point_2< Kernel >::x ( ) const

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

Exactness
This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

## ◆ y()

template<typename Kernel >
 Kernel::FT CGAL::Weighted_point_2< Kernel >::y ( ) const

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

Exactness
This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.