Point_3<Kernel>

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CGAL::Point_3<Kernel>

Definition

An object of the class Point_3<Kernel> is a point in the three-dimensional Euclidean space

³.

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>.

Types

Point_3<Kernel>::Cartesian_const_iterator
	An iterator for enumerating the Cartesian coordinates of a point.

Creation

Point_3<Kernel> p ( Origin ORIGIN);

introduces a point with Cartesian coordinates(0,0,0).

Point_3<Kernel> p ( int x, int y, int z);

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

Point_3<Kernel> p ( double x, double y, double z);

introduces a point p initialized to (x,y,z) provided RT supports it.

Point_3<Kernel> p ( Kernel::RT hx, Kernel::RT hy, Kernel::RT hz, Kernel::RT hw = RT(1));

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

Precondition:

hw ≠ 0.

Point_3<Kernel> p ( Kernel::FT x, Kernel::FT y, Kernel::FT z);

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

Operations

bool	p.operator== ( q) const	Test for equality: Two points are equal, iff their x, y and z coordinates are equal.

bool	p.operator!= ( q) const	Test for inequality.

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.

Kernel::RT	p.hx () const	returns the homogeneous x coordinate.
Kernel::RT	p.hy () const	returns the homogeneous y coordinate.
Kernel::RT	p.hz () const	returns the homogeneous z coordinate.
Kernel::RT	p.hw () const	returns the homogenizing coordinate.

Note that you do not loose information with the homogeneous representation, because the FieldNumberType is a quotient.

Kernel::FT	p.x () const	returns the Cartesian x coordinate, that is hx/hw.
Kernel::FT	p.y () const	returns the Cartesian y coordinate, that is hy/hw.
Kernel::FT	p.z () const	returns the Cartesian z coordinate, that is hz/hw.

The following operations are for convenience and for compatibility with code for higher dimensional points. Again they come in a Cartesian and in a homogeneous flavor.

Kernel::RT

p.homogeneous ( int i) const

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

Precondition:

0 ≤ i ≤ 3.

Kernel::FT

p.cartesian ( int i) const

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

Precondition:

0 ≤ i ≤ 2.

Kernel::FT

p.operator[] ( int i) const

returns cartesian(i).

Precondition:

0 ≤ i ≤ 2.

Cartesian_const_iterator

p.cartesian_begin () const

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

Cartesian_const_iterator

p.cartesian_end () const

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

int

p.dimension () const

returns the dimension (the constant 3).

Bbox_3

p.bbox () const

returns a bounding box containing p.

Point_3<Kernel>

p.transform ( Aff_transformation_3<Kernel> t) const

returns the point obtained by applying t on p.

Operators

The following operations can be applied on points:

bool	operator< ( p, q)	returns true iff p is lexicographically smaller than q (the lexicographical order being defined on the Cartesian coordinates).

bool	operator> ( p, q)	returns true iff p is lexicographically greater than q.

bool	operator<= ( p, q)	returns true iff p is lexicographically smaller or equal to q.

bool	operator>= ( p, q)	returns true iff p is lexicographically greater or equal to q.

Vector_3<Kernel>	operator- ( p, q)	returns the difference vector between q and p. You can substitute ORIGIN for either p or q, but not for both.

Point_3<Kernel>	operator+ ( p, Vector_3<Kernel> v)
		returns the point obtained by translating p by the vector v.

Point_3<Kernel>	operator- ( p, Vector_3<Kernel> v)
		returns the point obtained by translating p by the vector -v.

CGAL::Point_3<Kernel>

Definition

Types

Creation

Operations

Operators

See Also