CGAL::Ray_3< Kernel > Class Template Reference

#include <CGAL/Ray_3.h>

Definition

template<typename Kernel>
class CGAL::Ray_3< Kernel >

An object r of the data type Ray_3 is a directed straight ray in the three-dimensional Euclidean space \( \E^3\).

It starts in a point called the source of r and it goes to infinity.

Is model of

Kernel::Ray_3

Creation
	Ray_3 (const Point_3< Kernel > &p, const Point_3< Kernel > &q)
	introduces a ray r with source p and passing through point q.
	Ray_3 (const Point_3< Kernel > &p, const Direction_3< Kernel > &d)
	introduces a ray r with source p and with direction d.
	Ray_3 (const Point_3< Kernel > &p, const Vector_3< Kernel > &v)
	introduces a ray r with source p and with a direction given by v.
	Ray_3 (const Point_3< Kernel > &p, const Line_3< Kernel > &l)
	introduces a ray r starting at source p with the same direction as l.

Operations
bool	operator== (const Ray_3< Kernel > &h) const
	Test for equality: two rays are equal, iff they have the same source and the same direction.
bool	operator!= (const Ray_3< Kernel > &h) const
	Test for inequality.
Point_3< Kernel >	source () const
	returns the source of r
Point_3< Kernel >	point (const Kernel::FT i) const
	returns a point on r.
Direction_3< Kernel >	direction () const
	returns the direction of r.
Vector_3< Kernel >	to_vector () const
	returns a vector giving the direction of r.
Line_3< Kernel >	supporting_line () const
	returns the line supporting r which has the same direction.
Ray_3< Kernel >	opposite () const
	returns the ray with the same source and the opposite direction.
bool	is_degenerate () const
	ray r is degenerate, if the source and the second defining point fall together (that is if the direction is degenerate).
bool	has_on (const Point_3< Kernel > &p) const
	A point is on r, iff it is equal to the source of r, or if it is in the interior of r.
Ray_3< Kernel >	transform (const Aff_transformation_3< Kernel > &t) const
	returns the ray obtained by applying t on the source and on the direction of r.

Constructor & Destructor Documentation

Ray_3() [1/4]

template<typename Kernel >

CGAL::Ray_3< Kernel >::Ray_3	(	const Point_3< Kernel > &	p,
		const Point_3< Kernel > &	q
	)

introduces a ray r with source p and passing through point q.

Exactness

This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

Ray_3() [2/4]

template<typename Kernel >

CGAL::Ray_3< Kernel >::Ray_3	(	const Point_3< Kernel > &	p,
		const Direction_3< Kernel > &	d
	)

introduces a ray r with source p and with direction d.

Ray_3() [3/4]

template<typename Kernel >

CGAL::Ray_3< Kernel >::Ray_3	(	const Point_3< Kernel > &	p,
		const Vector_3< Kernel > &	v
	)

introduces a ray r with source p and with a direction given by v.

Ray_3() [4/4]

template<typename Kernel >

CGAL::Ray_3< Kernel >::Ray_3	(	const Point_3< Kernel > &	p,
		const Line_3< Kernel > &	l
	)

introduces a ray r starting at source p with the same direction as l.

Member Function Documentation

direction()

template<typename Kernel >

Direction_3< Kernel > CGAL::Ray_3< Kernel >::direction

(

)

const

returns the direction of r.

has_on()

template<typename Kernel >

bool CGAL::Ray_3< Kernel >::has_on

(

const Point_3< Kernel > &

p

)

const

A point is on r, iff it is equal to the source of r, or if it is in the interior of r.

is_degenerate()

template<typename Kernel >

bool CGAL::Ray_3< Kernel >::is_degenerate

(

)

const

ray r is degenerate, if the source and the second defining point fall together (that is if the direction is degenerate).

operator!=()

template<typename Kernel >

bool CGAL::Ray_3< Kernel >::operator!=

(

const Ray_3< Kernel > &

h

)

const

Test for inequality.

operator==()

template<typename Kernel >

bool CGAL::Ray_3< Kernel >::operator==

(

const Ray_3< Kernel > &

h

)

const

Test for equality: two rays are equal, iff they have the same source and the same direction.

opposite()

template<typename Kernel >

Ray_3< Kernel > CGAL::Ray_3< Kernel >::opposite

(

)

const

returns the ray with the same source and the opposite direction.

point()

template<typename Kernel >

Point_3< Kernel > CGAL::Ray_3< Kernel >::point

(

const Kernel::FT

i

)

const

returns a point on r.

point(0) is the source. point(i), with i>0, is different from the source.

Precondition

i >= 0.

source()

template<typename Kernel >

Point_3< Kernel > CGAL::Ray_3< Kernel >::source

(

)

const

returns the source of r

Exactness

This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

supporting_line()

template<typename Kernel >

Line_3< Kernel > CGAL::Ray_3< Kernel >::supporting_line

(

)

const

returns the line supporting r which has the same direction.

to_vector()

template<typename Kernel >

Vector_3< Kernel > CGAL::Ray_3< Kernel >::to_vector

(

)

const

returns a vector giving the direction of r.

transform()

template<typename Kernel >

Ray_3< Kernel > CGAL::Ray_3< Kernel >::transform

(

const Aff_transformation_3< Kernel > &

t

)

const

returns the ray obtained by applying t on the source and on the direction of r.