CGAL::Ray_d< Kernel > Class Template Reference

#include <CGAL/Kernel_d/Ray_d.h>

Definition

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

An instance of data type Ray_d is a ray in \( d\)-dimensional Euclidean space. It starts in a point called the source of r and it goes to infinity.

Implementation

Rays are implemented by a pair of points as an item type. All operations like creation, initialization, tests, direction calculation, input and output on a ray \( r\) take time \( O(r.dimension())\). dimension(), coordinate and point access, and identity test take constant time. The space requirement is \( O(r.dimension())\).

Related Functions
(Note that these are not member functions.)
bool	parallel (const Ray_d< Kernel > &r1, const Ray_d< Kernel > &r2)
	returns true if the unoriented supporting lines of r1 and r2 are parallel and false otherwise. More...

Types
typedef unspecified_type	LA
	the linear algebra layer. More...

Creation
	Ray_d ()
	introduces some ray in \( d\)-dimensional space. More...
	Ray_d (Point_d< Kernel > p, Point_d< Kernel > q)
	introduces a ray through p and q and starting at p. More...
	Ray_d (Point_d< Kernel > p, Direction_d< Kernel > dir)
	introduces a ray starting in p with direction dir. More...
	Ray_d (Segment_d< Kernel > s)
	introduces a ray through s.source() and s.target() and starting at s.source(). More...

Operations
int	dimension ()
	returns the dimension of the ambient space. More...
Point_d< Kernel >	source ()
	returns the source point of r. More...
Point_d< Kernel >	point (int i)
	returns a point on r. More...
Direction_d< Kernel >	direction ()
	returns the direction of r. More...
Line_d< Kernel >	supporting_line ()
	returns the supporting line of r. More...
Ray_d< Kernel >	opposite ()
	returns the ray with direction opposite to r and starting in source. More...
Ray_d< Kernel >	transform (const Aff_transformation_d< Kernel > &t)
	returns \( t(r)\). More...
Ray_d< Kernel >	operator+ (const Vector_d< Kernel > &v)
	returns r+v, i.e., r translated by vector \( v\). More...
bool	has_on (const Point_d< Kernel > &p)
	A point is on r, iff it is equal to the source of r, or if it is in the interior of r. More...

Member Typedef Documentation

LA

template<typename Kernel >

typedef unspecified_type CGAL::Ray_d< Kernel >::LA

the linear algebra layer.

Constructor & Destructor Documentation

Ray_d() [1/4]

template<typename Kernel >

CGAL::Ray_d< Kernel >::Ray_d

(

)

introduces some ray in \( d\)-dimensional space.

Ray_d() [2/4]

template<typename Kernel >

CGAL::Ray_d< Kernel >::Ray_d	(	Point_d< Kernel >	p,
		Point_d< Kernel >	q
	)

introduces a ray through p and q and starting at p.

Precondition

\( p\) and \( q\) are distinct and have the same dimension.

p.dimension()==q.dimension().

Ray_d() [3/4]

template<typename Kernel >

CGAL::Ray_d< Kernel >::Ray_d	(	Point_d< Kernel >	p,
		Direction_d< Kernel >	dir
	)

introduces a ray starting in p with direction dir.

Precondition

p and dir have the same dimension and dir is not degenerate.

p.dimension()==dir.dimension().

Ray_d() [4/4]

template<typename Kernel >

CGAL::Ray_d< Kernel >::Ray_d

(

Segment_d< Kernel >

s

)

introduces a ray through s.source() and s.target() and starting at s.source().

Precondition

\( s\) is not degenerate.

Member Function Documentation

dimension()

template<typename Kernel >

int CGAL::Ray_d< Kernel >::dimension

(

)

returns the dimension of the ambient space.

direction()

template<typename Kernel >

Direction_d<Kernel> CGAL::Ray_d< Kernel >::direction

(

)

returns the direction of r.

has_on()

template<typename Kernel >

bool CGAL::Ray_d< Kernel >::has_on

(

const Point_d< Kernel > &

p

)

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

Precondition

r.dimension()==p.dimension().

operator+()

template<typename Kernel >

Ray_d<Kernel> CGAL::Ray_d< Kernel >::operator+

(

const Vector_d< Kernel > &

v

)

returns r+v, i.e., r translated by vector \( v\).

Precondition

r.dimension()==v.dimension().

opposite()

template<typename Kernel >

Ray_d<Kernel> CGAL::Ray_d< Kernel >::opposite

(

)

returns the ray with direction opposite to r and starting in source.

point()

template<typename Kernel >

Point_d<Kernel> CGAL::Ray_d< Kernel >::point

(

int

i

)

returns a point on r.

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

Precondition

\( i \geq0\).

source()

template<typename Kernel >

Point_d<Kernel> CGAL::Ray_d< Kernel >::source

(

)

returns the source point of r.

supporting_line()

template<typename Kernel >

Line_d<Kernel> CGAL::Ray_d< Kernel >::supporting_line

(

)

returns the supporting line of r.

transform()

template<typename Kernel >

Ray_d<Kernel> CGAL::Ray_d< Kernel >::transform

(

const Aff_transformation_d< Kernel > &

t

)

returns \( t(r)\).

Precondition

r.dimension()==t.dimension().

Friends And Related Function Documentation

parallel()

template<typename Kernel >

bool parallel ( const Ray_d< Kernel > &  r1, const Ray_d< Kernel > &  r2  )

related

returns true if the unoriented supporting lines of r1 and r2 are parallel and false otherwise.

Precondition

r1.dimension()==r2.dimension().