CGAL::Line_3< Kernel > Class Template Reference

#include <CGAL/Line_3.h>

Definition

An object l of the data type Line_3 is a directed straight line in the three-dimensional Euclidean space \( \E^3\).

See also

Kernel::Line_3

Creation
	Line_3 (const Point_3< Kernel > &p, const Point_3< Kernel > &q)
	introduces a line l passing through the points p and q. More...
	Line_3 (const Point_3< Kernel > &p, const Direction_3< Kernel > &d)
	introduces a line l passing through point p with direction d. More...
	Line_3 (const Point_3< Kernel > &p, const Vector_3< Kernel > &v)
	introduces a line l passing through point p and oriented by v. More...
	Line_3 (const Segment_3< Kernel > &s)
	returns the line supporting the segment s, oriented from source to target. More...
	Line_3 (const Ray_3< Kernel > &r)
	returns the line supporting the ray r, with the same orientation. More...

Operations
bool	operator== (const Line_3< Kernel > &h) const
	Test for equality: two lines are equal, iff they have a non empty intersection and the same direction. More...
bool	operator!= (const Line_3< Kernel > &h) const
	Test for inequality. More...
Point_3< Kernel >	projection (const Point_3< Kernel > &p) const
	returns the orthogonal projection of p on l. More...
Point_3< Kernel >	point (int i) const
	returns an arbitrary point on l. More...

Predicates
bool	is_degenerate () const
	returns true iff line l is degenerated to a point. More...
bool	has_on (const Point_3< Kernel > &p) const
	returns true iff p lies on l. More...

Miscellaneous
Plane_3< Kernel >	perpendicular_plane (const Point_3< Kernel > &p) const
	returns the plane perpendicular to l passing through p. More...
Line_3< Kernel >	opposite () const
	returns the line with opposite direction. More...
Vector_3< Kernel >	to_vector () const
	returns a vector having the same direction as l. More...
Direction_3< Kernel >	direction () const
	returns the direction of l. More...
Line_3< Kernel >	transform (const Aff_transformation_3< Kernel > &t) const
	returns the line obtained by applying t on a point on l and the direction of l. More...

Constructor & Destructor Documentation

template<typename Kernel >

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

introduces a line l passing through the points p and q.

Line l is directed from p to q.

template<typename Kernel >

CGAL::Line_3< Kernel >::Line_3	(	const Point_3< Kernel > &	p,
		const Direction_3< Kernel > &	d
	)

introduces a line l passing through point p with direction d.

template<typename Kernel >

CGAL::Line_3< Kernel >::Line_3	(	const Point_3< Kernel > &	p,
		const Vector_3< Kernel > &	v
	)

introduces a line l passing through point p and oriented by v.

template<typename Kernel >

CGAL::Line_3< Kernel >::Line_3

(

const Segment_3< Kernel > &

s

)

returns the line supporting the segment s, oriented from source to target.

template<typename Kernel >

CGAL::Line_3< Kernel >::Line_3

(

const Ray_3< Kernel > &

r

)

returns the line supporting the ray r, with the same orientation.

Member Function Documentation

template<typename Kernel >

Direction_3<Kernel> CGAL::Line_3< Kernel >::direction

(

)

const

returns the direction of l.

template<typename Kernel >

bool CGAL::Line_3< Kernel >::has_on

(

const Point_3< Kernel > &

p

)

const

returns true iff p lies on l.

template<typename Kernel >

bool CGAL::Line_3< Kernel >::is_degenerate

(

)

const

returns true iff line l is degenerated to a point.

template<typename Kernel >

bool CGAL::Line_3< Kernel >::operator!=

(

const Line_3< Kernel > &

h

)

const

Test for inequality.

template<typename Kernel >

bool CGAL::Line_3< Kernel >::operator==

(

const Line_3< Kernel > &

h

)

const

Test for equality: two lines are equal, iff they have a non empty intersection and the same direction.

template<typename Kernel >

Line_3<Kernel> CGAL::Line_3< Kernel >::opposite

(

)

const

returns the line with opposite direction.

template<typename Kernel >

Plane_3<Kernel> CGAL::Line_3< Kernel >::perpendicular_plane

(

const Point_3< Kernel > &

p

)

const

returns the plane perpendicular to l passing through p.

template<typename Kernel >

Point_3<Kernel> CGAL::Line_3< Kernel >::point

(

int

i

)

const

returns an arbitrary point on l.

It holds point(i) = point(j), iff i=j.

template<typename Kernel >

Point_3<Kernel> CGAL::Line_3< Kernel >::projection

(

const Point_3< Kernel > &

p

)

const

returns the orthogonal projection of p on l.

template<typename Kernel >

Vector_3<Kernel> CGAL::Line_3< Kernel >::to_vector

(

)

const

returns a vector having the same direction as l.

template<typename Kernel >

Line_3<Kernel> CGAL::Line_3< Kernel >::transform

(

const Aff_transformation_3< Kernel > &

t

)

const

returns the line obtained by applying t on a point on l and the direction of l.