CGAL::Line_3< Kernel > Class Template Reference

#include <CGAL/Line_3.h>

Definition

template<typename Kernel>
class CGAL::Line_3< Kernel >

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

Is model of

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

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.
bool	operator!= (const Line_3< Kernel > &h) const
	Test for inequality.
Point_3< Kernel >	projection (const Point_3< Kernel > &p) const
	returns the orthogonal projection of p on l.
Point_3< Kernel >	point (const Kernel::FT i) const
	returns an arbitrary point on l.

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

Miscellaneous
Plane_3< Kernel >	perpendicular_plane (const Point_3< Kernel > &p) const
	returns the plane perpendicular to l passing through p.
Line_3< Kernel >	opposite () const
	returns the line with opposite direction.
Vector_3< Kernel >	to_vector () const
	returns a vector having the same direction as l.
Direction_3< Kernel >	direction () const
	returns the direction of l.
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.

Constructor & Destructor Documentation

Line_3() [1/3]

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.

Line_3() [2/3]

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.

Exactness

This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

Line_3() [3/3]

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.

Exactness

This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

Member Function Documentation

direction()

template<typename Kernel >

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

(

)

const

returns the direction of l.

Exactness

This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

opposite()

template<typename Kernel >

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

(

)

const

returns the line with opposite direction.

Exactness

This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

point()

template<typename Kernel >

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

(

const Kernel::FT

i

)

const

returns an arbitrary point on l.

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

to_vector()

template<typename Kernel >

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

(

)

const

returns a vector having the same direction as l.

Exactness

This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.