\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.10.1 - 2D and 3D Linear Geometry Kernel
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CGAL::Line_3< Kernel > Class Template Reference
3D Kernel Objects

#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 \( \E^3\).

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. More...
 
 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 (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.
 
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

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.

Member Function Documentation

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.