Represents a homogeneous 3D line using two points. More...

#include <vgl_homg_line_3d_2_points.h>

Public Member Functions
	vgl_homg_line_3d_2_points (void)
	Default constructor with (0,0,0,1) and (1,0,0,0), which is the line y=z=0.
	vgl_homg_line_3d_2_points (const vgl_homg_line_3d_2_points< Type > &that)
	Copy constructor.
	vgl_homg_line_3d_2_points (vgl_homg_point_3d< Type > const &point_1, vgl_homg_point_3d< Type > const &point_2)
	Construct from two points.
bool	operator== (vgl_homg_line_3d_2_points< Type > const &l) const
	comparison.
bool	operator!= (vgl_homg_line_3d_2_points< Type > const &l) const
vgl_homg_point_3d< Type >	point_finite () const
	Finite point (Could be an ideal point, if the whole line is at infinity.).
vgl_homg_point_3d< Type >	point_infinite () const
	Infinite point: the intersection of the line with the plane at infinity.
vgl_vector_3d< Type >	direction () const
	The point at infinity defines the direction of the line.
void	set (vgl_homg_point_3d< Type > const &p1, vgl_homg_point_3d< Type > const &p2)
	Assignment.
bool	ideal (Type tol=(Type) 0) const
	Return true iff line is at infinity.
Protected Member Functions
void	force_point2_infinite (void) const
	force the point point_infinite_ to infinity, without changing the line.
Private Attributes
vgl_homg_point_3d< Type >	point_finite_
	Any finite point on the line.
vgl_homg_point_3d< Type >	point_infinite_
	the (unique) point at infinity.
Related Functions
(Note that these are not member functions.)
template<class T >
vcl_pair< vgl_homg_point_3d< T > , vgl_homg_point_3d< T > >	vgl_closest_points (vgl_homg_line_3d_2_points< T > const &line1, vgl_homg_line_3d_2_points< T > const &line2)
	Return the two points of nearest approach of two 3D lines, one on each line.
template<class T >
double	vgl_distance_origin (vgl_homg_line_3d_2_points< T > const &l)
	find the shortest distance of the line to the origin.
template<class T >
double	vgl_distance (vgl_homg_line_3d_2_points< T > const &line1, vgl_homg_line_3d_2_points< T > const &line2)
	Return the perpendicular distance between two lines in 3D.
template<class T >
double	vgl_distance (vgl_homg_line_3d_2_points< T > const &l, vgl_homg_point_3d< T > const &p)
	Return the perpendicular distance from a point to a line in 3D.
template<class Type >
bool	is_ideal (l const &line, Type tol=(Type) 0)
	Return true iff line is at infinity.
template<class Type >
bool	coplanar (l const &l1, l const &l2)
	Are two lines coplanar, i.e., do they intersect?.
template<class Type >
bool	concurrent (l const &l1, l const &l2)
	Are two lines concurrent, i.e., do they intersect?.
template<class Type >
bool	coplanar (l const &l1, l const &l2, l const &l3)
	Are three lines coplanar, i.e., are they in a common plane?.
template<class Type >
vgl_homg_point_3d< Type >	intersection (l const &l1, l const &l2)
	Return the intersection point of two concurrent lines.
template<class Type >
bool	concurrent (l const &l1, l const &l2, l const &l3)
	Are three lines concurrent, i.e., do they pass through a common point?.
template<class Type >
vcl_ostream &	operator<< (vcl_ostream &s, l const &p)
	Write to stream (verbose).
template<class Type >
vcl_istream &	operator>> (vcl_istream &is, l &p)
	Read parameters from stream.

Detailed Description

template<class Type>
class vgl_homg_line_3d_2_points< Type >

Represents a homogeneous 3D line using two points.

A class to hold a homogeneous representation of a 3D Line. The line is stored as a pair of homogeneous 3d points.

Definition at line 25 of file vgl_homg_line_3d_2_points.h.

Constructor & Destructor Documentation

template<class Type>

vgl_homg_line_3d_2_points< Type >::vgl_homg_line_3d_2_points ( void ) [inline]

Default constructor with (0,0,0,1) and (1,0,0,0), which is the line y=z=0.

Definition at line 40 of file vgl_homg_line_3d_2_points.h.

template<class Type>

vgl_homg_line_3d_2_points< Type >::vgl_homg_line_3d_2_points ( const vgl_homg_line_3d_2_points< Type > & that ) [inline]

Copy constructor.

Definition at line 44 of file vgl_homg_line_3d_2_points.h.

template<class Type>

vgl_homg_line_3d_2_points< Type >::vgl_homg_line_3d_2_points	(	vgl_homg_point_3d< Type > const &	point_1,
		vgl_homg_point_3d< Type > const &	point_2
	)		`[inline]`

Construct from two points.

Definition at line 48 of file vgl_homg_line_3d_2_points.h.

Member Function Documentation

template<class Type>

vgl_vector_3d<Type> vgl_homg_line_3d_2_points< Type >::direction ( ) const [inline]

The point at infinity defines the direction of the line.

Definition at line 69 of file vgl_homg_line_3d_2_points.h.

template<class Type >

void vgl_homg_line_3d_2_points< Type >::force_point2_infinite ( void ) const [protected]

force the point point_infinite_ to infinity, without changing the line.

This is called by the constructors

Definition at line 41 of file vgl_homg_line_3d_2_points.txx.

template<class Type>

bool vgl_homg_line_3d_2_points< Type >::ideal ( Type tol = (Type)0 ) const [inline]

Return true iff line is at infinity.

Definition at line 80 of file vgl_homg_line_3d_2_points.h.

template<class Type>

bool vgl_homg_line_3d_2_points< Type >::operator!= ( vgl_homg_line_3d_2_points< Type > const & l ) const [inline]

Definition at line 59 of file vgl_homg_line_3d_2_points.h.

template<class Type >

bool vgl_homg_line_3d_2_points< Type >::operator== ( vgl_homg_line_3d_2_points< Type > const & l ) const

comparison.

Definition at line 22 of file vgl_homg_line_3d_2_points.txx.

template<class Type>

vgl_homg_point_3d<Type> vgl_homg_line_3d_2_points< Type >::point_finite ( ) const [inline]

Finite point (Could be an ideal point, if the whole line is at infinity.).

Definition at line 64 of file vgl_homg_line_3d_2_points.h.

template<class Type>

vgl_homg_point_3d<Type> vgl_homg_line_3d_2_points< Type >::point_infinite ( ) const [inline]

Infinite point: the intersection of the line with the plane at infinity.

Definition at line 66 of file vgl_homg_line_3d_2_points.h.

template<class Type>

void vgl_homg_line_3d_2_points< Type >::set	(	vgl_homg_point_3d< Type > const &	p1,
		vgl_homg_point_3d< Type > const &	p2
	)		`[inline]`

Assignment.

Definition at line 74 of file vgl_homg_line_3d_2_points.h.

Friends And Related Function Documentation

template<class Type >

bool concurrent	(	l const &	l1,
		l const &	l2
	)		`[related]`

Are two lines concurrent, i.e., do they intersect?.

Definition at line 112 of file vgl_homg_line_3d_2_points.h.

template<class Type >

bool concurrent	(	l const &	l1,
		l const &	l2,
		l const &	l3
	)		`[related]`

Are three lines concurrent, i.e., do they pass through a common point?.

Definition at line 141 of file vgl_homg_line_3d_2_points.h.

template<class Type >

bool coplanar	(	l const &	l1,
		l const &	l2
	)		`[related]`

Are two lines coplanar, i.e., do they intersect?.

Definition at line 106 of file vgl_homg_line_3d_2_points.h.

template<class Type >

bool coplanar	(	l const &	l1,
		l const &	l2,
		l const &	l3
	)		`[related]`

Are three lines coplanar, i.e., are they in a common plane?.

Definition at line 124 of file vgl_homg_line_3d_2_points.h.

template<class Type >

vgl_homg_point_3d< Type > intersection	(	l const &	l1,
		l const &	l2
	)		`[related]`

Return the intersection point of two concurrent lines.

template<class Type >

bool is_ideal	(	l const &	line,
		Type	tol = `(Type)0`
	)		`[related]`

Return true iff line is at infinity.

Definition at line 93 of file vgl_homg_line_3d_2_points.h.

template<class Type >

vcl_ostream & operator<<	(	vcl_ostream &	s,
		l const &	p
	)		`[related]`

Write to stream (verbose).

template<class Type >

vcl_istream & operator>>	(	vcl_istream &	is,
		l &	p
	)		`[related]`

Read parameters from stream.

template<class T >

vcl_pair< vgl_homg_point_3d< T >, vgl_homg_point_3d< T > > vgl_closest_points	(	vgl_homg_line_3d_2_points< T > const &	line1,
		vgl_homg_line_3d_2_points< T > const &	line2
	)		`[related]`

Return the two points of nearest approach of two 3D lines, one on each line.

There are 3 cases: the lines intersect (hence these two points are equal); the lines are parallel (an infinite number of solutions viz all points); the lines are neither parallel nor do they intersect (the general case). This method handles all 3 cases. In all cases, a pair of points is returned; in case 1, the two returned points are equal; in case 2, both points are the common point at infinity of the two lines.

Note that case 2 also comprises the case where the given lines are identical. Hence, when observing a point at infinity as a return value, one should interpret this as "all points are closest points".

Parameters:

line1
line2

Returns:: vcl_pair<vgl_homg_point_3d<T>,vgl_homg_point_3d<T> >

Author:: Paul Bourke, modified for use in VXL by Brendan McCane

Note:: This routine is adapted from code written by Paul Bourke and available online at http://astronomy.swin.edu.au/~pbourke/geometry/lineline3d/

template<class T >