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

#include <vgl_fwd.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. More...

	vgl_homg_line_3d_2_points (const vgl_homg_line_3d_2_points< Type > &that)
	Copy constructor. More...

	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. More...

bool	operator== (vgl_homg_line_3d_2_points< Type > const &l) const
	comparison. More...

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.). More...

vgl_homg_point_3d< Type >	point_infinite () const
	Infinite point: the intersection of the line with the plane at infinity. More...

vgl_vector_3d< Type >	direction () const
	The point at infinity defines the direction of the line. More...

void	set (vgl_homg_point_3d< Type > const &p1, vgl_homg_point_3d< Type > const &p2)
	Assignment. More...

bool	ideal (Type tol=(Type) 0) const
	Return true iff line is at infinity. More...

Protected Member Functions
void	force_point2_infinite (void) const
	force the point point_infinite_ to infinity, without changing the line. More...

Private Attributes
vgl_homg_point_3d< Type >	point_finite_
	Any finite point on the line. More...

vgl_homg_point_3d< Type >	point_infinite_
	the (unique) point at infinity. More...

Related Functions
(Note that these are not member functions.)
template<class T >
std::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. More...

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. More...

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. More...

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. More...

template<class Type >
bool	is_ideal (l const &line, Type tol=(Type) 0)
	Return true iff line is at infinity. More...

template<class Type >
bool	coplanar (l const &l1, l const &l2)
	Are two lines coplanar, i.e., do they intersect?. More...

template<class Type >
bool	concurrent (l const &l1, l const &l2)
	Are two lines concurrent, i.e., do they intersect?. More...

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?. More...

template<class Type >
vgl_homg_point_3d< Type >	intersection (l const &l1, l const &l2)
	Return the intersection point of two concurrent lines. More...

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?. More...

template<class Type >
std::ostream &	operator<< (std::ostream &s, l const &p)
	Write to stream (verbose). More...

template<class Type >
std::istream &	operator>> (std::istream &is, l &p)
	Read parameters from stream. More...

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 15 of file vgl_fwd.h.

Constructor & Destructor Documentation

◆ vgl_homg_line_3d_2_points() [1/3]

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.

◆ vgl_homg_line_3d_2_points() [2/3]

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.

◆ vgl_homg_line_3d_2_points() [3/3]

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

◆ direction()

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.

◆ force_point2_infinite()

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 44 of file vgl_homg_line_3d_2_points.hxx.

◆ ideal()

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.

◆ operator!=()

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.

◆ operator==()

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 25 of file vgl_homg_line_3d_2_points.hxx.

◆ point_finite()

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.

◆ point_infinite()

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.

◆ set()

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

◆ concurrent() [1/2]

template<class Type >

bool concurrent	(	l const &	l1,
		l const &	l2
	)

Definition at line 112 of file vgl_homg_line_3d_2_points.h.

◆ concurrent() [2/2]

template<class Type >

bool concurrent	(	l const &	l1,
		l const &	l2,
		l const &	l3
	)

Definition at line 141 of file vgl_homg_line_3d_2_points.h.

◆ coplanar() [1/2]

template<class Type >

bool coplanar	(	l const &	l1,
		l const &	l2
	)

Definition at line 106 of file vgl_homg_line_3d_2_points.h.

◆ coplanar() [2/2]

template<class Type >

bool coplanar	(	l const &	l1,
		l const &	l2,
		l const &	l3
	)

Definition at line 124 of file vgl_homg_line_3d_2_points.h.

◆ intersection()

template<class Type >

vgl_homg_point_3d< Type > intersection	(	l const &	l1,
		l const &	l2
	)

◆ is_ideal()

template<class Type >

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

Definition at line 93 of file vgl_homg_line_3d_2_points.h.

◆ operator<<()

template<class Type >

std::ostream & operator<<	(	std::ostream &	s,
		l const &	p
	)

◆ operator>>()

template<class Type >

std::istream & operator>>	(	std::istream &	is,
		l &	p
	)

◆ vgl_closest_points()

template<class T >

std::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
	)

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: std::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/

◆ vgl_distance() [1/2]

template<class T >

double vgl_distance	(	vgl_homg_line_3d_2_points< T > const &	line1,
		vgl_homg_line_3d_2_points< T > const &	line2
	)

See vgl_closest_point.h for more information.

◆ vgl_distance() [2/2]

template<class T >

double vgl_distance	(	vgl_homg_line_3d_2_points< T > const &	l,
		vgl_homg_point_3d< T > const &	p
	)

See vgl_closest_point.h for more information.

◆ vgl_distance_origin()

template<class T >

double vgl_distance_origin ( vgl_homg_line_3d_2_points< T > const & l )

Member Data Documentation

◆ point_finite_

template<class Type>

vgl_homg_point_3d<Type> vgl_homg_line_3d_2_points< Type >::point_finite_

mutableprivate

Any finite point on the line.

Definition at line 30 of file vgl_homg_line_3d_2_points.h.

◆ point_infinite_

template<class Type>

vgl_homg_point_3d<Type> vgl_homg_line_3d_2_points< Type >::point_infinite_

mutableprivate

the (unique) point at infinity.

Definition at line 32 of file vgl_homg_line_3d_2_points.h.

The documentation for this class was generated from the following files:

Public Member Functions

Protected Member Functions

Private Attributes

Related Functions

Detailed Description

template<class Type> class vgl_homg_line_3d_2_points< Type >

Constructor & Destructor Documentation

◆ vgl_homg_line_3d_2_points() [1/3]

◆ vgl_homg_line_3d_2_points() [2/3]

◆ vgl_homg_line_3d_2_points() [3/3]

Member Function Documentation

◆ direction()

◆ force_point2_infinite()

◆ ideal()

◆ operator!=()

◆ operator==()

◆ point_finite()

◆ point_infinite()

◆ set()

Friends And Related Function Documentation

◆ concurrent() [1/2]

◆ concurrent() [2/2]

◆ coplanar() [1/2]

◆ coplanar() [2/2]

◆ intersection()

◆ is_ideal()

◆ operator<<()

◆ operator>>()

◆ vgl_closest_points()

◆ vgl_distance() [1/2]

◆ vgl_distance() [2/2]

◆ vgl_distance_origin()

Member Data Documentation

◆ point_finite_

◆ point_infinite_

template<class Type>
class vgl_homg_line_3d_2_points< Type >