Represents a homogeneous 3D point. More...

#include <vgl_homg_point_3d.h>

Public Member Functions
	vgl_homg_point_3d ()
	Default constructor with (0,0,0,1).
	vgl_homg_point_3d (Type px, Type py, Type pz, Type pw=(Type) 1)
	Construct from three (nonhomogeneous) or four (homogeneous) Types.
	vgl_homg_point_3d (const Type v[4])
	Construct from homogeneous 4-array.
	vgl_homg_point_3d (vgl_vector_3d< Type >const &v)
	Construct point at infinity from direction vector.
	vgl_homg_point_3d (vgl_point_3d< Type > const &p)
	Construct from (non-homogeneous) vgl_point_3d<Type>.
	vgl_homg_point_3d (vgl_homg_plane_3d< Type > const &l1, vgl_homg_plane_3d< Type > const &l2, vgl_homg_plane_3d< Type > const &l3)
	Construct from 3 planes (intersection).
bool	operator== (vgl_homg_point_3d< Type > const &other) const
	the comparison operator.
bool	operator!= (vgl_homg_point_3d< Type >const &other) const
Type	x () const
Type	y () const
Type	z () const
Type	w () const
void	set (Type px, Type py, Type pz, Type pw=(Type) 1)
	Set x,y,z,w.
void	set (Type const p[4])
bool	ideal (Type tol=(Type) 0) const
	Return true iff the point is at infinity (an ideal point).
bool	get_nonhomogeneous (double &vx, double &vy, double &vz) const
bool	rescale_w (Type new_w=Type(1))
Private Attributes
Type	x_
Type	y_
Type	z_
Type	w_
Related Functions
(Note that these are not member functions.)
template<class T >
vgl_homg_point_3d< T >	vgl_closest_point_origin (vgl_homg_plane_3d< T > const &pl)
	Return the point on the given plane closest to the origin.
template<class T >
vgl_homg_point_3d< T >	vgl_closest_point_origin (vgl_homg_line_3d_2_points< T > const &l)
	Return the point on the given line closest to the origin.
template<class T >
vgl_homg_point_3d< T >	vgl_closest_point (vgl_homg_line_3d_2_points< T > const &l, vgl_homg_point_3d< T > const &p)
	Return the point on the given line which is closest to the given point.
template<class T >
double	vgl_distance (vgl_homg_point_3d< T >const &p1, vgl_homg_point_3d< T >const &p2)
	return the distance between two points.
template<class Type >
bool	collinear (l const &l1, vgl_homg_point_3d< Type > const &p)
	Does a line pass through a point, i.e., are the point and the line collinear?.
template<class Type >
bool	coplanar (l const &l1, vgl_homg_point_3d< Type > const &p1, vgl_homg_point_3d< Type > const &p2)
	Are two points coplanar with a line?.
template<class Type >
vcl_ostream &	operator<< (vcl_ostream &s, vgl_homg_point_3d< Type > const &p)
	Write "<vgl_homg_point_3d (x,y,z,w) >" to stream.
template<class Type >
vcl_istream &	operator>> (vcl_istream &s, vgl_homg_point_3d< Type > &p)
	Read x y z w from stream.
template<class Type >
bool	is_ideal (vgl_homg_point_3d< Type > const &p, Type tol=(Type) 0)
	Return true iff the point is at infinity (an ideal point).
template<class Type >
bool	coplanar (vgl_homg_point_3d< Type > const &p1, vgl_homg_point_3d< Type > const &p2, vgl_homg_point_3d< Type > const &p3, vgl_homg_point_3d< Type > const &p4)
	Return true iff the 4 points are coplanar, i.e., they belong to a common plane.
template<class Type >
vgl_vector_3d< Type >	operator- (vgl_homg_point_3d< Type > const &p1, vgl_homg_point_3d< Type > const &p2)
	The difference of two points is the vector from second to first point.
template<class Type >
vgl_homg_point_3d< Type >	operator+ (vgl_homg_point_3d< Type > const &p, vgl_vector_3d< Type > const &v)
	Adding a vector to a point gives a new point at the end of that vector.
template<class Type >
vgl_homg_point_3d< Type > &	operator+= (vgl_homg_point_3d< Type > &p, vgl_vector_3d< Type > const &v)
	Adding a vector to a point gives the point at the end of that vector.
template<class Type >
vgl_homg_point_3d< Type >	operator- (vgl_homg_point_3d< Type > const &p, vgl_vector_3d< Type > const &v)
	Subtracting a vector from a point is the same as adding the inverse vector.
template<class Type >
vgl_homg_point_3d< Type > &	operator-= (vgl_homg_point_3d< Type > &p, vgl_vector_3d< Type > const &v)
	Subtracting a vector from a point is the same as adding the inverse vector.
template<class T >
double	cross_ratio (vgl_homg_point_3d< T >const &p1, vgl_homg_point_3d< T >const &p2, vgl_homg_point_3d< T >const &p3, vgl_homg_point_3d< T >const &p4)
	cross ratio of four collinear points.
template<class Type >
bool	collinear (vgl_homg_point_3d< Type > const &p1, vgl_homg_point_3d< Type > const &p2, vgl_homg_point_3d< Type > const &p3)
	Are three points collinear, i.e., do they lie on a common line?.
template<class Type >
double	ratio (vgl_homg_point_3d< Type > const &p1, vgl_homg_point_3d< Type > const &p2, vgl_homg_point_3d< Type > const &p3)
	Return the relative distance to p1 wrt p1-p2 of p3.
template<class Type >
vgl_homg_point_3d< Type >	midpoint (vgl_homg_point_3d< Type > const &p1, vgl_homg_point_3d< Type > const &p2, Type f=(Type) 0.5)
	Return the point at a given ratio wrt two other points.
template<class Type >
vgl_homg_point_3d< Type >	centre (vgl_homg_point_3d< Type > const &p1, vgl_homg_point_3d< Type > const &p2)
	Return the point at the centre of gravity of two given points.
template<class Type >
vgl_homg_point_3d< Type >	centre (vcl_vector< vgl_homg_point_3d< Type > > const &v)
	Return the point at the centre of gravity of a set of given points.

Detailed Description

template<class Type>
class vgl_homg_point_3d< Type >

Represents a homogeneous 3D point.

Definition at line 26 of file vgl_homg_point_3d.h.

Constructor & Destructor Documentation

template<class Type>

vgl_homg_point_3d< Type >::vgl_homg_point_3d ( ) [inline]

Default constructor with (0,0,0,1).

Definition at line 39 of file vgl_homg_point_3d.h.

template<class Type>

vgl_homg_point_3d< Type >::vgl_homg_point_3d	(	Type	px,
		Type	py,
		Type	pz,
		Type	pw = `(Type)1`
	)		`[inline]`

Construct from three (nonhomogeneous) or four (homogeneous) Types.

Definition at line 42 of file vgl_homg_point_3d.h.

template<class Type>

vgl_homg_point_3d< Type >::vgl_homg_point_3d ( const Type v[4] ) [inline]

Construct from homogeneous 4-array.

Definition at line 46 of file vgl_homg_point_3d.h.

template<class Type>

vgl_homg_point_3d< Type >::vgl_homg_point_3d ( vgl_vector_3d< Type >const & v ) [inline]

Construct point at infinity from direction vector.

Definition at line 49 of file vgl_homg_point_3d.h.

template<class Type>

vgl_homg_point_3d< Type >::vgl_homg_point_3d ( vgl_point_3d< Type > const & p ) [inline, explicit]

Construct from (non-homogeneous) vgl_point_3d<Type>.

Definition at line 52 of file vgl_homg_point_3d.h.

template<class Type >

vgl_homg_point_3d< Type >::vgl_homg_point_3d	(	vgl_homg_plane_3d< Type > const &	l1,
		vgl_homg_plane_3d< Type > const &	l2,
		vgl_homg_plane_3d< Type > const &	l3
	)

Construct from 3 planes (intersection).

Definition at line 11 of file vgl_homg_point_3d.txx.

Member Function Documentation

template<class Type>

bool vgl_homg_point_3d< Type >::get_nonhomogeneous	(	double &	vx,
		double &	vy,
		double &	vz
	)		const `[inline]`

Definition at line 105 of file vgl_homg_point_3d.h.

template<class Type>

bool vgl_homg_point_3d< Type >::ideal ( Type tol = (Type)0 ) const [inline]

Return true iff the point is at infinity (an ideal point).

The method checks whether |w| <= tol * max(|x|,|y|,|z|)

Definition at line 96 of file vgl_homg_point_3d.h.

template<class Type>

bool vgl_homg_point_3d< Type >::operator!= ( vgl_homg_point_3d< Type >const & other ) const [inline]

Definition at line 78 of file vgl_homg_point_3d.h.

template<class Type >

bool vgl_homg_point_3d< Type >::operator== ( vgl_homg_point_3d< Type > const & other ) const

the comparison operator.

Definition at line 26 of file vgl_homg_point_3d.txx.

template<class Type>

bool vgl_homg_point_3d< Type >::rescale_w ( Type new_w = Type(1) ) [inline]

Definition at line 124 of file vgl_homg_point_3d.h.

template<class Type>

void vgl_homg_point_3d< Type >::set	(	Type	px,
		Type	py,
		Type	pz,
		Type	pw = `(Type)1`
	)		`[inline]`

Set x,y,z,w.

Note that it does not make sense to set x, y, z or w individually.

Definition at line 89 of file vgl_homg_point_3d.h.

template<class Type>

void vgl_homg_point_3d< Type >::set ( Type const p[4] ) [inline]

Definition at line 92 of file vgl_homg_point_3d.h.

template<class Type>

Type vgl_homg_point_3d< Type >::w ( ) const [inline]

Definition at line 85 of file vgl_homg_point_3d.h.

template<class Type>

Type vgl_homg_point_3d< Type >::x ( ) const [inline]

Definition at line 82 of file vgl_homg_point_3d.h.

template<class Type>

Type vgl_homg_point_3d< Type >::y ( ) const [inline]

Definition at line 83 of file vgl_homg_point_3d.h.

template<class Type>

Type vgl_homg_point_3d< Type >::z ( ) const [inline]

Definition at line 84 of file vgl_homg_point_3d.h.

Friends And Related Function Documentation

template<class Type >

vgl_homg_point_3d< Type > centre	(	vgl_homg_point_3d< Type > const &	p1,
		vgl_homg_point_3d< Type > const &	p2
	)		`[related]`

Return the point at the centre of gravity of two given points.

Identical to midpoint(p1,p2). Invalid when both points are at infinity. If only one point is at infinity, that point is returned. inline

Definition at line 294 of file vgl_homg_point_3d.h.

template<class Type >

vgl_homg_point_3d< Type > centre ( vcl_vector< vgl_homg_point_3d< Type > > const & v ) [related]

Return the point at the centre of gravity of a set of given points.

There are no rounding errors when Type is e.g. int, if all w() are 1.

Definition at line 307 of file vgl_homg_point_3d.h.

template<class Type >

bool collinear	(	l const &	l1,
		vgl_homg_point_3d< Type > const &	p
	)		`[related]`

Does a line pass through a point, i.e., are the point and the line collinear?.

Definition at line 100 of file vgl_homg_line_3d_2_points.h.

template<class Type >

bool collinear	(	vgl_homg_point_3d< Type > const &	p1,
		vgl_homg_point_3d< Type > const &	p2,
		vgl_homg_point_3d< Type > const &	p3
	)		`[related]`

Are three points collinear, i.e., do they lie on a common line?.

template<class Type >

bool coplanar	(	l const &	l1,
		vgl_homg_point_3d< Type > const &	p1,
		vgl_homg_point_3d< Type > const &	p2
	)		`[related]`

Are two points coplanar with a line?.

Definition at line 118 of file vgl_homg_line_3d_2_points.h.

template<class Type >

bool coplanar	(	vgl_homg_point_3d< Type > const &	p1,
		vgl_homg_point_3d< Type > const &	p2,
		vgl_homg_point_3d< Type > const &	p3,
		vgl_homg_point_3d< Type > const &	p4
	)		`[related]`

Return true iff the 4 points are coplanar, i.e., they belong to a common plane.

Definition at line 161 of file vgl_homg_point_3d.h.

template<class T >

double cross_ratio	(	vgl_homg_point_3d< T >const &	p1,
		vgl_homg_point_3d< T >const &	p2,
		vgl_homg_point_3d< T >const &	p3,
		vgl_homg_point_3d< T >const &	p4
	)		`[related]`

cross ratio of four collinear points.

This number is projectively invariant, and it is the coordinate of p4 in the reference frame where p2 is the origin (coordinate 0), p3 is the unity (coordinate 1) and p1 is the point at infinity. This cross ratio is often denoted as ((p1, p2; p3, p4)) (which also equals ((p3, p4; p1, p2)) or ((p2, p1; p4, p3)) or ((p4, p3; p2, p1)) ) and is calculated as

                        p1 - p3   p2 - p3      (p1-p3)(p2-p4)
                        ------- : --------  =  --------------
                        p1 - p4   p2 - p4      (p1-p4)(p2-p3)

If three of the given points coincide, the cross ratio is not defined.

In this implementation, a least-squares result is calculated when the points are not exactly collinear.

template<class Type >

bool is_ideal	(	vgl_homg_point_3d< Type > const &	p,
		Type	tol = `(Type)0`
	)		`[related]`

Return true iff the point is at infinity (an ideal point).

The method checks whether |w| <= tol * max(|x|,|y|,|z|)

Definition at line 156 of file vgl_homg_point_3d.h.

template<class Type >

vgl_homg_point_3d< Type > midpoint	(	vgl_homg_point_3d< Type > const &	p1,
		vgl_homg_point_3d< Type > const &	p2,
		Type	f = `(Type)0.5`
	)		`[related]`

Return the point at a given ratio wrt two other points.

By default, the mid point (ratio=0.5) is returned. Note that the third argument is Type, not double, so the midpoint of e.g. two vgl_homg_point_3d<int> is not a valid concept. But the reflection point of p2 wrt p1 is: in that case f=-1.

Definition at line 282 of file vgl_homg_point_3d.h.

template<class Type >

vgl_homg_point_3d< Type > operator+	(	vgl_homg_point_3d< Type > const &	p,
		vgl_vector_3d< Type > const &	v
	)		`[related]`

Adding a vector to a point gives a new point at the end of that vector.

If the point is at infinity, nothing happens. Note that vector + point is not defined! It's always point + vector.

Definition at line 198 of file vgl_homg_point_3d.h.

template<class Type >

vgl_homg_point_3d< Type > & operator+=	(	vgl_homg_point_3d< Type > &	p,
		vgl_vector_3d< Type > const &	v
	)		`[related]`

Adding a vector to a point gives the point at the end of that vector.

If the point is at infinity, nothing happens.

Definition at line 210 of file vgl_homg_point_3d.h.

template<class Type >

vgl_vector_3d< Type > operator-	(	vgl_homg_point_3d< Type > const &	p1,
		vgl_homg_point_3d< Type > const &	p2
	)		`[related]`

The difference of two points is the vector from second to first point.

This function is only valid if the points are not at infinity.

Definition at line 184 of file vgl_homg_point_3d.h.

template<class Type >

vgl_homg_point_3d< Type > operator-	(	vgl_homg_point_3d< Type > const &	p,
		vgl_vector_3d< Type > const &	v
	)		`[related]`

Subtracting a vector from a point is the same as adding the inverse vector.

Definition at line 219 of file vgl_homg_point_3d.h.

template<class Type >

vgl_homg_point_3d< Type > & operator-=	(	vgl_homg_point_3d< Type > &	p,
		vgl_vector_3d< Type > const &	v
	)		`[related]`

Subtracting a vector from a point is the same as adding the inverse vector.

Definition at line 226 of file vgl_homg_point_3d.h.

template<class Type >

vcl_ostream & operator<<	(	vcl_ostream &	s,
		vgl_homg_point_3d< Type > const &	p
	)		`[related]`

Write "<vgl_homg_point_3d (x,y,z,w) >" to stream.

template<class Type >

vcl_istream & operator>>	(	vcl_istream &	s,
		vgl_homg_point_3d< Type > &	p
	)		`[related]`

Read x y z w from stream.

template<class Type >

double ratio	(	vgl_homg_point_3d< Type > const &	p1,
		vgl_homg_point_3d< Type > const &	p2,
		vgl_homg_point_3d< Type > const &	p3
	)		`[related]`

Return the relative distance to p1 wrt p1-p2 of p3.

The three points should be collinear and p2 should not equal p1. This is the coordinate of p3 in the affine 1D reference frame (p1,p2). If p3=p1, the ratio is 0; if p1=p3, the ratio is 1. The mid point of p1 and p2 has ratio 0.5. Note that the return type is double, not Type, since the ratio of e.g. two vgl_vector_3d<int> need not be an int.

Definition at line 270 of file vgl_homg_point_3d.h.

template<class T >

vgl_homg_point_3d< T > vgl_closest_point	(	vgl_homg_line_3d_2_points< T > const &	l,
		vgl_homg_point_3d< T > const &	p
	)		`[related]`

Return the point on the given line which is closest to the given point.

If the given point is at infinity, the point at infinity of the line is returned.

template<class T >

vgl_homg_point_3d< T > vgl_closest_point_origin ( vgl_homg_plane_3d< T > const & pl ) [related]

Return the point on the given plane closest to the origin.

template<class T >

vgl_homg_point_3d< T > vgl_closest_point_origin ( vgl_homg_line_3d_2_points< T > const & l ) [related]

Return the point on the given line closest to the origin.

template<class T >

double vgl_distance	(	vgl_homg_point_3d< T >const &	p1,
		vgl_homg_point_3d< T >const &	p2
	)		`[related]`

return the distance between two points.

Definition at line 128 of file vgl_distance.h.

Member Data Documentation

template<class Type>

Type vgl_homg_point_3d< Type >::w_ [private]

Definition at line 32 of file vgl_homg_point_3d.h.

template<class Type>

Type vgl_homg_point_3d< Type >::x_ [private]

Definition at line 29 of file vgl_homg_point_3d.h.

template<class Type>

Type vgl_homg_point_3d< Type >::y_ [private]

Definition at line 30 of file vgl_homg_point_3d.h.

template<class Type>

Type vgl_homg_point_3d< Type >::z_ [private]

Definition at line 31 of file vgl_homg_point_3d.h.

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

Public Member Functions

Private Attributes

Related Functions

Detailed Description

template<class Type> class vgl_homg_point_3d< Type >

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation

template<class Type>
class vgl_homg_point_3d< Type >