point in projective 3D space More...

#include <vgl/vgl_point_3d.h>
#include <vgl/vgl_fwd.h>
#include <vcl_iosfwd.h>
#include <vcl_cassert.h>

Classes
class	vgl_homg_point_3d< Type >
	Represents a homogeneous 3D point. More...
Defines
#define	vgl_Abs(x) (x<0?-x:x)
#define	VGL_HOMG_POINT_3D_INSTANTIATE(T) extern "please include vgl/vgl_homg_point_3d.txx first"
Functions
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

point in projective 3D space

Author:: Don HAMILTON, Peter TU

    Modifications
     Peter Vanroose -  4 July 2001 - Added geometric interface like vgl_point_3d
     Peter Vanroose -  2 July 2001 - Added constructor from 3 planes
     Peter Vanroose -  1 July 2001 - Renamed data to x_ y_ z_ w_ and inlined constructors
     Peter Vanroose - 27 June 2001 - Implemented operator==
     Peter Vanroose - 15 July 2002 - Added coplanar()
     Guillaume Mersch- 10 Feb 2009 - bug fix in coplanar()

Definition in file vgl_homg_point_3d.h.

Define Documentation

#define vgl_Abs ( x ) (x<0?-x:x)

#define VGL_HOMG_POINT_3D_INSTANTIATE ( T ) extern "please include vgl/vgl_homg_point_3d.txx first"

Definition at line 317 of file vgl_homg_point_3d.h.

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
	)		`[inline]`

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 ) [inline]

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	(	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?.

Definition at line 38 of file vgl_homg_point_3d.txx.

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
	)		`[inline]`

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
	)

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.

Definition at line 63 of file vgl_homg_point_3d.txx.

template<class Type >

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

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
	)		`[inline]`

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
	)		`[inline]`

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
	)		`[inline]`

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
	)		`[inline]`

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
	)		`[inline]`

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
	)

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

Definition at line 78 of file vgl_homg_point_3d.txx.

template<class Type >

vcl_istream & operator>>	(	vcl_istream &	s,
		vgl_homg_point_3d< Type > &	p
	)

Read x y z w from stream.

Definition at line 86 of file vgl_homg_point_3d.txx.

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
	)		`[inline]`

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.

Classes

Defines

Functions

Detailed Description

Define Documentation

Function Documentation