core/vgl/vgl_point_3d.txx File Reference

#include "vgl_point_3d.h"
#include <vgl/vgl_homg_point_3d.h>
#include <vgl/vgl_plane_3d.h>
#include <vgl/vgl_homg_plane_3d.h>
#include <vcl_iostream.h>
#include <vcl_iomanip.h>

Go to the source code of this file.

Defines
#define	vgl_point_3d_txx_
#define	VGL_POINT_3D_INSTANTIATE(T)
Functions
template<class T >
double	cross_ratio (vgl_point_3d< T >const &p1, vgl_point_3d< T >const &p2, vgl_point_3d< T >const &p3, vgl_point_3d< T >const &p4)
	cross ratio of four collinear points.
template<class Type >
vcl_ostream &	operator<< (vcl_ostream &s, vgl_point_3d< Type > const &p)
	Write "<vgl_point_3d x,y,z> " to stream.
template<class Type >
vcl_istream &	operator>> (vcl_istream &is, vgl_point_3d< Type > &p)
	Read from stream, possibly with formatting.

---

Detailed Description

Definition in file vgl_point_3d.txx.

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Define Documentation

#define VGL_POINT_3D_INSTANTIATE

(

T

)

Value:

template class vgl_point_3d<T >; \
template double cross_ratio(vgl_point_3d<T >const&, vgl_point_3d<T >const&, \
                            vgl_point_3d<T >const&, vgl_point_3d<T >const&); \
template vcl_ostream& operator<<(vcl_ostream&, const vgl_point_3d<T >&); \
template vcl_istream& operator>>(vcl_istream&, vgl_point_3d<T >&)

Definition at line 99 of file vgl_point_3d.txx.

#define vgl_point_3d_txx_

Definition at line 3 of file vgl_point_3d.txx.

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Function Documentation

template<class T >

double cross_ratio	(	vgl_point_3d< T >const &	p1,
		vgl_point_3d< T >const &	p2,
		vgl_point_3d< T >const &	p3,
		vgl_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 36 of file vgl_point_3d.txx.

template<class Type >

vcl_ostream& operator<<	(	vcl_ostream &	s,
		vgl_point_3d< Type > const &	p
	)

Write "<vgl_point_3d x,y,z> " to stream.

Definition at line 52 of file vgl_point_3d.txx.

template<class Type >

vcl_istream& operator>>	(	vcl_istream &	is,
		vgl_point_3d< Type > &	p
	)

Read from stream, possibly with formatting.

Either just reads three blank-separated numbers, or reads three comma-separated numbers, or reads three numbers in parenthesized form "(123, 321, 567)"

Definition at line 93 of file vgl_point_3d.txx.