#include <iostream>
#include "vgl_homg_point_2d.h"
#include <vgl/vgl_homg_line_2d.h>

Macros
#define	VGL_HOMG_POINT_2D_INSTANTIATE(T)

Functions
template<class T >
double	cross_ratio (vgl_homg_point_2d< T >const &p1, vgl_homg_point_2d< T >const &p2, vgl_homg_point_2d< T >const &p3, vgl_homg_point_2d< T >const &p4)
	cross ratio of four collinear points. More...

template<class Type >
std::ostream &	operator<< (std::ostream &s, vgl_homg_point_2d< Type > const &p)

template<class Type >
std::istream &	operator>> (std::istream &s, vgl_homg_point_2d< Type > &p)

Macro Definition Documentation

◆ VGL_HOMG_POINT_2D_INSTANTIATE

#define VGL_HOMG_POINT_2D_INSTANTIATE ( T )

Value:

template class vgl_homg_point_2d<T >; \
template double cross_ratio(vgl_homg_point_2d<T >const&, vgl_homg_point_2d<T >const&, \
                            vgl_homg_point_2d<T >const&, vgl_homg_point_2d<T >const&); \
template std::ostream& operator<<(std::ostream&, vgl_homg_point_2d<T >const&); \
template std::istream& operator>>(std::istream&, vgl_homg_point_2d<T >&)

Definition at line 52 of file vgl_homg_point_2d.hxx.

Function Documentation

◆ cross_ratio()

template<class T >

double cross_ratio	(	vgl_homg_point_2d< T >const &	p1,
		vgl_homg_point_2d< T >const &	p2,
		vgl_homg_point_2d< T >const &	p3,
		vgl_homg_point_2d< 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 23 of file vgl_homg_point_2d.hxx.

◆ operator<<()

template<class Type >

std::ostream& operator<<	(	std::ostream &	s,
		vgl_homg_point_2d< Type > const &	p
	)

Definition at line 36 of file vgl_homg_point_2d.hxx.

◆ operator>>()