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vgl_point_3d< Type > Class Template Reference

#include <vgl_point_3d.h>

List of all members.


Detailed Description

template<class Type>
class vgl_point_3d< Type >

Represents a cartesian 3D point.

Definition at line 28 of file vgl_point_3d.h.

Public Member Functions

 vgl_point_3d ()
 Default constructor.
 vgl_point_3d (Type px, Type py, Type pz)
 Construct from three Types.
 vgl_point_3d (const Type v[3])
 Construct from 3-array.
 vgl_point_3d (vgl_homg_point_3d< Type > const &p)
 Construct from homogeneous point.
 vgl_point_3d (vgl_plane_3d< Type > const &pl1, vgl_plane_3d< Type > const &pl2, vgl_plane_3d< Type > const &pl3)
 Construct from 3 planes (intersection).
bool operator== (const vgl_point_3d< Type > &p) const
 Test for equality.
bool operator!= (vgl_point_3d< Type >const &p) const
Type x () const
Type y () const
Type z () const
void set (Type px, Type py, Type pz)
 Set x, y and z.
void set (Type const p[3])
 Set x, y and z.
bool ideal (Type=(Type) 0) const
 Return true iff the point is at infinity (an ideal point).

Private Attributes

Type x_
Type y_
Type z_

Related Functions

(Note that these are not member functions.)

vgl_point_3d< T > vgl_closest_point_origin (vgl_plane_3d< T > const &pl)
 Return the point on the given plane closest to the origin.
vgl_point_3d< T > vgl_closest_point_origin (vgl_line_3d_2_points< T > const &l)
 Return the point on the given line closest to the origin.
double vgl_distance (vgl_point_3d< T >const &p1, vgl_point_3d< T >const &p2)
 return the distance between two points.
bool collinear (l const &l1, vgl_point_3d< Type > const &p)
 Does a line pass through a point, i.e.
bool coplanar (l const &l1, vgl_point_3d< Type > const &p1, vgl_point_3d< Type > const &p2)
 Are two points coplanar with a line?.
vcl_ostream & operator<< (vcl_ostream &s, vgl_point_3d< Type > const &p)
 Write "<vgl_point_3d x,y,z> " to stream.
vcl_istream & operator>> (vcl_istream &s, vgl_point_3d< Type > &p)
 Read x y z from stream.
vgl_vector_3d< Type > operator- (vgl_point_3d< Type > const &p1, vgl_point_3d< Type > const &p2)
 The difference of two points is the vector from second to first point.
vgl_point_3d< Type > operator+ (vgl_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.
vgl_point_3d< Type > & operator+= (vgl_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.
vgl_point_3d< Type > operator- (vgl_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.
vgl_point_3d< Type > & operator-= (vgl_point_3d< Type > &p, vgl_vector_3d< Type > const &v)
 Subtracting a vector from a point is the same as adding the inverse vector.
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.
bool collinear (vgl_point_3d< Type > const &p1, vgl_point_3d< Type > const &p2, vgl_point_3d< Type > const &p3)
 Are three points collinear, i.e.
double ratio (vgl_point_3d< Type > const &p1, vgl_point_3d< Type > const &p2, vgl_point_3d< Type > const &p3)
 Return the relative distance to p1 wrt p1-p2 of p3.
vgl_point_3d< Type > midpoint (vgl_point_3d< Type > const &p1, vgl_point_3d< Type > const &p2, Type f=(Type) 0.5)
 Return the point at a given ratio wrt two other points.
vgl_point_3d< Type > centre (vgl_point_3d< Type > const &p1, vgl_point_3d< Type > const &p2)
 Return the point at the centre of gravity of two given points.
vgl_point_3d< Type > centre (vgl_point_3d< Type > const &p1, vgl_point_3d< Type > const &p2, vgl_point_3d< Type > const &p3)
 Return the point at the centre of gravity of three given points.
vgl_point_3d< Type > centre (vgl_point_3d< Type > const &p1, vgl_point_3d< Type > const &p2, vgl_point_3d< Type > const &p3, vgl_point_3d< Type > const &p4)
 Return the point at the centre of gravity of four given points.
vgl_point_3d< Type > centre (vcl_vector< vgl_point_3d< Type > > const &v)
 Return the point at the centre of gravity of a set of given points.
bool coplanar (vgl_point_3d< Type > const &p1, vgl_point_3d< Type > const &p2, vgl_point_3d< Type > const &p3, vgl_point_3d< Type > const &p4)
 Return true iff the 4 points are coplanar, i.e.


Constructor & Destructor Documentation

template<class Type>
vgl_point_3d< Type >::vgl_point_3d  )  [inline]
 

Default constructor.

Definition at line 40 of file vgl_point_3d.h.

template<class Type>
vgl_point_3d< Type >::vgl_point_3d Type  px,
Type  py,
Type  pz
[inline]
 

Construct from three Types.

Definition at line 43 of file vgl_point_3d.h.

template<class Type>
vgl_point_3d< Type >::vgl_point_3d const Type  v[3]  )  [inline]
 

Construct from 3-array.

Definition at line 46 of file vgl_point_3d.h.

template<class Type>
vgl_point_3d< Type >::vgl_point_3d vgl_homg_point_3d< Type > const &  p  ) 
 

Construct from homogeneous point.

Definition at line 16 of file vgl_point_3d.txx.

template<class Type>
vgl_point_3d< Type >::vgl_point_3d vgl_plane_3d< Type > const &  pl1,
vgl_plane_3d< Type > const &  pl2,
vgl_plane_3d< Type > const &  pl3
 

Construct from 3 planes (intersection).

Definition at line 23 of file vgl_point_3d.txx.


Member Function Documentation

template<class Type>
bool vgl_point_3d< Type >::ideal Type  = (Type)0  )  const [inline]
 

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

Always returns false.

Definition at line 89 of file vgl_point_3d.h.

template<class Type>
bool vgl_point_3d< Type >::operator!= vgl_point_3d< Type >const &  p  )  const [inline]
 

Definition at line 71 of file vgl_point_3d.h.

template<class Type>
bool vgl_point_3d< Type >::operator== const vgl_point_3d< Type > &  p  )  const [inline]
 

Test for equality.

Definition at line 67 of file vgl_point_3d.h.

template<class Type>
void vgl_point_3d< Type >::set Type const   p[3]  )  [inline]
 

Set x, y and z.

Note that x, y, or z cannot be set individually

Definition at line 85 of file vgl_point_3d.h.

template<class Type>
void vgl_point_3d< Type >::set Type  px,
Type  py,
Type  pz
[inline]
 

Set x, y and z.

Note that x, y, or z cannot be set individually

Definition at line 82 of file vgl_point_3d.h.

template<class Type>
Type vgl_point_3d< Type >::x  )  const [inline]
 

Definition at line 76 of file vgl_point_3d.h.

template<class Type>
Type vgl_point_3d< Type >::y  )  const [inline]
 

Definition at line 77 of file vgl_point_3d.h.

template<class Type>
Type vgl_point_3d< Type >::z  )  const [inline]
 

Definition at line 78 of file vgl_point_3d.h.


Friends And Related Function Documentation

template<class Type>
vgl_point_3d< Type > centre vcl_vector< vgl_point_3d< Type > > const &  v  )  [related]
 

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

Beware of possible rounding errors when Type is e.g. int.

Definition at line 251 of file vgl_point_3d.h.

template<class Type>
vgl_point_3d< Type > centre vgl_point_3d< Type > const &  p1,
vgl_point_3d< Type > const &  p2,
vgl_point_3d< Type > const &  p3,
vgl_point_3d< Type > const &  p4
[related]
 

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

Definition at line 237 of file vgl_point_3d.h.

template<class Type>
vgl_point_3d< Type > centre vgl_point_3d< Type > const &  p1,
vgl_point_3d< Type > const &  p2,
vgl_point_3d< Type > const &  p3
[related]
 

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

Definition at line 225 of file vgl_point_3d.h.

template<class Type>
vgl_point_3d< Type > centre vgl_point_3d< Type > const &  p1,
vgl_point_3d< Type > const &  p2
[related]
 

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

Identical to midpoint(p1,p2).

Definition at line 214 of file vgl_point_3d.h.

template<class Type>
bool collinear vgl_point_3d< Type > const &  p1,
vgl_point_3d< Type > const &  p2,
vgl_point_3d< Type > const &  p3
[related]
 

Are three points collinear, i.e.

, do they lie on a common line?.

Definition at line 174 of file vgl_point_3d.h.

template<class Type>
bool collinear l const &  l1,
vgl_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 91 of file vgl_line_3d_2_points.h.

template<class Type>
bool coplanar vgl_point_3d< Type > const &  p1,
vgl_point_3d< Type > const &  p2,
vgl_point_3d< Type > const &  p3,
vgl_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 263 of file vgl_point_3d.h.

template<class Type>
bool coplanar l const &  l1,
vgl_point_3d< Type > const &  p1,
vgl_point_3d< Type > const &  p2
[related]
 

Are two points coplanar with a line?.

Definition at line 114 of file vgl_line_3d_2_points.h.

template<class Type>
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
[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.

Definition at line 35 of file vgl_point_3d.txx.

template<class Type>
vgl_point_3d< Type > midpoint vgl_point_3d< Type > const &  p1,
vgl_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_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 200 of file vgl_point_3d.h.

template<class Type>
vgl_point_3d< Type > operator+ vgl_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.

Note that vector + point is not defined! It's always point + vector.

Definition at line 122 of file vgl_point_3d.h.

template<class Type>
vgl_point_3d< Type > & operator+= vgl_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.

Definition at line 129 of file vgl_point_3d.h.

template<class Type>
vgl_point_3d< Type > operator- vgl_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 136 of file vgl_point_3d.h.

template<class Type>
vgl_vector_3d< Type > operator- vgl_point_3d< Type > const &  p1,
vgl_point_3d< Type > const &  p2
[related]
 

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

Definition at line 114 of file vgl_point_3d.h.

template<class Type>
vgl_point_3d< Type > & operator-= vgl_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 143 of file vgl_point_3d.h.

template<class Type>
vcl_ostream & operator<< vcl_ostream &  s,
vgl_point_3d< Type > const &  p
[related]
 

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

Definition at line 51 of file vgl_point_3d.txx.

template<class Type>
vcl_istream & operator>> vcl_istream &  s,
vgl_point_3d< Type > &  p
[related]
 

Read x y z from stream.

Definition at line 58 of file vgl_point_3d.txx.

template<class Type>
double ratio vgl_point_3d< Type > const &  p1,
vgl_point_3d< Type > const &  p2,
vgl_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 188 of file vgl_point_3d.h.

template<class Type>
vgl_point_3d< T > vgl_closest_point_origin vgl_line_3d_2_points< T > const &  l  )  [related]
 

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

Definition at line 228 of file vgl_closest_point.txx.

template<class Type>
vgl_point_3d< T > vgl_closest_point_origin vgl_plane_3d< T > const &  pl  )  [related]
 

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

Definition at line 200 of file vgl_closest_point.txx.

template<class Type>
double vgl_distance vgl_point_3d< T >const &  p1,
vgl_point_3d< T >const &  p2
[related]
 

return the distance between two points.

Definition at line 110 of file vgl_distance.h.


Member Data Documentation

template<class Type>
Type vgl_point_3d< Type >::x_ [private]
 

Definition at line 31 of file vgl_point_3d.h.

template<class Type>
Type vgl_point_3d< Type >::y_ [private]
 

Definition at line 32 of file vgl_point_3d.h.

template<class Type>
Type vgl_point_3d< Type >::z_ [private]
 

Definition at line 33 of file vgl_point_3d.h.


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