Represents a homogeneous 2D point. More...
#include <vgl_fwd.h>
Public Member Functions | |
| vgl_homg_point_2d () | |
| Default constructor with (0,0,1). More... | |
| vgl_homg_point_2d (T px, T py, T pw=(T) 1) | |
| Construct from two (nonhomogeneous) or three (homogeneous) Types. More... | |
| vgl_homg_point_2d (const T v[3]) | |
| Construct from homogeneous 3-array. More... | |
| vgl_homg_point_2d (vgl_vector_2d< T >const &v) | |
| Construct point at infinity from direction vector. More... | |
| vgl_homg_point_2d (vgl_point_2d< T > const &p) | |
| Construct from (non-homogeneous) vgl_point_2d<T>. More... | |
| vgl_homg_point_2d (vgl_homg_line_2d< T > const &l1, vgl_homg_line_2d< T > const &l2) | |
| Construct from 2 lines (intersection). More... | |
| bool | operator== (vgl_homg_point_2d< T > const &p) const |
| the comparison operator. More... | |
| bool | operator!= (vgl_homg_point_2d< T > const &other) const |
| T | x () const |
| T | y () const |
| T | w () const |
| void | set (T px, T py, T pw=(T) 1) |
| Set x,y,w. More... | |
| void | set (T const p[3]) |
| bool | ideal (T tol=(T) 0) const |
| Return true iff the point is at infinity (an ideal point). More... | |
Private Attributes | |
| T | x_ |
| T | y_ |
| T | w_ |
Related Functions | |
(Note that these are not member functions.) | |
| template<class T > | |
| vgl_homg_point_2d< T > | operator * (vnl_matrix_fixed< T, 3, 3 > const &m, vgl_homg_point_2d< T > const &p) |
| Transform a point through a 3x3 projective transformation matrix. More... | |
| template<class T > | |
| vgl_homg_point_2d< T > | vgl_closest_point_origin (vgl_homg_line_2d< T > const &l) |
| Return the point on the given line closest to the origin. More... | |
| template<class T > | |
| double | vgl_distance (vgl_homg_point_2d< T >const &p1, vgl_homg_point_2d< T >const &p2) |
| return the distance between two points. More... | |
| template<class T > | |
| std::ostream & | operator<< (std::ostream &s, vgl_homg_point_2d< T > const &p) |
| Write "<vgl_homg_point_2d (x,y,w) >" to stream. More... | |
| template<class T > | |
| std::istream & | operator>> (std::istream &s, vgl_homg_point_2d< T > &p) |
| Read x y w from stream. More... | |
| template<class T > | |
| bool | is_ideal (vgl_homg_point_2d< T > const &p, T tol=(T) 0) |
| Return true iff the point is at infinity (an ideal point). More... | |
| template<class T > | |
| vgl_vector_2d< T > | operator- (vgl_homg_point_2d< T > const &p1, vgl_homg_point_2d< T > const &p2) |
| The difference of two points is the vector from second to first point. More... | |
| template<class T > | |
| vgl_homg_point_2d< T > | operator+ (vgl_homg_point_2d< T > const &p, vgl_vector_2d< T > const &v) |
| Adding a vector to a point gives a new point at the end of that vector. More... | |
| template<class T > | |
| vgl_homg_point_2d< T > & | operator+= (vgl_homg_point_2d< T > &p, vgl_vector_2d< T > const &v) |
| Adding a vector to a point gives the point at the end of that vector. More... | |
| template<class T > | |
| vgl_homg_point_2d< T > | operator- (vgl_homg_point_2d< T > const &p, vgl_vector_2d< T > const &v) |
| Subtracting a vector from a point is the same as adding the inverse vector. More... | |
| template<class T > | |
| vgl_homg_point_2d< T > & | operator-= (vgl_homg_point_2d< T > &p, vgl_vector_2d< T > const &v) |
| Subtracting a vector from a point is the same as adding the inverse vector. More... | |
| 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 T > | |
| bool | collinear (vgl_homg_point_2d< T > const &p1, vgl_homg_point_2d< T > const &p2, vgl_homg_point_2d< T > const &p3) |
| Are three points collinear, i.e., do they lie on a common line?. More... | |
| template<class T > | |
| double | ratio (vgl_homg_point_2d< T > const &p1, vgl_homg_point_2d< T > const &p2, vgl_homg_point_2d< T > const &p3) |
| Return the relative distance to p1 wrt p1-p2 of p3. More... | |
| template<class T > | |
| vgl_homg_point_2d< T > | centre (vgl_homg_point_2d< T > const &p1, vgl_homg_point_2d< T > const &p2) |
| Return the point at the centre of gravity of two given points. More... | |
| template<class T > | |
| vgl_homg_point_2d< T > | centre (std::vector< vgl_homg_point_2d< T > > const &v) |
| Return the point at the centre of gravity of a set of given points. More... | |
Detailed Description
template<class T>
class vgl_homg_point_2d< T >
Represents a homogeneous 2D point.
Constructor & Destructor Documentation
◆ vgl_homg_point_2d() [1/6]
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inline |
Default constructor with (0,0,1).
Definition at line 39 of file vgl_homg_point_2d.h.
◆ vgl_homg_point_2d() [2/6]
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inline |
Construct from two (nonhomogeneous) or three (homogeneous) Types.
Definition at line 42 of file vgl_homg_point_2d.h.
◆ vgl_homg_point_2d() [3/6]
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inline |
Construct from homogeneous 3-array.
Definition at line 46 of file vgl_homg_point_2d.h.
◆ vgl_homg_point_2d() [4/6]
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inline |
Construct point at infinity from direction vector.
Definition at line 49 of file vgl_homg_point_2d.h.
◆ vgl_homg_point_2d() [5/6]
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inlineexplicit |
Construct from (non-homogeneous) vgl_point_2d<T>.
Definition at line 52 of file vgl_homg_point_2d.h.
◆ vgl_homg_point_2d() [6/6]
| vgl_homg_point_2d< T >::vgl_homg_point_2d | ( | vgl_homg_line_2d< T > const & | l1, |
| vgl_homg_line_2d< T > const & | l2 | ||
| ) |
Construct from 2 lines (intersection).
Member Function Documentation
◆ ideal()
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inline |
Return true iff the point is at infinity (an ideal point).
The method checks whether |w| <= tol * max(|x|,|y|)
Definition at line 99 of file vgl_homg_point_2d.h.
◆ operator!=()
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inline |
Definition at line 82 of file vgl_homg_point_2d.h.
◆ operator==()
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inline |
the comparison operator.
Definition at line 76 of file vgl_homg_point_2d.h.
◆ set() [1/2]
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inline |
Set x,y,w.
Note that it does not make sense to set x, y or w individually.
Definition at line 92 of file vgl_homg_point_2d.h.
◆ set() [2/2]
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inline |
Definition at line 95 of file vgl_homg_point_2d.h.
◆ w()
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inline |
Definition at line 88 of file vgl_homg_point_2d.h.
◆ x()
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inline |
Definition at line 86 of file vgl_homg_point_2d.h.
◆ y()
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inline |
Definition at line 87 of file vgl_homg_point_2d.h.
Friends And Related Function Documentation
◆ centre() [1/2]
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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.
Definition at line 239 of file vgl_homg_point_2d.h.
◆ centre() [2/2]
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related |
Return the point at the centre of gravity of a set of given points.
There are no rounding errors when T is e.g. int, if all w() are 1.
Definition at line 251 of file vgl_homg_point_2d.h.
◆ collinear()
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related |
Are three points collinear, i.e., do they lie on a common line?.
Definition at line 198 of file vgl_homg_point_2d.h.
◆ cross_ratio()
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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.
◆ is_ideal()
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related |
Return true iff the point is at infinity (an ideal point).
The method checks whether |w| <= tol * max(|x|,|y|)
Definition at line 126 of file vgl_homg_point_2d.h.
◆ operator *()
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related |
Transform a point through a 3x3 projective transformation matrix.
Definition at line 898 of file vgl_homg_operators_2d.hxx.
◆ operator+()
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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 145 of file vgl_homg_point_2d.h.
◆ operator+=()
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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 153 of file vgl_homg_point_2d.h.
◆ operator-() [1/2]
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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 132 of file vgl_homg_point_2d.h.
◆ operator-() [2/2]
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related |
Subtracting a vector from a point is the same as adding the inverse vector.
Definition at line 160 of file vgl_homg_point_2d.h.
◆ operator-=()
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related |
Subtracting a vector from a point is the same as adding the inverse vector.
Definition at line 167 of file vgl_homg_point_2d.h.
◆ operator<<()
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related |
Write "<vgl_homg_point_2d (x,y,w) >" to stream.
◆ operator>>()
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related |
Read x y w from stream.
◆ ratio()
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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 T, since the ratio of e.g. two vgl_vector_2d<int> need not be an int.
Definition at line 216 of file vgl_homg_point_2d.h.
◆ vgl_closest_point_origin()
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related |
Return the point on the given line closest to the origin.
◆ vgl_distance()
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related |
return the distance between two points.
Definition at line 122 of file vgl_distance.h.
Member Data Documentation
◆ w_
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private |
Definition at line 32 of file vgl_homg_point_2d.h.
◆ x_
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private |
Definition at line 30 of file vgl_homg_point_2d.h.
◆ y_
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private |
Definition at line 31 of file vgl_homg_point_2d.h.
The documentation for this class was generated from the following files:
- core/vgl/vgl_fwd.h
- core/vgl/vgl_homg_point_2d.h
- core/vgl/algo/vgl_homg_operators_2d.h
- core/vgl/algo/vgl_homg_operators_2d.hxx
- core/vgl/vgl_closest_point.h
- core/vgl/vgl_distance.h
