Represents a cartesian 2D point. More...
#include <vgl_area.h>
Public Member Functions | |
| vgl_point_2d ()=default | |
| Default constructor. More... | |
| vgl_point_2d (Type px, Type py) | |
| Construct from two Types. More... | |
| vgl_point_2d (Type const v[2]) | |
| Construct from 2-array. More... | |
| vgl_point_2d (vgl_homg_point_2d< Type > const &p) | |
| Construct from homogeneous point. More... | |
| vgl_point_2d (vgl_line_2d< Type > const &l1, vgl_line_2d< Type > const &l2) | |
| Construct from 2 lines (intersection). More... | |
| bool | operator== (vgl_point_2d< Type >const &p) const |
| Test for equality. More... | |
| bool | operator!= (vgl_point_2d< Type >const &p) const |
| Type & | x () |
| Type & | y () |
| Type | x () const |
| Type | y () const |
| void | set (Type px, Type py) |
| Set x and y. More... | |
| void | set (Type const p[2]) |
| Set x and y. More... | |
| bool | ideal (Type=(Type) 0) const |
| Return true iff the point is at infinity (an ideal point). More... | |
| std::istream & | read (std::istream &is) |
| Read from stream, possibly with formatting. More... | |
Private Attributes | |
| Type | x_ |
| Type | y_ |
Related Functions | |
(Note that these are not member functions.) | |
| template<class T > | |
| vgl_point_2d< T > | vgl_closest_point_origin (vgl_line_2d< T > const &l) |
| Return the point on the given line closest to the origin. More... | |
| template<class T > | |
| double | vgl_distance (vgl_point_2d< T >const &p1, vgl_point_2d< T >const &p2) |
| return the distance between two points. More... | |
| template<class T > | |
| bool | vgl_intersection (vgl_point_2d< T > const &p0, vgl_point_2d< T > const &p1) |
| Return true if the two points intersect, i.e., coincide. More... | |
| template<class T > | |
| bool | vgl_intersection (vgl_point_3d< T > const &p0, vgl_point_3d< T > const &p1) |
| Return true if the two points intersect, i.e., coincide. More... | |
| template<class T > | |
| bool | vgl_intersection (vgl_point_2d< T > const &p1, vgl_point_2d< T > const &p2, vgl_point_2d< T > const &q1, vgl_point_2d< T > const &q2, double tol=1e-6) |
| Return true if any point on [p1,p2] is within tol of [q1,q2]. More... | |
| template<class T > | |
| std::vector< vgl_point_2d< T > > | vgl_intersection (vgl_polygon< T > const &poly, vgl_line_2d< T > const &line) |
| Find the intersections of a line with a polygon( can have multiple sheets). More... | |
| template<class Type > | |
| std::ostream & | operator<< (std::ostream &s, vgl_point_2d< Type > const &p) |
| Write "<vgl_point_2d x,y>" to stream. More... | |
| template<class Type > | |
| std::istream & | operator>> (std::istream &s, vgl_point_2d< Type > &p) |
| Read from stream, possibly with formatting. More... | |
| template<class Type > | |
| vgl_vector_2d< Type > | operator- (vgl_point_2d< Type > const &p1, vgl_point_2d< Type > const &p2) |
| The difference of two points is the vector from second to first point. More... | |
| template<class Type > | |
| vgl_point_2d< Type > | operator+ (vgl_point_2d< Type > const &p, vgl_vector_2d< Type > const &v) |
| Adding a vector to a point gives a new point at the end of that vector. More... | |
| template<class Type > | |
| vgl_point_2d< Type > & | operator+= (vgl_point_2d< Type > &p, vgl_vector_2d< Type > const &v) |
| Adding a vector to a point gives the point at the end of that vector. More... | |
| template<class Type > | |
| vgl_point_2d< Type > | operator- (vgl_point_2d< Type > const &p, vgl_vector_2d< Type > const &v) |
| Subtracting a vector from a point is the same as adding the inverse vector. More... | |
| template<class Type > | |
| vgl_point_2d< Type > & | operator-= (vgl_point_2d< Type > &p, vgl_vector_2d< Type > const &v) |
| Subtracting a vector from a point is the same as adding the inverse vector. More... | |
| template<class T > | |
| double | cross_ratio (vgl_point_2d< T >const &p1, vgl_point_2d< T >const &p2, vgl_point_2d< T >const &p3, vgl_point_2d< T >const &p4) |
| cross ratio of four collinear points. More... | |
| template<class Type > | |
| bool | collinear (vgl_point_2d< Type > const &p1, vgl_point_2d< Type > const &p2, vgl_point_2d< Type > const &p3) |
| Are three points collinear, i.e., do they lie on a common line?. More... | |
| template<class Type > | |
| double | ratio (vgl_point_2d< Type > const &p1, vgl_point_2d< Type > const &p2, vgl_point_2d< Type > const &p3) |
| Return the relative distance to p1 wrt p1-p2 of p3. More... | |
| template<class Type > | |
| vgl_point_2d< Type > | midpoint (vgl_point_2d< Type > const &p1, vgl_point_2d< Type > const &p2, Type f=(Type) 0.5) |
| Return the point at a given ratio wrt two other points. More... | |
| template<class Type > | |
| vgl_point_2d< Type > | centre (vgl_point_2d< Type > const &p1, vgl_point_2d< Type > const &p2) |
| Return the point at the centre of gravity of two given points. More... | |
| template<class Type > | |
| vgl_point_2d< Type > | centre (vgl_point_2d< Type > const &p1, vgl_point_2d< Type > const &p2, vgl_point_2d< Type > const &p3) |
| Return the point at the centre of gravity of three given points. More... | |
| template<class Type > | |
| vgl_point_2d< Type > | centre (vgl_point_2d< Type > const &p1, vgl_point_2d< Type > const &p2, vgl_point_2d< Type > const &p3, vgl_point_2d< Type > const &p4) |
| Return the point at the centre of gravity of four given points. More... | |
| template<class Type > | |
| vgl_point_2d< Type > | centre (std::vector< vgl_point_2d< Type > > const &v) |
| Return the point at the centre of gravity of a set of given points. More... | |
Detailed Description
template<class Type>
class vgl_point_2d< Type >
Represents a cartesian 2D point.
Definition at line 7 of file vgl_area.h.
Constructor & Destructor Documentation
◆ vgl_point_2d() [1/5]
|
inlinedefault |
Default constructor.
◆ vgl_point_2d() [2/5]
|
inline |
Construct from two Types.
Definition at line 41 of file vgl_point_2d.h.
◆ vgl_point_2d() [3/5]
|
inline |
Construct from 2-array.
Definition at line 44 of file vgl_point_2d.h.
◆ vgl_point_2d() [4/5]
| vgl_point_2d< Type >::vgl_point_2d | ( | vgl_homg_point_2d< Type > const & | p | ) |
Construct from homogeneous point.
Definition at line 21 of file vgl_point_2d.hxx.
◆ vgl_point_2d() [5/5]
| vgl_point_2d< Type >::vgl_point_2d | ( | vgl_line_2d< Type > const & | l1, |
| vgl_line_2d< Type > const & | l2 | ||
| ) |
Construct from 2 lines (intersection).
Definition at line 28 of file vgl_point_2d.hxx.
Member Function Documentation
◆ ideal()
|
inline |
Return true iff the point is at infinity (an ideal point).
Always returns false.
Definition at line 86 of file vgl_point_2d.h.
◆ operator!=()
|
inline |
Definition at line 66 of file vgl_point_2d.h.
◆ operator==()
|
inline |
Test for equality.
Definition at line 64 of file vgl_point_2d.h.
◆ read()
| std::istream & vgl_point_2d< Type >::read | ( | std::istream & | is | ) |
Read from stream, possibly with formatting.
Either just reads two blank-separated numbers, or reads two comma-separated numbers, or reads two numbers in parenthesized form "(123, 321)"
Either just reads two blank-separated numbers, or reads two comma-separated numbers, or reads two numbers in parenthesized form "(123, 321)" or reads form written by <<, "<vgl_point_2d 123, 321 >"
Definition at line 63 of file vgl_point_2d.hxx.
◆ set() [1/2]
|
inline |
Set x and y.
Note that x and y can also be set individually.
Definition at line 79 of file vgl_point_2d.h.
◆ set() [2/2]
|
inline |
Set x and y.
Note that x and y can also be set individually.
Definition at line 82 of file vgl_point_2d.h.
◆ x() [1/2]
|
inline |
Definition at line 71 of file vgl_point_2d.h.
◆ x() [2/2]
|
inline |
Definition at line 74 of file vgl_point_2d.h.
◆ y() [1/2]
|
inline |
Definition at line 72 of file vgl_point_2d.h.
◆ y() [2/2]
|
inline |
Definition at line 75 of file vgl_point_2d.h.
Friends And Related Function Documentation
◆ centre() [1/4]
|
related |
Return the point at the centre of gravity of two given points.
Identical to midpoint(p1,p2).
Definition at line 219 of file vgl_point_2d.h.
◆ centre() [2/4]
|
related |
Return the point at the centre of gravity of three given points.
Definition at line 229 of file vgl_point_2d.h.
◆ centre() [3/4]
|
related |
Return the point at the centre of gravity of four given points.
Definition at line 240 of file vgl_point_2d.h.
◆ centre() [4/4]
|
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 253 of file vgl_point_2d.h.
◆ collinear()
|
related |
Are three points collinear, i.e., do they lie on a common line?.
Definition at line 180 of file vgl_point_2d.h.
◆ cross_ratio()
|
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.
◆ midpoint()
|
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_2d<int> is not a valid concept. But the reflection point of p2 wrt p1 is: in that case f=-1.
Definition at line 206 of file vgl_point_2d.h.
◆ operator+()
|
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 128 of file vgl_point_2d.h.
◆ operator+=()
|
related |
Adding a vector to a point gives the point at the end of that vector.
Definition at line 135 of file vgl_point_2d.h.
◆ operator-() [1/2]
|
related |
The difference of two points is the vector from second to first point.
Definition at line 120 of file vgl_point_2d.h.
◆ operator-() [2/2]
|
related |
Subtracting a vector from a point is the same as adding the inverse vector.
Definition at line 142 of file vgl_point_2d.h.
◆ operator-=()
|
related |
Subtracting a vector from a point is the same as adding the inverse vector.
Definition at line 149 of file vgl_point_2d.h.
◆ operator<<()
|
related |
Write "<vgl_point_2d x,y>" to stream.
◆ operator>>()
|
related |
Read from stream, possibly with formatting.
Either just reads two blank-separated numbers, or reads two comma-separated numbers, or reads two numbers in parenthesized form "(123, 321)"
◆ ratio()
|
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_2d<int> need not be an int.
Definition at line 194 of file vgl_point_2d.h.
◆ vgl_closest_point_origin()
|
related |
Return the point on the given line closest to the origin.
◆ vgl_distance()
|
related |
return the distance between two points.
Definition at line 104 of file vgl_distance.h.
◆ vgl_intersection() [1/4]
|
related |
Return true if the two points intersect, i.e., coincide.
Definition at line 36 of file vgl_intersection.h.
◆ vgl_intersection() [2/4]
|
related |
Return true if the two points intersect, i.e., coincide.
Definition at line 43 of file vgl_intersection.h.
◆ vgl_intersection() [3/4]
|
related |
Return true if any point on [p1,p2] is within tol of [q1,q2].
Tests two line segments for intersection or near intersection (within given tolerance).
◆ vgl_intersection() [4/4]
|
related |
Find the intersections of a line with a polygon( can have multiple sheets).
Member Data Documentation
◆ x_
|
private |
Definition at line 30 of file vgl_point_2d.h.
◆ y_
|
private |
Definition at line 31 of file vgl_point_2d.h.
The documentation for this class was generated from the following files:
- core/vgl/vgl_area.h
- core/vgl/vgl_point_2d.h
- core/vgl/vgl_closest_point.h
- core/vgl/vgl_distance.h
- core/vgl/vgl_intersection.h
- core/vgl/vgl_point_2d.hxx
