Represents a Euclidean 3D plane. More...
#include <vgl_fwd.h>
Public Member Functions | |
| vgl_plane_3d () | |
| vgl_plane_3d (T ta, T tb, T tc, T td) | |
| Construct a vgl_plane_3d from its equation $ax+by+cz+d=0$. More... | |
| vgl_plane_3d (const T v[4]) | |
| Construct a vgl_plane_3d from its equation $v[0]x+v[1]y+v[2]z+v[3]=0$. More... | |
| vgl_plane_3d (vgl_homg_plane_3d< T > const &p) | |
| Construct from a homogeneous plane. More... | |
| vgl_plane_3d (vgl_vector_3d< T > const &normal, vgl_point_3d< T > const &p) | |
| Construct from Normal and a point. More... | |
| vgl_plane_3d (vgl_point_3d< T > const &p1, vgl_point_3d< T > const &p2, vgl_point_3d< T > const &p3) | |
| Construct from three non-collinear points. More... | |
| vgl_plane_3d (vgl_ray_3d< T > const &r0, vgl_ray_3d< T > const &r1) | |
| Construct from two non-skew rays. The rays intersect at their origins. More... | |
| T | a () const |
| Return x coefficient. More... | |
| T | nx () const |
| T | b () const |
| Return y coefficient. More... | |
| T | ny () const |
| T | c () const |
| Return z coefficient. More... | |
| T | nz () const |
| T | d () const |
| Return constant coefficient. More... | |
| void | set (T ta, T tb, T tc, T td) |
| Set this vgl_plane_3d to have the equation $ax+by+cz+d=0$. More... | |
| bool | operator== (vgl_plane_3d< T > const &p) const |
| the comparison operator. More... | |
| bool | operator!= (vgl_plane_3d< T >const &p) const |
| bool | ideal (T=(T) 0) const |
| Return true iff the plane is the plane at infinity. More... | |
| bool | normalize () |
| vgl_vector_3d< T > | normal () const |
| Return the normal direction, i.e., a unit vector orthogonal to this plane. More... | |
| bool | contains (vgl_point_3d< T > const &p, T tol=(T) 0) const |
| Return true if p is on the plane. More... | |
| bool | plane_coords (vgl_point_3d< T > const &p3d, vgl_point_2d< T > &p2d, T tol=(T) 0) const |
| Given a 3-d point, return a 2-d point in the coord. system of the plane. More... | |
| vgl_point_3d< T > | world_coords (vgl_point_2d< T > const &p2d) const |
| inverse map from plane coordinates to world coordinates. More... | |
| void | plane_coord_vectors (vgl_vector_3d< T > &uvec, vgl_vector_3d< T > &vvec) const |
| plane coordinate unit vectors. More... | |
Private Attributes | |
| T | a_ |
| T | b_ |
| T | c_ |
| T | d_ |
Related Functions | |
(Note that these are not member functions.) | |
| template<class T > | |
| vgl_point_3d< T > | vgl_intersection (const std::vector< vgl_plane_3d< T > > &p) |
| Return the intersection point of vector of planes. More... | |
| template<class T > | |
| vgl_point_3d< T > | vgl_closest_point (vgl_plane_3d< T > const &pl, vgl_point_3d< T > const &p) |
| Return the point on the given plane closest to the given point. More... | |
| template<class T > | |
| double | vgl_distance_origin (vgl_plane_3d< T > const &pl) |
| find the shortest distance of the plane to the origin. More... | |
| template<class T > | |
| double | vgl_distance (vgl_plane_3d< T > const &l, vgl_point_3d< T > const &p) |
| return the perpendicular distance from a point to a plane in 3D. More... | |
| template<class T > | |
| vgl_point_3d< T > | vgl_intersection (vgl_line_3d_2_points< T > const &line, vgl_plane_3d< T > const &plane) |
| Return the intersection point of a line and a plane. More... | |
| template<class T > | |
| bool | vgl_intersection (vgl_line_segment_3d< T > const &line, vgl_plane_3d< T > const &plane, vgl_point_3d< T > &i_pt) |
| Return the intersection point of a line and a plane. More... | |
| template<class T > | |
| bool | vgl_intersection (vgl_infinite_line_3d< T > const &line, vgl_plane_3d< T > const &plane, vgl_point_3d< T > &i_pt) |
| Return the intersection point of a line and a plane. More... | |
| template<class T > | |
| bool | vgl_intersection (vgl_ray_3d< T > const &ray, vgl_plane_3d< T > const &plane, vgl_point_3d< T > &i_pt) |
| Return the intersection point of a ray and a plane. More... | |
| template<class T > | |
| bool | vgl_intersection (vgl_plane_3d< T > const &plane0, vgl_plane_3d< T > const &plane1, vgl_line_segment_3d< T > &line) |
| Return the intersection line of two planes. More... | |
| template<class T > | |
| vgl_point_3d< T > | vgl_intersection (vgl_plane_3d< T > const &p1, vgl_plane_3d< T > const &p2, vgl_plane_3d< T > const &p3) |
| Return the intersection point of three planes. More... | |
| template<class T > | |
| bool | vgl_intersection (vgl_plane_3d< T > const &plane0, vgl_plane_3d< T > const &plane1, vgl_infinite_line_3d< T > &line) |
| Return the intersection line of two planes. Returns false if planes. More... | |
| template<class T > | |
| std::ostream & | operator<< (std::ostream &s, const vgl_plane_3d< T > &p) |
| Write to stream. More... | |
| template<class T > | |
| std::istream & | operator>> (std::istream &is, vgl_plane_3d< T > &p) |
| Read in four plane parameters from stream. More... | |
Detailed Description
template<class T>
class vgl_plane_3d< T >
Represents a Euclidean 3D plane.
The equation of the plane is 
Constructor & Destructor Documentation
◆ vgl_plane_3d() [1/7]
|
inline |
Definition at line 45 of file vgl_plane_3d.h.
◆ vgl_plane_3d() [2/7]
|
inline |
Construct a vgl_plane_3d from its equation $ax+by+cz+d=0$.
At least one of a, b or c should be nonzero.
Definition at line 60 of file vgl_plane_3d.h.
◆ vgl_plane_3d() [3/7]
|
inline |
Construct a vgl_plane_3d from its equation $v[0]x+v[1]y+v[2]z+v[3]=0$.
At least one of v[0], v[1] or v[2] should be nonzero.
Definition at line 65 of file vgl_plane_3d.h.
◆ vgl_plane_3d() [4/7]
| vgl_plane_3d< T >::vgl_plane_3d | ( | vgl_homg_plane_3d< T > const & | p | ) |
Construct from a homogeneous plane.
Construct from homogeneous plane.
Definition at line 25 of file vgl_plane_3d.hxx.
◆ vgl_plane_3d() [5/7]
| vgl_plane_3d< T >::vgl_plane_3d | ( | vgl_vector_3d< T > const & | normal, |
| vgl_point_3d< T > const & | p | ||
| ) |
Construct from Normal and a point.
Construct from normal and a point.
The plane goes through the point p and will be orthogonal to normal.
Definition at line 51 of file vgl_plane_3d.hxx.
◆ vgl_plane_3d() [6/7]
| vgl_plane_3d< T >::vgl_plane_3d | ( | vgl_point_3d< T > const & | p1, |
| vgl_point_3d< T > const & | p2, | ||
| vgl_point_3d< T > const & | p3 | ||
| ) |
Construct from three non-collinear points.
Construct from three points.
The plane will contain all three points p1, p2 and p3.
Definition at line 30 of file vgl_plane_3d.hxx.
◆ vgl_plane_3d() [7/7]
| vgl_plane_3d< T >::vgl_plane_3d | ( | vgl_ray_3d< T > const & | r0, |
| vgl_ray_3d< T > const & | r1 | ||
| ) |
Construct from two non-skew rays. The rays intersect at their origins.
or are parallel. The plane will contain the two rays
Definition at line 59 of file vgl_plane_3d.hxx.
Member Function Documentation
◆ a()
|
inline |
Return x coefficient.
Definition at line 89 of file vgl_plane_3d.h.
◆ b()
|
inline |
Return y coefficient.
Definition at line 92 of file vgl_plane_3d.h.
◆ c()
|
inline |
Return z coefficient.
Definition at line 95 of file vgl_plane_3d.h.
◆ contains()
| bool vgl_plane_3d< T >::contains | ( | vgl_point_3d< T > const & | p, |
| T | tol = (T)0 |
||
| ) | const |
Return true if p is on the plane.
Definition at line 111 of file vgl_plane_3d.hxx.
◆ d()
|
inline |
Return constant coefficient.
Definition at line 98 of file vgl_plane_3d.h.
◆ ideal()
|
inline |
Return true iff the plane is the plane at infinity.
Always returns false
Definition at line 110 of file vgl_plane_3d.h.
◆ normal()
|
inline |
Return the normal direction, i.e., a unit vector orthogonal to this plane.
Definition at line 116 of file vgl_plane_3d.h.
◆ normalize()
| bool vgl_plane_3d< T >::normalize | ( | ) |
Definition at line 93 of file vgl_plane_3d.hxx.
◆ nx()
|
inline |
Definition at line 90 of file vgl_plane_3d.h.
◆ ny()
|
inline |
Definition at line 93 of file vgl_plane_3d.h.
◆ nz()
|
inline |
Definition at line 96 of file vgl_plane_3d.h.
◆ operator!=()
|
inline |
Definition at line 106 of file vgl_plane_3d.h.
◆ operator==()
| bool vgl_plane_3d< T >::operator== | ( | vgl_plane_3d< T > const & | p | ) | const |
the comparison operator.
The equations need not be identical, but just equivalent.
Definition at line 120 of file vgl_plane_3d.hxx.
◆ plane_coord_vectors()
| void vgl_plane_3d< T >::plane_coord_vectors | ( | vgl_vector_3d< T > & | uvec, |
| vgl_vector_3d< T > & | vvec | ||
| ) | const |
plane coordinate unit vectors.
Definition at line 203 of file vgl_plane_3d.hxx.
◆ plane_coords()
| bool vgl_plane_3d< T >::plane_coords | ( | vgl_point_3d< T > const & | p3d, |
| vgl_point_2d< T > & | p2d, | ||
| T | tol = (T)0 |
||
| ) | const |
Given a 3-d point, return a 2-d point in the coord. system of the plane.
If the point is not on the plane then false is returned
Definition at line 226 of file vgl_plane_3d.hxx.
◆ set()
|
inline |
Set this vgl_plane_3d to have the equation $ax+by+cz+d=0$.
Definition at line 101 of file vgl_plane_3d.h.
◆ world_coords()
| vgl_point_3d< T > vgl_plane_3d< T >::world_coords | ( | vgl_point_2d< T > const & | p2d | ) | const |
inverse map from plane coordinates to world coordinates.
Definition at line 247 of file vgl_plane_3d.hxx.
Friends And Related Function Documentation
◆ operator<<()
|
related |
Write to stream.
◆ operator>>()
|
related |
Read in four plane parameters from stream.
Either just reads four blank-separated numbers, or reads four comma-separated numbers, or reads four numbers in parenthesized form "(123, 321, -456, 777)" or reads a formatted line equation "123x+321y-456z+777=0"
◆ vgl_closest_point()
|
related |
Return the point on the given plane closest to the given point.
◆ vgl_distance()
|
related |
return the perpendicular distance from a point to a plane in 3D.
◆ vgl_distance_origin()
|
related |
find the shortest distance of the plane to the origin.
◆ vgl_intersection() [1/8]
|
related |
Return the intersection point of vector of planes.
◆ vgl_intersection() [2/8]
|
related |
Return the intersection point of a line and a plane.
Definition at line 598 of file vgl_intersection.hxx.
◆ vgl_intersection() [3/8]
|
related |
Return the intersection point of a line and a plane.
Definition at line 638 of file vgl_intersection.hxx.
◆ vgl_intersection() [4/8]
|
related |
Return the intersection point of a line and a plane.
◆ vgl_intersection() [5/8]
|
related |
Return the intersection point of a ray and a plane.
◆ vgl_intersection() [6/8]
|
related |
Return the intersection line of two planes.
Returns false if planes are effectively parallel
Definition at line 161 of file vgl_intersection.h.
◆ vgl_intersection() [7/8]
|
related |
Return the intersection point of three planes.
Definition at line 858 of file vgl_intersection.hxx.
◆ vgl_intersection() [8/8]
|
related |
Return the intersection line of two planes. Returns false if planes.
are effectively parallel
Definition at line 780 of file vgl_intersection.hxx.
Member Data Documentation
◆ a_
|
private |
Definition at line 35 of file vgl_plane_3d.h.
◆ b_
|
private |
Definition at line 36 of file vgl_plane_3d.h.
◆ c_
|
private |
Definition at line 37 of file vgl_plane_3d.h.
◆ d_
|
private |
Definition at line 38 of file vgl_plane_3d.h.
The documentation for this class was generated from the following files:
- core/vgl/vgl_fwd.h
- core/vgl/vgl_plane_3d.h
- core/vgl/algo/vgl_intersection.h
- core/vgl/vgl_closest_point.h
- core/vgl/vgl_distance.h
- core/vgl/vgl_intersection.hxx
- core/vgl/vgl_plane_3d.hxx
