vtb::geometry::Plane< T, N > Class Template Reference

Three- and two-dimensional plane. More...

#include <plane.hh>

Public Types
using	scalar_type = T
using	value_type = Vertex< T, N >
using	reference = value_type &
using	const_reference = const value_type &

Public Member Functions
	Plane (const_reference normal, const_reference origin)
	Plane (const_reference normal)
	Plane (const_reference a, const_reference b, const_reference c)
	Construct plane from plane equation. More...
const_reference	normal () const
	A vector that is orthogonal to the plane.
const_reference	origin () const
	A point on the plane.
void	invert ()
	Invert plane orientation (the direction of the normal).
T	operator() (const_reference point) const
	Substitute point p to the plane equation. More...
T	operator() () const
	Substitute nought into the plane equation to get \(d\). More...
value_type	project (const_reference point) const
	Project point on the plane. More...
value_type	project_vector (const_reference vector) const
	Project vector on the plane. More...
int	redundant_dimension () const
	The index of dimension that has nought basis vector. More...
Basis< T, N >	basis () const
	Vector basis for the coordinate system defined by the and the origin. More...
Coordinate_system< T, N >	coordinate_system () const
	Coordinate system defined by the and the origin. More...
void	clear ()
void	gnuplot (std::ostream &out) const
template<>
	Plane (const_reference a, const_reference b, const_reference c)
template<>
int	redundant_dimension () const
template<>
vtb::geometry::Basis< T, 3 >	basis () const
template<>
vtb::geometry::Coordinate_system< T, 3 >	coordinate_system () const

Static Public Attributes
static constexpr const int	dimensions = N

Detailed Description

template<class T, int N>
class vtb::geometry::Plane< T, N >

Three- and two-dimensional plane.

Date

2019-04-09

Author

Ivan Gankevich

• Two-dimensional plane is a line defined by its normal and a point on the line. Normal is computed by rotating the line by 90 degrees clockwise.
• Three-dimensional plane is a plane define by its normal and a point on the plane.
• See line_normal and surface_normal global functions.

Definition at line 28 of file plane.hh.

Constructor & Destructor Documentation

Plane()

template<class T, int N>

vtb::geometry::Plane< T, N >::Plane ( const_reference  a, const_reference  b, const_reference  c  )

explicit

Construct plane from plane equation.

Date

2019-04-05

Author

Ivan Gankevich

The plane is defined by equation \(ax+by+cz+d=0\), where \((a,b,c)\) is plane normal and \(d\) is a normal multiplied by any point lying on the plane.

Member Function Documentation

basis()

template<class T, int N>

Basis<T,N> vtb::geometry::Plane< T, N >::basis

(

)

const

Vector basis for the coordinate system defined by the and the origin.

Date

2019-04-09

Author

Ivan Gankevich

coordinate_system()

template<class T, int N>

Coordinate_system<T,N> vtb::geometry::Plane< T, N >::coordinate_system

(

)

const

Coordinate system defined by the and the origin.

Date

2019-04-09

Author

Ivan Gankevich

This system can be used to project arbitrary points on the plane and then "unproject" them back. After projecting the point on the plane one of its coordinates becomes redundant. The redundant dimension is returned by method. See puncture and restore global functions that reduce and add dimensions to a vertex.

operator()() [1/2]

template<class T, int N>

T vtb::geometry::Plane< T, N >::operator() ( const_reference  point ) const

inline

Substitute point p to the plane equation.

Date

2019-04-05

Author

Ivan Gankevich

• If the result is less than nought, then point p lies behind the plane.
• If the result is greater than nought, then point p lies in front of the plane.
• If the result is nought, then point p lies on the plane.

Definition at line 87 of file plane.hh.

References vtb::geometry::Plane< T, N >::normal(), and vtb::geometry::Plane< T, N >::origin().

operator()() [2/2]

template<class T, int N>

T vtb::geometry::Plane< T, N >::operator() ( ) const

inline

Substitute nought into the plane equation to get \(d\).

Date

2019-04-09

Author

Ivan Gankevich

Returns

\(d\)

Definition at line 97 of file plane.hh.

References vtb::geometry::Plane< T, N >::normal(), and vtb::geometry::Plane< T, N >::origin().

project()

template<class T, int N>

value_type vtb::geometry::Plane< T, N >::project ( const_reference  point ) const

inline

Project point on the plane.

Date

2019-04-09

Author

Ivan Gankevich

Definition at line 105 of file plane.hh.

References vtb::geometry::Plane< T, N >::normal(), and vtb::geometry::Plane< T, N >::origin().

project_vector()

template<class T, int N>

value_type vtb::geometry::Plane< T, N >::project_vector ( const_reference  vector ) const

inline

Project vector on the plane.

Date

2019-11-06

Definition at line 114 of file plane.hh.

References vtb::geometry::Plane< T, N >::normal().

redundant_dimension()

template<class T, int N>

int vtb::geometry::Plane< T, N >::redundant_dimension

(

)

const

The index of dimension that has nought basis vector.

Date

2019-04-09

Author

Ivan Gankevich

Method still returns unit vector instead of nought for this dimension.