A hyperplane. More...

#include <Hyperplane.h>

Public Types
enum	{ AmbientDimAtCompileTime = _AmbientDim, Options = _Options }

typedef _Scalar	Scalar

typedef NumTraits< Scalar >::Real	RealScalar

typedef Eigen::Index	Index

typedef Matrix< Scalar, AmbientDimAtCompileTime, 1 >	VectorType

typedef Matrix< Scalar, Index(AmbientDimAtCompileTime)==Dynamic ? Dynamic :Index(AmbientDimAtCompileTime)+1, 1, Options >	Coefficients

typedef Block< Coefficients, AmbientDimAtCompileTime, 1 >	NormalReturnType

typedef const Block< const Coefficients, AmbientDimAtCompileTime, 1 >	ConstNormalReturnType

Public Member Functions
EIGEN_DEVICE_FUNC	Hyperplane ()

template<int OtherOptions>
EIGEN_DEVICE_FUNC	Hyperplane (const Hyperplane< Scalar, AmbientDimAtCompileTime, OtherOptions > &other)

EIGEN_DEVICE_FUNC	Hyperplane (Index _dim)

EIGEN_DEVICE_FUNC	Hyperplane (const VectorType &n, const VectorType &e)

EIGEN_DEVICE_FUNC	Hyperplane (const VectorType &n, const Scalar &d)

EIGEN_DEVICE_FUNC	Hyperplane (const ParametrizedLine< Scalar, AmbientDimAtCompileTime > &parametrized)

EIGEN_DEVICE_FUNC Index	dim () const

EIGEN_DEVICE_FUNC void	normalize (void)

EIGEN_DEVICE_FUNC Scalar	signedDistance (const VectorType &p) const

EIGEN_DEVICE_FUNC Scalar	absDistance (const VectorType &p) const

EIGEN_DEVICE_FUNC VectorType	projection (const VectorType &p) const

EIGEN_DEVICE_FUNC ConstNormalReturnType	normal () const

EIGEN_DEVICE_FUNC NormalReturnType	normal ()

EIGEN_DEVICE_FUNC const Scalar &	offset () const

EIGEN_DEVICE_FUNC Scalar &	offset ()

EIGEN_DEVICE_FUNC const Coefficients &	coeffs () const

EIGEN_DEVICE_FUNC Coefficients &	coeffs ()

EIGEN_DEVICE_FUNC VectorType	intersection (const Hyperplane &other) const

template<typename XprType >
EIGEN_DEVICE_FUNC Hyperplane &	transform (const MatrixBase< XprType > &mat, TransformTraits traits=Affine)

template<int TrOptions>
EIGEN_DEVICE_FUNC Hyperplane &	transform (const Transform< Scalar, AmbientDimAtCompileTime, Affine, TrOptions > &t, TransformTraits traits=Affine)

template<typename NewScalarType >
EIGEN_DEVICE_FUNC internal::cast_return_type< Hyperplane, Hyperplane< NewScalarType, AmbientDimAtCompileTime, Options > >::type	cast () const

template<typename OtherScalarType , int OtherOptions>
EIGEN_DEVICE_FUNC	Hyperplane (const Hyperplane< OtherScalarType, AmbientDimAtCompileTime, OtherOptions > &other)

template<int OtherOptions>
EIGEN_DEVICE_FUNC bool	isApprox (const Hyperplane< Scalar, AmbientDimAtCompileTime, OtherOptions > &other, const typename NumTraits< Scalar >::Real &prec=NumTraits< Scalar >::dummy_precision()) const

Static Public Member Functions
static EIGEN_DEVICE_FUNC Hyperplane	Through (const VectorType &p0, const VectorType &p1)

static EIGEN_DEVICE_FUNC Hyperplane	Through (const VectorType &p0, const VectorType &p1, const VectorType &p2)

Protected Attributes
Coefficients	m_coeffs

Detailed Description

template<typename _Scalar, int _AmbientDim, int _Options>
class Eigen::Hyperplane< _Scalar, _AmbientDim, _Options >

A hyperplane.

\geometry_module

A hyperplane is an affine subspace of dimension n-1 in a space of dimension n. For example, a hyperplane in a plane is a line; a hyperplane in 3-space is a plane.

Template Parameters

_Scalar	the scalar type, i.e., the type of the coefficients
_AmbientDim	the dimension of the ambient space, can be a compile time value or Dynamic. Notice that the dimension of the hyperplane is _AmbientDim-1.

This class represents an hyperplane as the zero set of the implicit equation $n \cdot x + d = 0$ where $ n $ is a unit normal vector of the plane (linear part) and $ d $ is the distance (offset) to the origin.

Member Typedef Documentation

◆ Index

template<typename _Scalar , int _AmbientDim, int _Options>

typedef Eigen::Index Eigen::Hyperplane< _Scalar, _AmbientDim, _Options >::Index

Deprecated:: since Eigen 3.3

Constructor & Destructor Documentation

◆ Hyperplane() [1/6]

template<typename _Scalar , int _AmbientDim, int _Options>

EIGEN_DEVICE_FUNC Eigen::Hyperplane< _Scalar, _AmbientDim, _Options >::Hyperplane ( )

inline

Default constructor without initialization

◆ Hyperplane() [2/6]

template<typename _Scalar , int _AmbientDim, int _Options>

EIGEN_DEVICE_FUNC Eigen::Hyperplane< _Scalar, _AmbientDim, _Options >::Hyperplane ( Index _dim )

inlineexplicit

Constructs a dynamic-size hyperplane with _dim the dimension of the ambient space

◆ Hyperplane() [3/6]

template<typename _Scalar , int _AmbientDim, int _Options>

EIGEN_DEVICE_FUNC Eigen::Hyperplane< _Scalar, _AmbientDim, _Options >::Hyperplane	(	const VectorType &	n,
		const VectorType &	e
	)

inline

Construct a plane from its normal n and a point e onto the plane.

Warning: the vector normal is assumed to be normalized.

◆ Hyperplane() [4/6]

template<typename _Scalar , int _AmbientDim, int _Options>

EIGEN_DEVICE_FUNC Eigen::Hyperplane< _Scalar, _AmbientDim, _Options >::Hyperplane	(	const VectorType &	n,
		const Scalar &	d
	)

inline

Constructs a plane from its normal n and distance to the origin d such that the algebraic equation of the plane is $n \cdot x + d = 0$ .

Warning: the vector normal is assumed to be normalized.

◆ Hyperplane() [5/6]

template<typename _Scalar , int _AmbientDim, int _Options>

EIGEN_DEVICE_FUNC Eigen::Hyperplane< _Scalar, _AmbientDim, _Options >::Hyperplane ( const ParametrizedLine< Scalar, AmbientDimAtCompileTime > & parametrized )

inlineexplicit

Constructs a hyperplane passing through the parametrized line parametrized. If the dimension of the ambient space is greater than 2, then there isn't uniqueness, so an arbitrary choice is made.

◆ Hyperplane() [6/6]

template<typename _Scalar , int _AmbientDim, int _Options>

template<typename OtherScalarType , int OtherOptions>

EIGEN_DEVICE_FUNC Eigen::Hyperplane< _Scalar, _AmbientDim, _Options >::Hyperplane ( const Hyperplane< OtherScalarType, AmbientDimAtCompileTime, OtherOptions > & other )

inlineexplicit

Copy constructor with scalar type conversion

Member Function Documentation

◆ absDistance()

template<typename _Scalar , int _AmbientDim, int _Options>

EIGEN_DEVICE_FUNC Scalar Eigen::Hyperplane< _Scalar, _AmbientDim, _Options >::absDistance ( const VectorType & p ) const

inline

Returns: the absolute distance between the plane *this and a point p.

See also: signedDistance()

◆ cast()

template<typename _Scalar , int _AmbientDim, int _Options>

template<typename NewScalarType >

EIGEN_DEVICE_FUNC internal::cast_return_type<Hyperplane, Hyperplane<NewScalarType,AmbientDimAtCompileTime,Options> >::type Eigen::Hyperplane< _Scalar, _AmbientDim, _Options >::cast ( ) const

inline

Returns: *this with scalar type casted to NewScalarType

Note that if NewScalarType is equal to the current scalar type of *this then this function smartly returns a const reference to *this.

◆ coeffs() [1/2]

template<typename _Scalar , int _AmbientDim, int _Options>

EIGEN_DEVICE_FUNC Coefficients& Eigen::Hyperplane< _Scalar, _AmbientDim, _Options >::coeffs ( )

inline

Returns: a non-constant reference to the coefficients c_i of the plane equation: $c_0*x_0 + ... + c_{d-1}*x_{d-1} + c_d = 0$

◆ coeffs() [2/2]

template<typename _Scalar , int _AmbientDim, int _Options>

EIGEN_DEVICE_FUNC const Coefficients& Eigen::Hyperplane< _Scalar, _AmbientDim, _Options >::coeffs ( ) const

inline

Returns: a constant reference to the coefficients c_i of the plane equation: $c_0*x_0 + ... + c_{d-1}*x_{d-1} + c_d = 0$

◆ dim()

template<typename _Scalar , int _AmbientDim, int _Options>

EIGEN_DEVICE_FUNC Index Eigen::Hyperplane< _Scalar, _AmbientDim, _Options >::dim ( ) const

inline

Returns: the dimension in which the plane holds

◆ intersection()

template<typename _Scalar , int _AmbientDim, int _Options>

EIGEN_DEVICE_FUNC VectorType Eigen::Hyperplane< _Scalar, _AmbientDim, _Options >::intersection ( const Hyperplane< _Scalar, _AmbientDim, _Options > & other ) const

inline

Returns: the intersection of *this with other.

Warning: The ambient space must be a plane, i.e. have dimension 2, so that *this and other are lines.

Note: If other is approximately parallel to *this, this method will return any point on *this.

◆ isApprox()

template<typename _Scalar , int _AmbientDim, int _Options>

template<int OtherOptions>

EIGEN_DEVICE_FUNC bool Eigen::Hyperplane< _Scalar, _AmbientDim, _Options >::isApprox	(	const Hyperplane< Scalar, AmbientDimAtCompileTime, OtherOptions > &	other,
		const typename NumTraits< Scalar >::Real &	prec = `NumTraits<Scalar>::dummy_precision()`
	)		const

inline

Returns: true if *this is approximately equal to other, within the precision determined by prec.

See also: MatrixBase::isApprox()

◆ normal() [1/2]

template<typename _Scalar , int _AmbientDim, int _Options>

EIGEN_DEVICE_FUNC NormalReturnType Eigen::Hyperplane< _Scalar, _AmbientDim, _Options >::normal ( )

inline

Returns: a non-constant reference to the unit normal vector of the plane, which corresponds to the linear part of the implicit equation.

◆ normal() [2/2]

template<typename _Scalar , int _AmbientDim, int _Options>

EIGEN_DEVICE_FUNC ConstNormalReturnType Eigen::Hyperplane< _Scalar, _AmbientDim, _Options >::normal ( ) const

inline

Returns: a constant reference to the unit normal vector of the plane, which corresponds to the linear part of the implicit equation.

◆ normalize()

template<typename _Scalar , int _AmbientDim, int _Options>

EIGEN_DEVICE_FUNC void Eigen::Hyperplane< _Scalar, _AmbientDim, _Options >::normalize ( void )

inline

normalizes *this

◆ offset() [1/2]

template<typename _Scalar , int _AmbientDim, int _Options>

EIGEN_DEVICE_FUNC Scalar& Eigen::Hyperplane< _Scalar, _AmbientDim, _Options >::offset ( )

inline

Returns: a non-constant reference to the distance to the origin, which is also the constant part of the implicit equation

◆ offset() [2/2]

template<typename _Scalar , int _AmbientDim, int _Options>

EIGEN_DEVICE_FUNC const Scalar& Eigen::Hyperplane< _Scalar, _AmbientDim, _Options >::offset ( ) const

inline

Returns: the distance to the origin, which is also the "constant term" of the implicit equation

Warning: the vector normal is assumed to be normalized.

◆ projection()

template<typename _Scalar , int _AmbientDim, int _Options>

EIGEN_DEVICE_FUNC VectorType Eigen::Hyperplane< _Scalar, _AmbientDim, _Options >::projection ( const VectorType & p ) const

inline

Returns: the projection of a point p onto the plane *this.

◆ signedDistance()

template<typename _Scalar , int _AmbientDim, int _Options>

EIGEN_DEVICE_FUNC Scalar Eigen::Hyperplane< _Scalar, _AmbientDim, _Options >::signedDistance ( const VectorType & p ) const

inline

Returns: the signed distance between the plane *this and a point p.

See also: absDistance()

◆ Through() [1/2]

template<typename _Scalar , int _AmbientDim, int _Options>

static EIGEN_DEVICE_FUNC Hyperplane Eigen::Hyperplane< _Scalar, _AmbientDim, _Options >::Through	(	const VectorType &	p0,
		const VectorType &	p1
	)

inlinestatic

Constructs a hyperplane passing through the two points. If the dimension of the ambient space is greater than 2, then there isn't uniqueness, so an arbitrary choice is made.

◆ Through() [2/2]

template<typename _Scalar , int _AmbientDim, int _Options>

static EIGEN_DEVICE_FUNC Hyperplane Eigen::Hyperplane< _Scalar, _AmbientDim, _Options >::Through	(	const VectorType &	p0,
		const VectorType &	p1,
		const VectorType &	p2
	)

inlinestatic

Constructs a hyperplane passing through the three points. The dimension of the ambient space is required to be exactly 3.

◆ transform() [1/2]

template<typename _Scalar , int _AmbientDim, int _Options>

template<typename XprType >

EIGEN_DEVICE_FUNC Hyperplane& Eigen::Hyperplane< _Scalar, _AmbientDim, _Options >::transform	(	const MatrixBase< XprType > &	mat,
		TransformTraits	traits = `Affine`
	)

inline

Applies the transformation matrix mat to *this and returns a reference to *this.

Parameters

mat	the Dim x Dim transformation matrix
traits	specifies whether the matrix mat represents an Isometry or a more generic Affine transformation. The default is Affine.

◆ transform() [2/2]

template<typename _Scalar , int _AmbientDim, int _Options>

template<int TrOptions>

EIGEN_DEVICE_FUNC Hyperplane& Eigen::Hyperplane< _Scalar, _AmbientDim, _Options >::transform	(	const Transform< Scalar, AmbientDimAtCompileTime, Affine, TrOptions > &	t,
		TransformTraits	traits = `Affine`
	)

inline

Applies the transformation t to *this and returns a reference to *this.

Parameters

t	the transformation of dimension Dim
traits	specifies whether the transformation t represents an Isometry or a more generic Affine transformation. The default is Affine. Other kind of transformations are not supported.

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

Public Types

Public Member Functions

Static Public Member Functions

Protected Attributes

Detailed Description

template<typename _Scalar, int _AmbientDim, int _Options> class Eigen::Hyperplane< _Scalar, _AmbientDim, _Options >

Member Typedef Documentation

◆ Index

Constructor & Destructor Documentation

◆ Hyperplane() [1/6]

◆ Hyperplane() [2/6]

◆ Hyperplane() [3/6]

◆ Hyperplane() [4/6]

◆ Hyperplane() [5/6]

◆ Hyperplane() [6/6]

Member Function Documentation

◆ absDistance()

◆ cast()

◆ coeffs() [1/2]

◆ coeffs() [2/2]

◆ dim()

◆ intersection()

◆ isApprox()

◆ normal() [1/2]

◆ normal() [2/2]

◆ normalize()

◆ offset() [1/2]

◆ offset() [2/2]

◆ projection()

◆ signedDistance()

◆ Through() [1/2]

◆ Through() [2/2]

◆ transform() [1/2]

◆ transform() [2/2]

template<typename _Scalar, int _AmbientDim, int _Options>
class Eigen::Hyperplane< _Scalar, _AmbientDim, _Options >