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Eigen::Hyperplane

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

A hyperplane.

This is defined in the Geometry module.

#include <Eigen/Geometry>

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.


typedef Eigen::Index	Index


Scalar	absDistance (const VectorType &p) const

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

Coefficients &	coeffs ()

const Coefficients &	coeffs () const

Index	dim () const

	Hyperplane ()

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

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

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

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

	Hyperplane (Index _dim)

VectorType	intersection (const Hyperplane &other) const

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

NormalReturnType	normal ()

ConstNormalReturnType	normal () const

void	normalize (void)

Scalar &	offset ()

const Scalar &	offset () const

VectorType	projection (const VectorType &p) const

Scalar	signedDistance (const VectorType &p) const

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

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


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

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

Index

template<typename _Scalar , int _AmbientDim, int _Options>

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

Deprecated:: since Eigen 3.3

Hyperplane() [1/6]

template<typename _Scalar , int _AmbientDim, int _Options>

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

(

)

inline

Default constructor without initialization

Hyperplane() [2/6]

template<typename _Scalar , int _AmbientDim, int _Options>

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::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::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::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::Hyperplane< _Scalar, _AmbientDim, _Options >::Hyperplane

(

const Hyperplane< OtherScalarType, AmbientDimAtCompileTime, OtherOptions > &

other

)

inlineexplicit

Copy constructor with scalar type conversion

absDistance()

template<typename _Scalar , int _AmbientDim, int _Options>

Scalar Eigen::Hyperplane< _Scalar, _AmbientDim, _Options >::absDistance

(

const VectorType &

)

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 >

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>

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>

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>

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>

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>

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>

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>

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>

void Eigen::Hyperplane< _Scalar, _AmbientDim, _Options >::normalize

(

void

)

inline

normalizes *this

offset() [1/2]

template<typename _Scalar , int _AmbientDim, int _Options>

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>

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>

VectorType Eigen::Hyperplane< _Scalar, _AmbientDim, _Options >::projection

(

const VectorType &

)

const

inline

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

signedDistance()

template<typename _Scalar , int _AmbientDim, int _Options>

Scalar Eigen::Hyperplane< _Scalar, _AmbientDim, _Options >::signedDistance

(

const VectorType &

)

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 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 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 >

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>

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 file:

Hyperplane.h

Eigen::Hyperplane

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

Index

Hyperplane() [1/6]

Hyperplane() [2/6]

Hyperplane() [3/6]

Hyperplane() [4/6]

Hyperplane() [5/6]

Hyperplane() [6/6]

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 >