Eigen: Eigen::Hyperplane< Scalar_, AmbientDim_, Options

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#include <Eigen/src/Geometry/Hyperplane.h>

Detailed Description

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.

Public Types
typedef Eigen::Index	Index

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

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

Member Typedef Documentation

◆ Index

template<typename Scalar_, int AmbientDim_, int Options_>

typedef Eigen::Index Eigen::Hyperplane< Scalar_, AmbientDim_, Options_ >::Index

Constructor & Destructor Documentation

◆ 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

Member Function Documentation

◆ absDistance()

template<typename Scalar_, int AmbientDim_, int Options_>

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>

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 & p ) 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 & 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 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 files:

/builds/libeigen/eigen/Eigen/src/Core/util/ForwardDeclarations.h
/builds/libeigen/eigen/Eigen/src/Geometry/Hyperplane.h

Detailed Description

Public Types

Public Member Functions

Static Public Member Functions

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]