A hyperplane. More...

#include <ForwardDeclarations.h>

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

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

typedef Eigen::Index	Index

typedef Block< Coefficients, AmbientDimAtCompileTime, 1 >	NormalReturnType

typedef NumTraits< Scalar >::Real	RealScalar

typedef _Scalar	Scalar

typedef Matrix< Scalar, AmbientDimAtCompileTime, 1 >	VectorType

Public Member Functions
EIGEN_DEVICE_FUNC Scalar	absDistance (const VectorType &p) const

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

EIGEN_DEVICE_FUNC Coefficients &	coeffs ()

const EIGEN_DEVICE_FUNC Coefficients &	coeffs () const

EIGEN_DEVICE_FUNC Index	dim () const

EIGEN_DEVICE_FUNC	Hyperplane ()

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

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

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

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

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

EIGEN_DEVICE_FUNC	Hyperplane (Index _dim)

EIGEN_DEVICE_FUNC VectorType	intersection (const Hyperplane &other) const

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

EIGEN_DEVICE_FUNC NormalReturnType	normal ()

EIGEN_DEVICE_FUNC ConstNormalReturnType	normal () const

EIGEN_DEVICE_FUNC void	normalize (void)

EIGEN_DEVICE_FUNC Scalar &	offset ()

const EIGEN_DEVICE_FUNC Scalar &	offset () const

EIGEN_DEVICE_FUNC VectorType	projection (const VectorType &p) const

EIGEN_DEVICE_FUNC Scalar	signedDistance (const VectorType &p) 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)

EIGEN_DEVICE_FUNC	~Hyperplane ()

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)

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

Protected Attributes
Coefficients	m_coeffs

Detailed Description

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.

Definition at line 296 of file ForwardDeclarations.h.

Member Typedef Documentation

◆ Coefficients

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

Definition at line 48 of file Hyperplane.h.

◆ Index

typedef Eigen::Index Eigen::Hyperplane::Index

Deprecated:: since Eigen 3.3

Definition at line 44 of file Hyperplane.h.

◆ NormalReturnType

typedef Block<Coefficients,AmbientDimAtCompileTime,1> Eigen::Hyperplane::NormalReturnType

Definition at line 49 of file Hyperplane.h.

◆ RealScalar

typedef NumTraits<Scalar>::Real Eigen::Hyperplane::RealScalar

Definition at line 43 of file Hyperplane.h.

◆ Scalar

typedef _Scalar Eigen::Hyperplane::Scalar

Definition at line 42 of file Hyperplane.h.

◆ VectorType

typedef Matrix<Scalar,AmbientDimAtCompileTime,1> Eigen::Hyperplane::VectorType

Definition at line 45 of file Hyperplane.h.

Member Enumeration Documentation

◆ anonymous enum

anonymous enum

Enumerator
AmbientDimAtCompileTime
Options

Definition at line 38 of file Hyperplane.h.

Constructor & Destructor Documentation

◆ Hyperplane() [1/7]

EIGEN_DEVICE_FUNC Eigen::Hyperplane::Hyperplane ( )

inline

Default constructor without initialization

Definition at line 53 of file Hyperplane.h.

◆ Hyperplane() [2/7]

template<int OtherOptions>

EIGEN_DEVICE_FUNC Eigen::Hyperplane::Hyperplane ( const Hyperplane< Scalar, AmbientDimAtCompileTime, OtherOptions > & other )

inline

Definition at line 56 of file Hyperplane.h.

◆ Hyperplane() [3/7]

EIGEN_DEVICE_FUNC Eigen::Hyperplane::Hyperplane ( Index _dim )

inlineexplicit

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

Definition at line 62 of file Hyperplane.h.

◆ Hyperplane() [4/7]

EIGEN_DEVICE_FUNC Eigen::Hyperplane::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.

Definition at line 67 of file Hyperplane.h.

◆ Hyperplane() [5/7]

EIGEN_DEVICE_FUNC Eigen::Hyperplane::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.

Definition at line 78 of file Hyperplane.h.

◆ Hyperplane() [6/7]

EIGEN_DEVICE_FUNC Eigen::Hyperplane::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.

Definition at line 123 of file Hyperplane.h.

◆ ~Hyperplane()

EIGEN_DEVICE_FUNC Eigen::Hyperplane::~Hyperplane ( )

inline

Definition at line 129 of file Hyperplane.h.

◆ Hyperplane() [7/7]

template<typename OtherScalarType , int OtherOptions>

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

inlineexplicit

Copy constructor with scalar type conversion

Definition at line 264 of file Hyperplane.h.

Member Function Documentation

◆ absDistance()

EIGEN_DEVICE_FUNC Scalar Eigen::Hyperplane::absDistance ( const VectorType & p ) const

inline

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

See also: signedDistance()

Definition at line 148 of file Hyperplane.h.

◆ cast()

template<typename NewScalarType >

EIGEN_DEVICE_FUNC internal::cast_return_type<Hyperplane, Hyperplane<NewScalarType,AmbientDimAtCompileTime,Options> >::type Eigen::Hyperplane::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.

Definition at line 256 of file Hyperplane.h.

◆ coeffs() [1/2]

EIGEN_DEVICE_FUNC Coefficients& Eigen::Hyperplane::coeffs ( )

inline

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

Definition at line 181 of file Hyperplane.h.

◆ coeffs() [2/2]

const EIGEN_DEVICE_FUNC Coefficients& Eigen::Hyperplane::coeffs ( ) const

inline

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

Definition at line 176 of file Hyperplane.h.

◆ dim()

EIGEN_DEVICE_FUNC Index Eigen::Hyperplane::dim ( ) const

inline

Returns: the dimension in which the plane holds

Definition at line 132 of file Hyperplane.h.

◆ intersection()

EIGEN_DEVICE_FUNC VectorType Eigen::Hyperplane::intersection ( const Hyperplane & 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.

Definition at line 189 of file Hyperplane.h.

◆ isApprox()

template<int OtherOptions>

EIGEN_DEVICE_FUNC bool Eigen::Hyperplane::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()

Definition at line 272 of file Hyperplane.h.

◆ normal() [1/2]

EIGEN_DEVICE_FUNC NormalReturnType Eigen::Hyperplane::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.

Definition at line 162 of file Hyperplane.h.

◆ normal() [2/2]

EIGEN_DEVICE_FUNC ConstNormalReturnType Eigen::Hyperplane::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.

Definition at line 157 of file Hyperplane.h.

◆ normalize()

EIGEN_DEVICE_FUNC void Eigen::Hyperplane::normalize ( void )

inline

normalizes *this

Definition at line 135 of file Hyperplane.h.

◆ offset() [1/2]

EIGEN_DEVICE_FUNC Scalar& Eigen::Hyperplane::offset ( )

inline

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

Definition at line 171 of file Hyperplane.h.

◆ offset() [2/2]

const EIGEN_DEVICE_FUNC Scalar& Eigen::Hyperplane::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.

Definition at line 167 of file Hyperplane.h.

◆ projection()

EIGEN_DEVICE_FUNC VectorType Eigen::Hyperplane::projection ( const VectorType & p ) const

inline

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

Definition at line 152 of file Hyperplane.h.

◆ signedDistance()

EIGEN_DEVICE_FUNC Scalar Eigen::Hyperplane::signedDistance ( const VectorType & p ) const

inline

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

See also: absDistance()

Definition at line 143 of file Hyperplane.h.

◆ Through() [1/2]

static EIGEN_DEVICE_FUNC Hyperplane Eigen::Hyperplane::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.

Definition at line 88 of file Hyperplane.h.

◆ Through() [2/2]

static EIGEN_DEVICE_FUNC Hyperplane Eigen::Hyperplane::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.

Definition at line 99 of file Hyperplane.h.

◆ transform() [1/2]

template<typename XprType >

EIGEN_DEVICE_FUNC Hyperplane& Eigen::Hyperplane::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.

Definition at line 217 of file Hyperplane.h.

◆ transform() [2/2]

template<int TrOptions>

EIGEN_DEVICE_FUNC Hyperplane& Eigen::Hyperplane::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.

Definition at line 241 of file Hyperplane.h.

Member Data Documentation

◆ ConstNormalReturnType

const typedef Block<const Coefficients,AmbientDimAtCompileTime,1> Eigen::Hyperplane::ConstNormalReturnType

Definition at line 50 of file Hyperplane.h.

◆ m_coeffs

Coefficients Eigen::Hyperplane::m_coeffs

protected

Definition at line 277 of file Hyperplane.h.

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

Public Types

Public Member Functions

Static Public Member Functions

Public Attributes

Protected Attributes

Detailed Description

Member Typedef Documentation

◆ Coefficients

◆ Index

◆ NormalReturnType

◆ RealScalar

◆ Scalar

◆ VectorType

Member Enumeration Documentation

◆ anonymous enum

Constructor & Destructor Documentation

◆ Hyperplane() [1/7]

◆ Hyperplane() [2/7]

◆ Hyperplane() [3/7]

◆ Hyperplane() [4/7]

◆ Hyperplane() [5/7]

◆ Hyperplane() [6/7]

◆ ~Hyperplane()

◆ Hyperplane() [7/7]

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]

Member Data Documentation

◆ ConstNormalReturnType

◆ m_coeffs