Detailed Description

template<typename _Scalar, int _AmbientDim, int Options = AutoAlign>
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.

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 Member Functions
Scalar	absDistance (const VectorType &p) const

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

const Coefficients &	coeffs () const

Coefficients &	coeffs ()

Index	dim () const

	Hyperplane ()

	Hyperplane (Index _dim)

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

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

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

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

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

ConstNormalReturnType	normal () const

NormalReturnType	normal ()

void	normalize (void)

const Scalar &	offset () const

Scalar &	offset ()

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)

Constructor & Destructor Documentation

Hyperplane ( )

inline

Default constructor without initialization

Referenced by Hyperplane< _Scalar, _AmbientDim, Options >::cast().

Hyperplane ( Index _dim )

inlineexplicit

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

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.

References Hyperplane< _Scalar, _AmbientDim, Options >::normal(), and Hyperplane< _Scalar, _AmbientDim, Options >::offset().

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.

References Hyperplane< _Scalar, _AmbientDim, Options >::normal(), and Hyperplane< _Scalar, _AmbientDim, Options >::offset().

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.

References Hyperplane< _Scalar, _AmbientDim, Options >::normal(), and Hyperplane< _Scalar, _AmbientDim, Options >::offset().

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

inlineexplicit

Copy constructor with scalar type conversion

Member Function Documentation

Scalar absDistance ( const VectorType & p ) const

inline

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

See Also: signedDistance()

References Hyperplane< _Scalar, _AmbientDim, Options >::signedDistance().

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

References Hyperplane< _Scalar, _AmbientDim, Options >::Hyperplane().

const Coefficients& coeffs ( ) const

inline

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

Referenced by Hyperplane< _Scalar, _AmbientDim, Options >::intersection().

Coefficients& coeffs ( )

inline

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

Index dim ( ) const

inline

Returns: the dimension in which the plane holds

References Eigen::Dynamic.

Referenced by Hyperplane< _Scalar, _AmbientDim, Options >::normal(), and Hyperplane< _Scalar, _AmbientDim, Options >::offset().

VectorType 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.

References Hyperplane< _Scalar, _AmbientDim, Options >::coeffs().

bool 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()

ConstNormalReturnType 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.

References Hyperplane< _Scalar, _AmbientDim, Options >::dim().

NormalReturnType 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.

References Hyperplane< _Scalar, _AmbientDim, Options >::dim().

void normalize ( void )

inline

normalizes *this

References Hyperplane< _Scalar, _AmbientDim, Options >::normal().

const Scalar& 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.

References Hyperplane< _Scalar, _AmbientDim, Options >::dim().

Referenced by Hyperplane< _Scalar, _AmbientDim, Options >::Hyperplane(), ParametrizedLine< _Scalar, _AmbientDim, Options >::intersectionParameter(), ParametrizedLine< _Scalar, _AmbientDim, Options >::ParametrizedLine(), Hyperplane< _Scalar, _AmbientDim, Options >::signedDistance(), and Hyperplane< _Scalar, _AmbientDim, Options >::transform().

Scalar& offset ( )

inline

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

References Hyperplane< _Scalar, _AmbientDim, Options >::dim().

VectorType projection ( const VectorType & p ) const

inline

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

References Hyperplane< _Scalar, _AmbientDim, Options >::normal(), and Hyperplane< _Scalar, _AmbientDim, Options >::signedDistance().

Scalar signedDistance ( const VectorType & p ) const

inline

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

See Also: absDistance()

References Hyperplane< _Scalar, _AmbientDim, Options >::normal(), and Hyperplane< _Scalar, _AmbientDim, Options >::offset().

Referenced by Hyperplane< _Scalar, _AmbientDim, Options >::absDistance(), and Hyperplane< _Scalar, _AmbientDim, Options >::projection().

static 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.

References Hyperplane< _Scalar, _AmbientDim, Options >::normal().

static 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.

References Eigen::ComputeFullV, JacobiSVD< MatrixType, QRPreconditioner >::matrixV(), and DenseBase< Derived >::transpose().

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.

References Eigen::Affine, MatrixBase< Derived >::inverse(), Eigen::Isometry, and Hyperplane< _Scalar, _AmbientDim, Options >::normal().

Referenced by Hyperplane< _Scalar, _AmbientDim, Options >::transform().

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.

References Transform< Scalar, Dim, Mode, _Options >::linear(), Hyperplane< _Scalar, _AmbientDim, Options >::normal(), Hyperplane< _Scalar, _AmbientDim, Options >::offset(), Hyperplane< _Scalar, _AmbientDim, Options >::transform(), and Transform< Scalar, Dim, Mode, _Options >::translation().

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

Detailed Description

template<typename _Scalar, int _AmbientDim, int Options = AutoAlign> class Eigen::Hyperplane< _Scalar, _AmbientDim, Options >

Public Member Functions

Static Public Member Functions

Constructor & Destructor Documentation

Member Function Documentation

template<typename _Scalar, int _AmbientDim, int Options = AutoAlign>
class Eigen::Hyperplane< _Scalar, _AmbientDim, Options >