#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 ()
	Default constructor without initialization.

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

EIGEN_DEVICE_FUNC	Hyperplane (Index _dim)
	Constructs a dynamic-size hyperplane with _dim the dimension of the ambient space.

EIGEN_DEVICE_FUNC	Hyperplane (const VectorType &n, const VectorType &e)
	Construct a plane from its normal n and a point e onto the plane. More...

EIGEN_DEVICE_FUNC	Hyperplane (const VectorType &n, const Scalar &d)
	Constructs a plane from its normal n and distance to the origin d such that the algebraic equation of the plane is \( n \cdot x + d = 0 \). More...

EIGEN_DEVICE_FUNC	Hyperplane (const ParametrizedLine< Scalar, AmbientDimAtCompileTime > &parametrized)
	Constructs a hyperplane passing through the parametrized line parametrized. More...

EIGEN_DEVICE_FUNC Index	dim () const

EIGEN_DEVICE_FUNC void	normalize (void)
	normalizes `*this`

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)
	Applies the transformation matrix mat to `this` and returns a reference to `this`. More...

template<int TrOptions>
EIGEN_DEVICE_FUNC Hyperplane &	transform (const Transform< Scalar, AmbientDimAtCompileTime, Affine, TrOptions > &t, TransformTraits traits=Affine)
	Applies the transformation t to `this` and returns a reference to `this`. More...

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)
	Copy constructor with scalar type conversion.

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)
	Constructs a hyperplane passing through the two points. More...

static EIGEN_DEVICE_FUNC Hyperplane	Through (const VectorType &p0, const VectorType &p1, const VectorType &p2)
	Constructs a hyperplane passing through the three points. More...

Protected Attributes
Coefficients	m_coeffs

Detailed Description

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

A hyperplane

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() [1/3]

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() [2/3]

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() [3/3]

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.

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

inline

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

§ coeffs() [2/2]

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: \( c_0*x_0 + ... + c_{d-1}*x_{d-1} + c_d = 0 \)

§ 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 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.

§ normal() [2/2]

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.

§ offset() [1/2]

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.

§ offset() [2/2]

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

§ 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:

third-party-libs/eigen3/Eigen/src/Core/util/ForwardDeclarations.h
third-party-libs/eigen3/Eigen/src/Geometry/Hyperplane.h

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() [1/3]

§ Hyperplane() [2/3]

§ Hyperplane() [3/3]

Member Function Documentation

§ absDistance()

§ cast()

§ coeffs() [1/2]

§ coeffs() [2/2]

§ dim()

§ intersection()

§ isApprox()

§ normal() [1/2]

§ normal() [2/2]

§ 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 >