\geometry_module More...

#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
	Hyperplane ()
	Default constructor without initialization.

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

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

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

	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 $n \cdot x + d = 0$ .

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

Index	dim () const

void	normalize (void)
	normalizes `*this`

Scalar	signedDistance (const VectorType &p) const

Scalar	absDistance (const VectorType &p) const

VectorType	projection (const VectorType &p) const

ConstNormalReturnType	normal () const

NormalReturnType	normal ()

const Scalar &	offset () const

Scalar &	offset ()

const Coefficients &	coeffs () const

Coefficients &	coeffs ()

VectorType	intersection (const Hyperplane &other) const

template<typename XprType >
Hyperplane &	transform (const MatrixBase< XprType > &mat, TransformTraits traits=Affine)
	Applies the transformation matrix mat to `this` and returns a reference to `this`.

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

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

template<typename OtherScalarType , int OtherOptions>
	Hyperplane (const Hyperplane< OtherScalarType, AmbientDimAtCompileTime, OtherOptions > &other)
	Copy constructor with scalar type conversion.

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

Static Public Member Functions
static Hyperplane	Through (const VectorType &p0, const VectorType &p1)
	Constructs a hyperplane passing through the two points.

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

Protected Attributes
Coefficients	m_coeffs

Detailed Description

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

\geometry_module

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.

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::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::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::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>

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.

◆ 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:

External/Eigen/src/Core/util/ForwardDeclarations.h
External/Eigen/src/Geometry/Hyperplane.h

Public Types

Public Member Functions

Static Public Member Functions

Protected Attributes

Detailed Description

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]