A hyperplane. More...

#include <Hyperplane.h>

Public Types
enum	{ AmbientDimAtCompileTime = _AmbientDim }
enum	{ AmbientDimAtCompileTime = _AmbientDim, Options = _Options }
typedef _Scalar	Scalar
typedef NumTraits< Scalar >::Real	RealScalar
typedef Matrix< Scalar, AmbientDimAtCompileTime, 1 >	VectorType
typedef Matrix< Scalar, int(AmbientDimAtCompileTime)==Dynamic?Dynamic:int(AmbientDimAtCompileTime)+1, 1 >	Coefficients
typedef Block< Coefficients, AmbientDimAtCompileTime, 1 >	NormalReturnType
typedef _Scalar	Scalar
typedef NumTraits< Scalar >::Real	RealScalar
typedef DenseIndex	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 ()
	Hyperplane (int _dim)
	Hyperplane (const VectorType &n, const VectorType &e)
	Hyperplane (const VectorType &n, Scalar d)
	Hyperplane (const ParametrizedLine< Scalar, AmbientDimAtCompileTime > &parametrized)
	~Hyperplane ()
int	dim () const
void	normalize (void)
Scalar	signedDistance (const VectorType &p) const
Scalar	absDistance (const VectorType &p) const
VectorType	projection (const VectorType &p) const
const NormalReturnType	normal () const
NormalReturnType	normal ()
const Scalar &	offset () const
Scalar &	offset ()
const Coefficients &	coeffs () const
Coefficients &	coeffs ()
VectorType	intersection (const Hyperplane &other)
template<typename XprType >
Hyperplane &	transform (const MatrixBase< XprType > &mat, TransformTraits traits=Affine)
Hyperplane &	transform (const Transform< Scalar, AmbientDimAtCompileTime > &t, TransformTraits traits=Affine)
template<typename NewScalarType >
internal::cast_return_type < Hyperplane, Hyperplane < NewScalarType, AmbientDimAtCompileTime > >::type	cast () const
template<typename OtherScalarType >
	Hyperplane (const Hyperplane< OtherScalarType, AmbientDimAtCompileTime > &other)
bool	isApprox (const Hyperplane &other, typename NumTraits< Scalar >::Real prec=precision< Scalar >()) const
	Hyperplane ()
template<int OtherOptions>
	Hyperplane (const Hyperplane< Scalar, AmbientDimAtCompileTime, OtherOptions > &other)
	Hyperplane (Index _dim)
	Hyperplane (const VectorType &n, const VectorType &e)
	Hyperplane (const VectorType &n, Scalar d)
	Hyperplane (const ParametrizedLine< Scalar, AmbientDimAtCompileTime > &parametrized)
	~Hyperplane ()
Index	dim () const
void	normalize (void)
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)
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)
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)
template<int OtherOptions>
bool	isApprox (const Hyperplane< Scalar, AmbientDimAtCompileTime, OtherOptions > &other, typename NumTraits< Scalar >::Real prec=NumTraits< Scalar >::dummy_precision()) const
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)
static Hyperplane	Through (const VectorType &p0, const VectorType &p1)
static Hyperplane	Through (const VectorType &p0, const VectorType &p1, const VectorType &p2)
Protected Attributes
Coefficients	m_coeffs

Detailed Description

template<typename _Scalar, int _AmbientDim>
class Hyperplane< _Scalar, _AmbientDim >

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

template<typename _Scalar, int _AmbientDim>

typedef Matrix<Scalar,int(AmbientDimAtCompileTime)==Dynamic ? Dynamic : int(AmbientDimAtCompileTime)+1,1> Hyperplane< _Scalar, _AmbientDim >::Coefficients

template<typename _Scalar, int _AmbientDim>

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

template<typename _Scalar, int _AmbientDim>

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

template<typename _Scalar, int _AmbientDim>

typedef DenseIndex Hyperplane< _Scalar, _AmbientDim >::Index

template<typename _Scalar, int _AmbientDim>

typedef Block<Coefficients,AmbientDimAtCompileTime,1> Hyperplane< _Scalar, _AmbientDim >::NormalReturnType

template<typename _Scalar, int _AmbientDim>

typedef Block<Coefficients,AmbientDimAtCompileTime,1> Hyperplane< _Scalar, _AmbientDim >::NormalReturnType

template<typename _Scalar, int _AmbientDim>

typedef NumTraits<Scalar>::Real Hyperplane< _Scalar, _AmbientDim >::RealScalar

template<typename _Scalar, int _AmbientDim>

typedef NumTraits<Scalar>::Real Hyperplane< _Scalar, _AmbientDim >::RealScalar

template<typename _Scalar, int _AmbientDim>

typedef _Scalar Hyperplane< _Scalar, _AmbientDim >::Scalar

template<typename _Scalar, int _AmbientDim>

typedef _Scalar Hyperplane< _Scalar, _AmbientDim >::Scalar

template<typename _Scalar, int _AmbientDim>

typedef Matrix<Scalar,AmbientDimAtCompileTime,1> Hyperplane< _Scalar, _AmbientDim >::VectorType

template<typename _Scalar, int _AmbientDim>

typedef Matrix<Scalar,AmbientDimAtCompileTime,1> Hyperplane< _Scalar, _AmbientDim >::VectorType

Member Enumeration Documentation

template<typename _Scalar, int _AmbientDim>

anonymous enum

Enumerator:

AmbientDimAtCompileTime

template<typename _Scalar, int _AmbientDim>

anonymous enum

Enumerator:

AmbientDimAtCompileTime
Options

Constructor & Destructor Documentation

template<typename _Scalar, int _AmbientDim>

Hyperplane< _Scalar, _AmbientDim >::Hyperplane ( ) [inline, explicit]

Default constructor without initialization

template<typename _Scalar, int _AmbientDim>

Hyperplane< _Scalar, _AmbientDim >::Hyperplane ( int _dim ) [inline, explicit]

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

template<typename _Scalar, int _AmbientDim>

Hyperplane< _Scalar, _AmbientDim >::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.

template<typename _Scalar, int _AmbientDim>

Hyperplane< _Scalar, _AmbientDim >::Hyperplane	(	const VectorType &	n,
		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.

template<typename _Scalar, int _AmbientDim>

Hyperplane< _Scalar, _AmbientDim >::Hyperplane ( const ParametrizedLine< Scalar, AmbientDimAtCompileTime > & parametrized ) [inline, explicit]

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.

template<typename _Scalar, int _AmbientDim>

Hyperplane< _Scalar, _AmbientDim >::~Hyperplane ( ) [inline]

template<typename _Scalar, int _AmbientDim>

template<typename OtherScalarType >

Hyperplane< _Scalar, _AmbientDim >::Hyperplane ( const Hyperplane< OtherScalarType, AmbientDimAtCompileTime > & other ) [inline, explicit]

Copy constructor with scalar type conversion

template<typename _Scalar, int _AmbientDim>

Hyperplane< _Scalar, _AmbientDim >::Hyperplane ( ) [inline, explicit]

Default constructor without initialization

template<typename _Scalar, int _AmbientDim>

template<int OtherOptions>

Hyperplane< _Scalar, _AmbientDim >::Hyperplane ( const Hyperplane< Scalar, AmbientDimAtCompileTime, OtherOptions > & other ) [inline]

template<typename _Scalar, int _AmbientDim>

Hyperplane< _Scalar, _AmbientDim >::Hyperplane ( Index _dim ) [inline, explicit]

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

template<typename _Scalar, int _AmbientDim>

Hyperplane< _Scalar, _AmbientDim >::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.

template<typename _Scalar, int _AmbientDim>

Hyperplane< _Scalar, _AmbientDim >::Hyperplane	(	const VectorType &	n,
		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.

template<typename _Scalar, int _AmbientDim>

Hyperplane< _Scalar, _AmbientDim >::Hyperplane ( const ParametrizedLine< Scalar, AmbientDimAtCompileTime > & parametrized ) [inline, explicit]

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.

template<typename _Scalar, int _AmbientDim>

Hyperplane< _Scalar, _AmbientDim >::~Hyperplane ( ) [inline]

template<typename _Scalar, int _AmbientDim>

template<typename OtherScalarType , int OtherOptions>

Hyperplane< _Scalar, _AmbientDim >::Hyperplane ( const Hyperplane< OtherScalarType, AmbientDimAtCompileTime, OtherOptions > & other ) [inline, explicit]

Copy constructor with scalar type conversion

Member Function Documentation

template<typename _Scalar, int _AmbientDim>

Scalar Hyperplane< _Scalar, _AmbientDim >::absDistance ( const VectorType & p ) const [inline]

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

See also:: signedDistance()

template<typename _Scalar, int _AmbientDim>

Scalar Hyperplane< _Scalar, _AmbientDim >::absDistance ( const VectorType & p ) const [inline]

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

See also:: signedDistance()

template<typename _Scalar, int _AmbientDim>

template<typename NewScalarType >

internal::cast_return_type<Hyperplane, Hyperplane<NewScalarType,AmbientDimAtCompileTime> >::type Hyperplane< _Scalar, _AmbientDim >::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.

template<typename _Scalar, int _AmbientDim>

template<typename NewScalarType >

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

template<typename _Scalar, int _AmbientDim>

const Coefficients& Hyperplane< _Scalar, _AmbientDim >::coeffs ( ) const [inline]

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

template<typename _Scalar, int _AmbientDim>

Coefficients& Hyperplane< _Scalar, _AmbientDim >::coeffs ( ) [inline]

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

template<typename _Scalar, int _AmbientDim>

const Coefficients& Hyperplane< _Scalar, _AmbientDim >::coeffs ( ) const [inline]

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

template<typename _Scalar, int _AmbientDim>

Coefficients& Hyperplane< _Scalar, _AmbientDim >::coeffs ( ) [inline]

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

template<typename _Scalar, int _AmbientDim>

Index Hyperplane< _Scalar, _AmbientDim >::dim ( ) const [inline]

Returns:: the dimension in which the plane holds

template<typename _Scalar, int _AmbientDim>

int Hyperplane< _Scalar, _AmbientDim >::dim ( ) const [inline]

Returns:: the dimension in which the plane holds

template<typename _Scalar, int _AmbientDim>

VectorType Hyperplane< _Scalar, _AmbientDim >::intersection ( const Hyperplane< _Scalar, _AmbientDim > & other ) [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.

template<typename _Scalar, int _AmbientDim>

VectorType Hyperplane< _Scalar, _AmbientDim >::intersection ( const Hyperplane< _Scalar, _AmbientDim > & other ) [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.

template<typename _Scalar, int _AmbientDim>

bool Hyperplane< _Scalar, _AmbientDim >::isApprox	(	const Hyperplane< _Scalar, _AmbientDim > &	other,
		typename NumTraits< Scalar >::Real	prec = `precision<Scalar>()`
	)			const `[inline]`

Returns:: true if *this is approximately equal to other, within the precision determined by prec.

See also:: MatrixBase::isApprox()

template<typename _Scalar, int _AmbientDim>

template<int OtherOptions>

bool Hyperplane< _Scalar, _AmbientDim >::isApprox	(	const Hyperplane< Scalar, AmbientDimAtCompileTime, OtherOptions > &	other,
		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()

template<typename _Scalar, int _AmbientDim>

NormalReturnType Hyperplane< _Scalar, _AmbientDim >::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.

template<typename _Scalar, int _AmbientDim>

const NormalReturnType Hyperplane< _Scalar, _AmbientDim >::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.

template<typename _Scalar, int _AmbientDim>

ConstNormalReturnType Hyperplane< _Scalar, _AmbientDim >::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.

template<typename _Scalar, int _AmbientDim>

NormalReturnType Hyperplane< _Scalar, _AmbientDim >::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.

template<typename _Scalar, int _AmbientDim>

void Hyperplane< _Scalar, _AmbientDim >::normalize ( void ) [inline]

normalizes *this

template<typename _Scalar, int _AmbientDim>

void Hyperplane< _Scalar, _AmbientDim >::normalize ( void ) [inline]

normalizes *this

template<typename _Scalar, int _AmbientDim>

Scalar& Hyperplane< _Scalar, _AmbientDim >::offset ( ) [inline]

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

template<typename _Scalar, int _AmbientDim>

const Scalar& Hyperplane< _Scalar, _AmbientDim >::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.

template<typename _Scalar, int _AmbientDim>

Scalar& Hyperplane< _Scalar, _AmbientDim >::offset ( ) [inline]

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

template<typename _Scalar, int _AmbientDim>

const Scalar& Hyperplane< _Scalar, _AmbientDim >::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.

template<typename _Scalar, int _AmbientDim>

VectorType Hyperplane< _Scalar, _AmbientDim >::projection ( const VectorType & p ) const [inline]

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

template<typename _Scalar, int _AmbientDim>

VectorType Hyperplane< _Scalar, _AmbientDim >::projection ( const VectorType & p ) const [inline]

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

template<typename _Scalar, int _AmbientDim>

Scalar Hyperplane< _Scalar, _AmbientDim >::signedDistance ( const VectorType & p ) const [inline]

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

See also:: absDistance()

template<typename _Scalar, int _AmbientDim>

Scalar Hyperplane< _Scalar, _AmbientDim >::signedDistance ( const VectorType & p ) const [inline]

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

See also:: absDistance()

template<typename _Scalar, int _AmbientDim>

static Hyperplane Hyperplane< _Scalar, _AmbientDim >::Through	(	const VectorType &	p0,
		const VectorType &	p1
	)			`[inline, static]`

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.

template<typename _Scalar, int _AmbientDim>

static Hyperplane Hyperplane< _Scalar, _AmbientDim >::Through	(	const VectorType &	p0,
		const VectorType &	p1
	)			`[inline, static]`

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.

template<typename _Scalar, int _AmbientDim>

static Hyperplane Hyperplane< _Scalar, _AmbientDim >::Through	(	const VectorType &	p0,
		const VectorType &	p1,
		const VectorType &	p2
	)			`[inline, static]`

Constructs a hyperplane passing through the three points. The dimension of the ambient space is required to be exactly 3.

template<typename _Scalar, int _AmbientDim>

static Hyperplane Hyperplane< _Scalar, _AmbientDim >::Through	(	const VectorType &	p0,
		const VectorType &	p1,
		const VectorType &	p2
	)			`[inline, static]`

Constructs a hyperplane passing through the three points. The dimension of the ambient space is required to be exactly 3.

template<typename _Scalar, int _AmbientDim>

Hyperplane& Hyperplane< _Scalar, _AmbientDim >::transform	(	const Transform< Scalar, AmbientDimAtCompileTime > &	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.

template<typename _Scalar, int _AmbientDim>

template<typename XprType >

Hyperplane& Hyperplane< _Scalar, _AmbientDim >::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.

template<typename _Scalar, int _AmbientDim>

template<int TrOptions>

Hyperplane& Hyperplane< _Scalar, _AmbientDim >::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.

template<typename _Scalar, int _AmbientDim>

template<typename XprType >

Hyperplane& Hyperplane< _Scalar, _AmbientDim >::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.

Member Data Documentation

template<typename _Scalar, int _AmbientDim>

Coefficients Hyperplane< _Scalar, _AmbientDim >::m_coeffs [protected]

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

/home/hauberg/Dokumenter/Capture/humim-tracker-0.1/src/ntk/geometry/Eigen/src/Eigen2Support/Geometry/Hyperplane.h
/home/hauberg/Dokumenter/Capture/humim-tracker-0.1/src/ntk/geometry/Eigen/src/Geometry/Hyperplane.h

Hyperplane< _Scalar, _AmbientDim > Class Template Reference [Geometry_Module]

Public Types

Public Member Functions

Static Public Member Functions

Protected Attributes

Detailed Description

template<typename _Scalar, int _AmbientDim> class Hyperplane< _Scalar, _AmbientDim >

Member Typedef Documentation

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

Hyperplane< _Scalar, _AmbientDim > Class Template Reference
[Geometry_Module]

template<typename _Scalar, int _AmbientDim>
class Hyperplane< _Scalar, _AmbientDim >