A hyperplane. More...

#include <Hyperplane.h>

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

Definition at line 46 of file Eigen2Support/Geometry/Hyperplane.h.

Member Typedef Documentation

template<typename _Scalar, int _AmbientDim>

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

Definition at line 56 of file Eigen2Support/Geometry/Hyperplane.h.

template<typename _Scalar, int _AmbientDim>

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

Definition at line 61 of file Geometry/Hyperplane.h.

template<typename _Scalar, int _AmbientDim>

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

Definition at line 63 of file Geometry/Hyperplane.h.

template<typename _Scalar, int _AmbientDim>

typedef DenseIndex Hyperplane< _Scalar, _AmbientDim >::Index

Definition at line 57 of file Geometry/Hyperplane.h.

template<typename _Scalar, int _AmbientDim>

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

Definition at line 57 of file Eigen2Support/Geometry/Hyperplane.h.

template<typename _Scalar, int _AmbientDim>

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

Definition at line 62 of file Geometry/Hyperplane.h.

template<typename _Scalar, int _AmbientDim>

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

Definition at line 52 of file Eigen2Support/Geometry/Hyperplane.h.

template<typename _Scalar, int _AmbientDim>

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

Definition at line 56 of file Geometry/Hyperplane.h.

template<typename _Scalar, int _AmbientDim>

typedef _Scalar Hyperplane< _Scalar, _AmbientDim >::Scalar

Definition at line 51 of file Eigen2Support/Geometry/Hyperplane.h.

template<typename _Scalar, int _AmbientDim>

typedef _Scalar Hyperplane< _Scalar, _AmbientDim >::Scalar

Definition at line 55 of file Geometry/Hyperplane.h.

template<typename _Scalar, int _AmbientDim>

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

Definition at line 53 of file Eigen2Support/Geometry/Hyperplane.h.

template<typename _Scalar, int _AmbientDim>

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

Definition at line 58 of file Geometry/Hyperplane.h.

Member Enumeration Documentation

template<typename _Scalar, int _AmbientDim>

anonymous enum

Enumerator:

AmbientDimAtCompileTime

Definition at line 50 of file Eigen2Support/Geometry/Hyperplane.h.

template<typename _Scalar, int _AmbientDim>

anonymous enum

Enumerator:

AmbientDimAtCompileTime
Options

Definition at line 51 of file Geometry/Hyperplane.h.

Constructor & Destructor Documentation

template<typename _Scalar, int _AmbientDim>

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

Default constructor without initialization

Definition at line 60 of file Eigen2Support/Geometry/Hyperplane.h.

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

Definition at line 64 of file Eigen2Support/Geometry/Hyperplane.h.

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.

Definition at line 69 of file Eigen2Support/Geometry/Hyperplane.h.

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.

Definition at line 80 of file Eigen2Support/Geometry/Hyperplane.h.

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.

Definition at line 115 of file Eigen2Support/Geometry/Hyperplane.h.

template<typename _Scalar, int _AmbientDim>

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

Definition at line 121 of file Eigen2Support/Geometry/Hyperplane.h.

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

Definition at line 252 of file Eigen2Support/Geometry/Hyperplane.h.

template<typename _Scalar, int _AmbientDim>

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

Default constructor without initialization

Definition at line 66 of file Geometry/Hyperplane.h.

template<typename _Scalar, int _AmbientDim>

template<int OtherOptions>

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

Definition at line 69 of file Geometry/Hyperplane.h.

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

Definition at line 75 of file Geometry/Hyperplane.h.

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.

Definition at line 80 of file Geometry/Hyperplane.h.

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.

Definition at line 91 of file Geometry/Hyperplane.h.

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.

Definition at line 126 of file Geometry/Hyperplane.h.

template<typename _Scalar, int _AmbientDim>

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

Definition at line 132 of file Geometry/Hyperplane.h.

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

Definition at line 264 of file Geometry/Hyperplane.h.

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()

Definition at line 140 of file Eigen2Support/Geometry/Hyperplane.h.

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()

Definition at line 151 of file Geometry/Hyperplane.h.

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.

Definition at line 244 of file Eigen2Support/Geometry/Hyperplane.h.

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.

Definition at line 256 of file Geometry/Hyperplane.h.

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

Definition at line 168 of file Eigen2Support/Geometry/Hyperplane.h.

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

Definition at line 173 of file Eigen2Support/Geometry/Hyperplane.h.

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

Definition at line 179 of file Geometry/Hyperplane.h.

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

Definition at line 184 of file Geometry/Hyperplane.h.

template<typename _Scalar, int _AmbientDim>

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

Returns:: the dimension in which the plane holds

Definition at line 124 of file Eigen2Support/Geometry/Hyperplane.h.

template<typename _Scalar, int _AmbientDim>

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

Returns:: the dimension in which the plane holds

Definition at line 135 of file Geometry/Hyperplane.h.

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.

Definition at line 181 of file Eigen2Support/Geometry/Hyperplane.h.

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.

Definition at line 192 of file Geometry/Hyperplane.h.

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()

Definition at line 259 of file Eigen2Support/Geometry/Hyperplane.h.

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()

Definition at line 272 of file Geometry/Hyperplane.h.

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.

Definition at line 149 of file Eigen2Support/Geometry/Hyperplane.h.

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.

Definition at line 154 of file Eigen2Support/Geometry/Hyperplane.h.

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.

Definition at line 160 of file Geometry/Hyperplane.h.

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.

Definition at line 165 of file Geometry/Hyperplane.h.

template<typename _Scalar, int _AmbientDim>

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

normalizes *this

Definition at line 127 of file Eigen2Support/Geometry/Hyperplane.h.

template<typename _Scalar, int _AmbientDim>

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

normalizes *this

Definition at line 138 of file Geometry/Hyperplane.h.

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.

Definition at line 159 of file Eigen2Support/Geometry/Hyperplane.h.

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

Definition at line 163 of file Eigen2Support/Geometry/Hyperplane.h.

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.

Definition at line 170 of file Geometry/Hyperplane.h.

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

Definition at line 174 of file Geometry/Hyperplane.h.

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.

Definition at line 144 of file Eigen2Support/Geometry/Hyperplane.h.

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.

Definition at line 155 of file Geometry/Hyperplane.h.

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()

Definition at line 135 of file Eigen2Support/Geometry/Hyperplane.h.

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()

Definition at line 146 of file Geometry/Hyperplane.h.

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.

Definition at line 90 of file Eigen2Support/Geometry/Hyperplane.h.

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.

Definition at line 101 of file Eigen2Support/Geometry/Hyperplane.h.

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.

Definition at line 101 of file Geometry/Hyperplane.h.

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.

Definition at line 112 of file Geometry/Hyperplane.h.

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.

Definition at line 209 of file Eigen2Support/Geometry/Hyperplane.h.

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.

Definition at line 220 of file Geometry/Hyperplane.h.

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.

Definition at line 229 of file Eigen2Support/Geometry/Hyperplane.h.

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.

Definition at line 241 of file Geometry/Hyperplane.h.

Member Data Documentation

template<typename _Scalar, int _AmbientDim>

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

Definition at line 264 of file Eigen2Support/Geometry/Hyperplane.h.

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

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

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