A hyperplane. More...

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, 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, 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)

Detailed Description

template<typename _Scalar, int _AmbientDim, int _Options>
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.

Constructor & Destructor Documentation

Hyperplane ( ) [inline, explicit]

Default constructor without initialization

Hyperplane ( Index _dim ) [inline, explicit]

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.

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.

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.

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

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()

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.

const Coefficients& coeffs ( ) const [inline]

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

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

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.

bool 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()

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.

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.

void normalize ( void ) [inline]

normalizes *this

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.

Scalar& offset ( ) [inline]

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

VectorType projection ( const VectorType & p ) const [inline]

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

Scalar signedDistance ( const VectorType & p ) const [inline]

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

See also:: absDistance()

static Hyperplane 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.

static Hyperplane 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.

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.

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.

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

Public Member Functions

Static Public Member Functions

Detailed Description

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

Constructor & Destructor Documentation

Member Function Documentation

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