#include <Hyperplane.h>

Public Member Functions
	Hyperplane ()
	Default constructor without initialization.
	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.

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.

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 34 of file Hyperplane.h.

Constructor & Destructor Documentation

Hyperplane ( )

Default constructor without initialization.

Definition at line 53 of file Hyperplane.h.

Hyperplane ( Index _dim ) [explicit]

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

Definition at line 62 of file Hyperplane.h.

Hyperplane	(	const VectorType &	n,
		const VectorType &	e
	)

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 67 of file Hyperplane.h.

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 $n \cdot x + d = 0$ .

Warning:: the vector normal is assumed to be normalized.

Definition at line 78 of file Hyperplane.h.

Hyperplane ( const ParametrizedLine< Scalar, AmbientDimAtCompileTime > & parametrized ) [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 123 of file Hyperplane.h.

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

Copy constructor with scalar type conversion.

Definition at line 262 of file Hyperplane.h.

Member Function Documentation

Scalar absDistance ( const VectorType & p ) const

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

See also:: signedDistance()

Definition at line 148 of file Hyperplane.h.

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

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 254 of file Hyperplane.h.

const Coefficients& coeffs ( ) const

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 176 of file Hyperplane.h.

Coefficients& coeffs ( )

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 181 of file Hyperplane.h.

Index dim ( ) const

Returns:: the dimension in which the plane holds

Definition at line 132 of file Hyperplane.h.

VectorType intersection ( const Hyperplane< _Scalar, _AmbientDim, _Options > & other ) const

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 189 of file Hyperplane.h.

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

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

See also:: MatrixBase::isApprox()

Definition at line 270 of file Hyperplane.h.

ConstNormalReturnType normal ( ) const

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 157 of file Hyperplane.h.

NormalReturnType normal ( )

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 162 of file Hyperplane.h.

void normalize ( void )

normalizes *this

Definition at line 135 of file Hyperplane.h.

const Scalar& offset ( ) const

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 167 of file Hyperplane.h.

Scalar& offset ( )

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

Definition at line 171 of file Hyperplane.h.

VectorType projection ( const VectorType & p ) const

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

Definition at line 152 of file Hyperplane.h.

Scalar signedDistance ( const VectorType & p ) const

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

See also:: absDistance()

Definition at line 143 of file Hyperplane.h.

static Hyperplane Through	(	const VectorType &	p0,
		const VectorType &	p1,
		const VectorType &	p2
	)		`[static]`

Constructs a hyperplane passing through the three points.

The dimension of the ambient space is required to be exactly 3.

Definition at line 99 of file Hyperplane.h.

static Hyperplane Through	(	const VectorType &	p0,
		const VectorType &	p1
	)		`[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 88 of file Hyperplane.h.

Hyperplane& transform	(	const Transform< Scalar, AmbientDimAtCompileTime, Affine, TrOptions > &	t,
		TransformTraits	traits = `Affine`
	)

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 239 of file Hyperplane.h.

Hyperplane& transform	(	const MatrixBase< XprType > &	mat,
		TransformTraits	traits = `Affine`
	)

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 218 of file Hyperplane.h.

Type:	Library
Created:	13 Oct 2016
Imports:	256
Forks:	0
Commits:	1
Dependents:	31
Dependencies:	0
Followers:	8

Hyperplane< _Scalar, _AmbientDim, _Options > Class Template Reference
[Geometry module]

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

Repository toolbox

Repository details

Important Information for this Arm website

Hyperplane< _Scalar, _AmbientDim, _Options > Class Template Reference [Geometry module]

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

Repository toolbox

Repository details

Important Information for this Arm website

Access Warning

Hyperplane< _Scalar, _AmbientDim, _Options > Class Template Reference
[Geometry module]

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