Eigen::Map< Quaternion< _Scalar >, _Options > Class Template Reference

---

Detailed Description

template<typename _Scalar, int _Options>
class Eigen::Map< Quaternion< _Scalar >, _Options >

Expression of a quaternion from a memory buffer.

Parameters:

_Scalar	the type of the Quaternion coefficients
_Options	see class Map

This is a specialization of class Map for Quaternion. This class allows to view a 4 scalar memory buffer as an Eigen's Quaternion object.

See also:

class Map, class Quaternion, class QuaternionBase

Definition at line 381 of file Geometry.

Inheritance diagram for Eigen::Map< Quaternion< _Scalar >, _Options >:

List of all members.

Public Types
typedef _Scalar	Scalar
	the scalar type of the coefficients
typedef internal::traits< Map > ::Coefficients	Coefficients
enum
typedef NumTraits< Scalar >::Real	RealScalar
typedef Matrix< Scalar, 3, 1 >	Vector3
	the type of a 3D vector
typedef Matrix< Scalar, 3, 3 >	Matrix3
	the equivalent rotation matrix type
typedef AngleAxis< Scalar >	AngleAxisType
	the equivalent angle-axis type
enum
typedef Matrix< Scalar, Dim, Dim >	RotationMatrixType
	corresponding linear transformation matrix type
typedef Matrix< Scalar, Dim, 1 >	VectorType
Public Member Functions
EIGEN_STRONG_INLINE	Map (Scalar *coeffs)
	Constructs a Mapped Quaternion object from the pointer coeffs.
Coefficients &	coeffs ()
const Coefficients &	coeffs () const
Scalar	x () const
Scalar &	x ()
Scalar	y () const
Scalar &	y ()
Scalar	z () const
Scalar &	z ()
Scalar	w () const
Scalar &	w ()
const VectorBlock< const Coefficients, 3 >	vec () const
VectorBlock< Coefficients, 3 >	vec ()
QuaternionBase &	setIdentity ()
Scalar	squaredNorm () const
Scalar	norm () const
void	normalize ()
	Normalizes the quaternion *this.
Quaternion< Scalar >	normalized () const
Scalar	dot (const QuaternionBase< OtherDerived > &other) const
Scalar	angularDistance (const QuaternionBase< OtherDerived > &other) const
Matrix3	toRotationMatrix () const
Map< Quaternion< _Scalar > , _Options > &	setFromTwoVectors (const MatrixBase< Derived1 > &a, const MatrixBase< Derived2 > &b)
EIGEN_STRONG_INLINE Quaternion < Scalar >	operator* (const QuaternionBase< OtherDerived > &q) const
Transform< Scalar, Dim, Isometry >	operator* (const Translation< Scalar, Dim > &t) const
RotationMatrixType	operator* (const UniformScaling< Scalar > &s) const
EIGEN_STRONG_INLINE internal::rotation_base_generic_product_selector < Map< Quaternion< _Scalar > , _Options >, OtherDerived, OtherDerived::IsVectorAtCompileTime > ::ReturnType	operator* (const EigenBase< OtherDerived > &e) const
Transform< Scalar, Dim, Mode >	operator* (const Transform< Scalar, Dim, Mode, Options > &t) const
EIGEN_STRONG_INLINE Map < Quaternion< _Scalar > , _Options > &	operator*= (const QuaternionBase< OtherDerived > &q)
Quaternion< Scalar >	inverse () const
Quaternion< Scalar >	conjugate () const
Quaternion< Scalar >	slerp (Scalar t, const QuaternionBase< OtherDerived > &other) const
bool	isApprox (const QuaternionBase< OtherDerived > &other, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
EIGEN_STRONG_INLINE Vector3	_transformVector (Vector3 v) const
	return the result vector of v through the rotation
VectorType	_transformVector (const OtherVectorType &v) const
internal::cast_return_type < Map< Quaternion< _Scalar > , _Options >, Quaternion < NewScalarType > >::type	cast () const
const Map< Quaternion< _Scalar > , _Options > &	derived () const
Map< Quaternion< _Scalar > , _Options > &	derived ()
RotationMatrixType	matrix () const
Static Public Member Functions
static Quaternion< Scalar >	Identity ()
Protected Attributes
Coefficients	m_coeffs
Private Types
typedef QuaternionBase< Map < Quaternion< _Scalar > , _Options > >	Base
Friends
RotationMatrixType	operator* (const EigenBase< OtherDerived > &l, const Map< Quaternion< _Scalar >, _Options > &r)
Transform< Scalar, Dim, Affine >	operator* (const DiagonalMatrix< Scalar, Dim > &l, const Map< Quaternion< _Scalar >, _Options > &r)

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Member Typedef Documentation

typedef AngleAxis<Scalar> Eigen::QuaternionBase< Map< Quaternion< _Scalar >, _Options > >::AngleAxisType [inherited]

the equivalent angle-axis type

Definition at line 63 of file Geometry.

template<typename _Scalar , int _Options>

typedef QuaternionBase<Map<Quaternion<_Scalar>, _Options> > Eigen::Map< Quaternion< _Scalar >, _Options >::Base [private]

Reimplemented from Eigen::QuaternionBase< Map< Quaternion< _Scalar >, _Options > >.

Definition at line 384 of file Geometry.

template<typename _Scalar , int _Options>

typedef internal::traits<Map>::Coefficients Eigen::Map< Quaternion< _Scalar >, _Options >::Coefficients

Reimplemented from Eigen::QuaternionBase< Map< Quaternion< _Scalar >, _Options > >.

Definition at line 388 of file Geometry.

typedef Matrix<Scalar,3,3> Eigen::QuaternionBase< Map< Quaternion< _Scalar >, _Options > >::Matrix3 [inherited]

the equivalent rotation matrix type

Definition at line 61 of file Geometry.

typedef NumTraits<Scalar>::Real Eigen::QuaternionBase< Map< Quaternion< _Scalar >, _Options > >::RealScalar [inherited]

Definition at line 51 of file Geometry.

typedef Matrix<Scalar,Dim,Dim> Eigen::RotationBase< Map< Quaternion< _Scalar >, _Options > , _Dim >::RotationMatrixType [inherited]

corresponding linear transformation matrix type

Definition at line 51 of file Geometry.

template<typename _Scalar , int _Options>

typedef _Scalar Eigen::Map< Quaternion< _Scalar >, _Options >::Scalar

the scalar type of the coefficients

Reimplemented from Eigen::QuaternionBase< Map< Quaternion< _Scalar >, _Options > >.

Definition at line 387 of file Geometry.

typedef Matrix<Scalar,3,1> Eigen::QuaternionBase< Map< Quaternion< _Scalar >, _Options > >::Vector3 [inherited]

the type of a 3D vector

Definition at line 59 of file Geometry.

typedef Matrix<Scalar,Dim,1> Eigen::RotationBase< Map< Quaternion< _Scalar >, _Options > , _Dim >::VectorType [inherited]

Definition at line 52 of file Geometry.

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Member Enumeration Documentation

anonymous enum [inherited]

Definition at line 46 of file Geometry.

anonymous enum [inherited]

Definition at line 53 of file Geometry.

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Constructor & Destructor Documentation

template<typename _Scalar , int _Options>

EIGEN_STRONG_INLINE Eigen::Map< Quaternion< _Scalar >, _Options >::Map

(

Scalar *

coeffs

)

[inline]

Constructs a Mapped Quaternion object from the pointer coeffs.

The pointer coeffs must reference the four coeffecients of Quaternion in the following order:

 *coeffs == {x, y, z, w} 

If the template parameter _Options is set to Aligned, then the pointer coeffs must be aligned.

Definition at line 398 of file Geometry.

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Member Function Documentation

EIGEN_STRONG_INLINE Vector3 Eigen::QuaternionBase< Map< Quaternion< _Scalar >, _Options > >::_transformVector

(

Vector3

v

)

const [inherited]

return the result vector of v through the rotation

Rotation of a vector by a quaternion.

Remarks:

If the quaternion is used to rotate several points (>1) then it is much more efficient to first convert it to a 3x3 Matrix. Comparison of the operation cost for n transformations:

• Quaternion2: 30n
• Via a Matrix3: 24 + 15n

VectorType Eigen::RotationBase< Map< Quaternion< _Scalar >, _Options > , _Dim >::_transformVector

(

const OtherVectorType &

v

)

const [inline, inherited]

Definition at line 107 of file Geometry.

Scalar Eigen::QuaternionBase< Map< Quaternion< _Scalar >, _Options > >::angularDistance

(

const QuaternionBase< OtherDerived > &

other

)

const [inherited]

Returns:

the angle (in radian) between two rotations

See also:

dot()

internal::cast_return_type<Map< Quaternion< _Scalar >, _Options > ,Quaternion<NewScalarType> >::type Eigen::QuaternionBase< Map< Quaternion< _Scalar >, _Options > >::cast

(

)

const [inline, inherited]

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 184 of file Geometry.

template<typename _Scalar , int _Options>

Coefficients& Eigen::Map< Quaternion< _Scalar >, _Options >::coeffs

(

)

[inline]

Returns:

a vector expression of the coefficients (x,y,z,w)

Reimplemented from Eigen::QuaternionBase< Map< Quaternion< _Scalar >, _Options > >.

Definition at line 400 of file Geometry.

template<typename _Scalar , int _Options>

const Coefficients& Eigen::Map< Quaternion< _Scalar >, _Options >::coeffs

(

)

const [inline]

Returns:

a read-only vector expression of the coefficients (x,y,z,w)

Reimplemented from Eigen::QuaternionBase< Map< Quaternion< _Scalar >, _Options > >.

Definition at line 401 of file Geometry.

Quaternion<Scalar> Eigen::QuaternionBase< Map< Quaternion< _Scalar >, _Options > >::conjugate

(

)

const [inherited]

Returns:

the conjugated quaternion

the conjugate of the *this which is equal to the multiplicative inverse if the quaternion is normalized. The conjugate of a quaternion represents the opposite rotation.

See also:

Quaternion2::inverse()

const Map< Quaternion< _Scalar >, _Options > & Eigen::RotationBase< Map< Quaternion< _Scalar >, _Options > , _Dim >::derived

(

)

const [inline, inherited]

Definition at line 55 of file Geometry.

Map< Quaternion< _Scalar >, _Options > & Eigen::RotationBase< Map< Quaternion< _Scalar >, _Options > , _Dim >::derived

(

)

[inline, inherited]

Definition at line 56 of file Geometry.

Scalar Eigen::QuaternionBase< Map< Quaternion< _Scalar >, _Options > >::dot

(

const QuaternionBase< OtherDerived > &

other

)

const [inline, inherited]

Returns:

the dot product of *this and other Geometrically speaking, the dot product of two unit quaternions corresponds to the cosine of half the angle between the two rotations.

See also:

angularDistance()

Definition at line 141 of file Geometry.

static Quaternion<Scalar> Eigen::QuaternionBase< Map< Quaternion< _Scalar >, _Options > >::Identity

(

)

[inline, static, inherited]

Returns:

a quaternion representing an identity rotation

See also:

MatrixBase::Identity()

Definition at line 113 of file Geometry.

Quaternion<Scalar> Eigen::QuaternionBase< Map< Quaternion< _Scalar >, _Options > >::inverse

(

)

const [inherited]

Returns:

the quaternion describing the inverse rotation

the multiplicative inverse of *this Note that in most cases, i.e., if you simply want the opposite rotation, and/or the quaternion is normalized, then it is enough to use the conjugate.

See also:

QuaternionBase::conjugate()

Reimplemented from Eigen::RotationBase< Map< Quaternion< _Scalar >, _Options >, 3 >.

bool Eigen::QuaternionBase< Map< Quaternion< _Scalar >, _Options > >::isApprox	(	const QuaternionBase< OtherDerived > &	other,
		RealScalar	prec = NumTraits<Scalar>::dummy_precision()
	)		const [inline, inherited]

Returns:

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

See also:

MatrixBase::isApprox()

Definition at line 172 of file Geometry.

RotationMatrixType Eigen::RotationBase< Map< Quaternion< _Scalar >, _Options > , _Dim >::matrix

(

)

const [inline, inherited]

Returns:

an equivalent rotation matrix This function is added to be conform with the Transform class' naming scheme.

Definition at line 64 of file Geometry.

Scalar Eigen::QuaternionBase< Map< Quaternion< _Scalar >, _Options > >::norm

(

)

const [inline, inherited]

Returns:

the norm of the quaternion's coefficients

See also:

QuaternionBase::squaredNorm(), MatrixBase::norm()

Definition at line 127 of file Geometry.

void Eigen::QuaternionBase< Map< Quaternion< _Scalar >, _Options > >::normalize

(

void

)

[inline, inherited]

Normalizes the quaternion *this.

See also:

normalized(), MatrixBase::normalize()

Definition at line 131 of file Geometry.

Quaternion<Scalar> Eigen::QuaternionBase< Map< Quaternion< _Scalar >, _Options > >::normalized

(

)

const [inline, inherited]

Returns:

a normalized copy of *this

See also:

normalize(), MatrixBase::normalized()

Definition at line 134 of file Geometry.

Transform<Scalar,Dim,Mode> Eigen::RotationBase< Map< Quaternion< _Scalar >, _Options > , _Dim >::operator*

(

const Transform< Scalar, Dim, Mode, Options > &

t

)

const [inline, inherited]

Returns:

the concatenation of the rotation *this with a transformation t

Definition at line 103 of file Geometry.

EIGEN_STRONG_INLINE Quaternion<Scalar> Eigen::QuaternionBase< Map< Quaternion< _Scalar >, _Options > >::operator*

(

const QuaternionBase< OtherDerived > &

q

)

const [inherited]

Returns:

the concatenation of two rotations as a quaternion-quaternion product

Transform<Scalar,Dim,Isometry> Eigen::RotationBase< Map< Quaternion< _Scalar >, _Options > , _Dim >::operator*

(

const Translation< Scalar, Dim > &

t

)

const [inline, inherited]

Returns:

the concatenation of the rotation *this with a translation t

Definition at line 70 of file Geometry.

RotationMatrixType Eigen::RotationBase< Map< Quaternion< _Scalar >, _Options > , _Dim >::operator*

(

const UniformScaling< Scalar > &

s

)

const [inline, inherited]

Returns:

the concatenation of the rotation *this with a uniform scaling s

Definition at line 74 of file Geometry.

EIGEN_STRONG_INLINE internal::rotation_base_generic_product_selector<Map< Quaternion< _Scalar >, _Options > ,OtherDerived,OtherDerived::IsVectorAtCompileTime>::ReturnType Eigen::RotationBase< Map< Quaternion< _Scalar >, _Options > , _Dim >::operator*

(

const EigenBase< OtherDerived > &

e

)

const [inline, inherited]

Returns:

the concatenation of the rotation *this with a generic expression e e can be:

• a DimxDim linear transformation matrix
• a DimxDim diagonal matrix (axis aligned scaling)
• a vector of size Dim

Definition at line 85 of file Geometry.

EIGEN_STRONG_INLINE Map< Quaternion< _Scalar >, _Options > & Eigen::QuaternionBase< Map< Quaternion< _Scalar >, _Options > >::operator*=

(

const QuaternionBase< OtherDerived > &

q

)

[inherited]

See also:

operator*(Quaternion)

Map< Quaternion< _Scalar >, _Options > & Eigen::QuaternionBase< Map< Quaternion< _Scalar >, _Options > >::setFromTwoVectors	(	const MatrixBase< Derived1 > &	a,
		const MatrixBase< Derived2 > &	b
	)		[inherited]

Sets *this to be a quaternion representing a rotation between the two arbitrary vectors a and b.

Returns:

the quaternion which transform a into b through a rotation

In other words, the built rotation represent a rotation sending the line of direction a to the line of direction b, both lines passing through the origin.

Returns:

a reference to *this.

Note that the two input vectors do not have to be normalized, and do not need to have the same norm.

QuaternionBase& Eigen::QuaternionBase< Map< Quaternion< _Scalar >, _Options > >::setIdentity

(

)

[inline, inherited]

See also:

QuaternionBase::Identity(), MatrixBase::setIdentity()

Definition at line 117 of file Geometry.

Quaternion<Scalar> Eigen::QuaternionBase< Map< Quaternion< _Scalar >, _Options > >::slerp	(	Scalar	t,
		const QuaternionBase< OtherDerived > &	other
	)		const [inherited]

Returns:

an interpolation for a constant motion between other and *this t in [0;1] see http://en.wikipedia.org/wiki/Slerp

the spherical linear interpolation between the two quaternions *this and other at the parameter t

Scalar Eigen::QuaternionBase< Map< Quaternion< _Scalar >, _Options > >::squaredNorm

(

)

const [inline, inherited]

Returns:

the squared norm of the quaternion's coefficients

See also:

QuaternionBase::norm(), MatrixBase::squaredNorm()

Definition at line 122 of file Geometry.

Matrix3 Eigen::QuaternionBase< Map< Quaternion< _Scalar >, _Options > >::toRotationMatrix

(

)

const [inherited]

Convert the quaternion to a 3x3 rotation matrix.

Returns:

an equivalent 3x3 rotation matrix

The quaternion is required to be normalized, otherwise the result is undefined.

Reimplemented from Eigen::RotationBase< Map< Quaternion< _Scalar >, _Options >, 3 >.

VectorBlock<Coefficients,3> Eigen::QuaternionBase< Map< Quaternion< _Scalar >, _Options > >::vec

(

)

[inline, inherited]

Returns:

a vector expression of the imaginary part (x,y,z)

Definition at line 89 of file Geometry.

const VectorBlock<const Coefficients,3> Eigen::QuaternionBase< Map< Quaternion< _Scalar >, _Options > >::vec

(

)

const [inline, inherited]

Returns:

a read-only vector expression of the imaginary part (x,y,z)

Definition at line 86 of file Geometry.

Scalar& Eigen::QuaternionBase< Map< Quaternion< _Scalar >, _Options > >::w

(

)

[inline, inherited]

Returns:

a reference to the w coefficient

Definition at line 83 of file Geometry.

Scalar Eigen::QuaternionBase< Map< Quaternion< _Scalar >, _Options > >::w

(

)

const [inline, inherited]

Returns:

the w coefficient

Definition at line 74 of file Geometry.

Scalar Eigen::QuaternionBase< Map< Quaternion< _Scalar >, _Options > >::x

(

)

const [inline, inherited]

Returns:

the x coefficient

Definition at line 68 of file Geometry.

Scalar& Eigen::QuaternionBase< Map< Quaternion< _Scalar >, _Options > >::x

(

)

[inline, inherited]

Returns:

a reference to the x coefficient

Definition at line 77 of file Geometry.

Scalar Eigen::QuaternionBase< Map< Quaternion< _Scalar >, _Options > >::y

(

)

const [inline, inherited]

Returns:

the y coefficient

Definition at line 70 of file Geometry.

Scalar& Eigen::QuaternionBase< Map< Quaternion< _Scalar >, _Options > >::y

(

)

[inline, inherited]

Returns:

a reference to the y coefficient

Definition at line 79 of file Geometry.

Scalar Eigen::QuaternionBase< Map< Quaternion< _Scalar >, _Options > >::z

(

)

const [inline, inherited]

Returns:

the z coefficient

Definition at line 72 of file Geometry.

Scalar& Eigen::QuaternionBase< Map< Quaternion< _Scalar >, _Options > >::z

(

)

[inline, inherited]

Returns:

a reference to the z coefficient

Definition at line 81 of file Geometry.

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Friends And Related Function Documentation

RotationMatrixType operator*	(	const EigenBase< OtherDerived > &	l,
		const Map< Quaternion< _Scalar >, _Options > &	r
	)		[friend, inherited]

Returns:

the concatenation of a linear transformation l with the rotation r

Definition at line 90 of file Geometry.

Transform<Scalar,Dim,Affine> operator*	(	const DiagonalMatrix< Scalar, Dim > &	l,
		const Map< Quaternion< _Scalar >, _Options > &	r
	)		[friend, inherited]

Returns:

the concatenation of a scaling l with the rotation r

Definition at line 94 of file Geometry.

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Member Data Documentation

template<typename _Scalar , int _Options>

Coefficients Eigen::Map< Quaternion< _Scalar >, _Options >::m_coeffs [protected]

Definition at line 404 of file Geometry.