Eigen::QuaternionBase< Derived > Class Template Reference

---

Detailed Description

template<class Derived>
class Eigen::QuaternionBase< Derived >

Definition at line 43 of file Geometry.

Inheritance diagram for Eigen::QuaternionBase< Derived >:

List of all members.

Public Types
enum	{ Flags = Eigen::internal::traits<Derived>::Flags }
typedef internal::traits < Derived >::Scalar	Scalar
	the scalar type of the coefficients
typedef NumTraits< Scalar >::Real	RealScalar
typedef internal::traits < Derived >::Coefficients	Coefficients
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
Scalar	x () const
Scalar	y () const
Scalar	z () const
Scalar	w () const
Scalar &	x ()
Scalar &	y ()
Scalar &	z ()
Scalar &	w ()
const VectorBlock< const Coefficients, 3 >	vec () const
VectorBlock< Coefficients, 3 >	vec ()
const internal::traits < Derived >::Coefficients &	coeffs () const
internal::traits< Derived > ::Coefficients &	coeffs ()
EIGEN_STRONG_INLINE QuaternionBase< Derived > &	operator= (const QuaternionBase< Derived > &other)
template<class OtherDerived >
EIGEN_STRONG_INLINE Derived &	operator= (const QuaternionBase< OtherDerived > &other)
Derived &	operator= (const AngleAxisType &aa)
	Set *this from an angle-axis aa and returns a reference to *this.
template<class OtherDerived >
Derived &	operator= (const MatrixBase< OtherDerived > &m)
QuaternionBase &	setIdentity ()
Scalar	squaredNorm () const
Scalar	norm () const
void	normalize ()
	Normalizes the quaternion *this.
Quaternion< Scalar >	normalized () const
template<class OtherDerived >
Scalar	dot (const QuaternionBase< OtherDerived > &other) const
template<class OtherDerived >
Scalar	angularDistance (const QuaternionBase< OtherDerived > &other) const
Matrix3	toRotationMatrix () const
	Convert the quaternion to a 3x3 rotation matrix.
template<typename Derived1 , typename Derived2 >
Derived &	setFromTwoVectors (const MatrixBase< Derived1 > &a, const MatrixBase< Derived2 > &b)
	Sets *this to be a quaternion representing a rotation between the two arbitrary vectors a and b.
template<class OtherDerived >
EIGEN_STRONG_INLINE Quaternion < Scalar >	operator* (const QuaternionBase< OtherDerived > &q) const
template<class OtherDerived >
EIGEN_STRONG_INLINE Derived &	operator*= (const QuaternionBase< OtherDerived > &q)
Quaternion< Scalar >	inverse () const
Quaternion< Scalar >	conjugate () const
template<class OtherDerived >
Quaternion< Scalar >	slerp (Scalar t, const QuaternionBase< OtherDerived > &other) const
template<class OtherDerived >
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
template<typename NewScalarType >
internal::cast_return_type < Derived, Quaternion < NewScalarType > >::type	cast () const
template<class MatrixDerived >
Derived &	operator= (const MatrixBase< MatrixDerived > &xpr)
	Set *this from the expression xpr:
const Derived &	derived () const
Derived &	derived ()
RotationMatrixType	matrix () 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 < Derived, OtherDerived, OtherDerived::IsVectorAtCompileTime > ::ReturnType	operator* (const EigenBase< OtherDerived > &e) const
Transform< Scalar, Dim, Mode >	operator* (const Transform< Scalar, Dim, Mode, Options > &t) const
VectorType	_transformVector (const OtherVectorType &v) const
Static Public Member Functions
static Quaternion< Scalar >	Identity ()
Private Types
typedef RotationBase< Derived, 3 >	Base
Friends
RotationMatrixType	operator* (const EigenBase< OtherDerived > &l, const Derived &r)
Transform< Scalar, Dim, Affine >	operator* (const DiagonalMatrix< Scalar, Dim > &l, const Derived &r)

---

Member Typedef Documentation

template<class Derived>

typedef AngleAxis<Scalar> Eigen::QuaternionBase< Derived >::AngleAxisType

the equivalent angle-axis type

Reimplemented in Eigen::Quaternion< _Scalar, _Options >.

Definition at line 63 of file Geometry.

template<class Derived>

typedef RotationBase<Derived, 3> Eigen::QuaternionBase< Derived >::Base [private]

Reimplemented in Eigen::Quaternion< _Scalar, _Options >, Eigen::Map< const Quaternion< _Scalar >, _Options >, and Eigen::Map< Quaternion< _Scalar >, _Options >.

Definition at line 45 of file Geometry.

template<class Derived>

typedef internal::traits<Derived>::Coefficients Eigen::QuaternionBase< Derived >::Coefficients

Reimplemented in Eigen::Quaternion< _Scalar, _Options >, Eigen::Map< const Quaternion< _Scalar >, _Options >, and Eigen::Map< Quaternion< _Scalar >, _Options >.

Definition at line 52 of file Geometry.

template<class Derived>

typedef Matrix<Scalar,3,3> Eigen::QuaternionBase< Derived >::Matrix3

the equivalent rotation matrix type

Definition at line 61 of file Geometry.

template<class Derived>

typedef NumTraits<Scalar>::Real Eigen::QuaternionBase< Derived >::RealScalar

Definition at line 51 of file Geometry.

typedef Matrix<Scalar,Dim,Dim> Eigen::RotationBase< Derived, _Dim >::RotationMatrixType [inherited]

corresponding linear transformation matrix type

Definition at line 51 of file Geometry.

template<class Derived>

typedef internal::traits<Derived>::Scalar Eigen::QuaternionBase< Derived >::Scalar

the scalar type of the coefficients

Reimplemented from Eigen::RotationBase< Derived, 3 >.

Reimplemented in Eigen::Quaternion< _Scalar, _Options >, Eigen::Map< const Quaternion< _Scalar >, _Options >, and Eigen::Map< Quaternion< _Scalar >, _Options >.

Definition at line 50 of file Geometry.

template<class Derived>

typedef Matrix<Scalar,3,1> Eigen::QuaternionBase< Derived >::Vector3

the type of a 3D vector

Definition at line 59 of file Geometry.

typedef Matrix<Scalar,Dim,1> Eigen::RotationBase< Derived, _Dim >::VectorType [inherited]

Definition at line 52 of file Geometry.

---

Member Enumeration Documentation

anonymous enum [inherited]

Definition at line 46 of file Geometry.

template<class Derived>

anonymous enum

Enumerator:

Flags

Definition at line 53 of file Geometry.

---

Member Function Documentation

template<class Derived >

EIGEN_STRONG_INLINE QuaternionBase< Derived >::Vector3 Eigen::QuaternionBase< Derived >::_transformVector

(

Vector3

v

)

const

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

Definition at line 472 of file Geometry.

VectorType Eigen::RotationBase< Derived, _Dim >::_transformVector

(

const OtherVectorType &

v

)

const [inline, inherited]

Definition at line 107 of file Geometry.

template<class Derived >

template<class OtherDerived >

internal::traits< Derived >::Scalar Eigen::QuaternionBase< Derived >::angularDistance

(

const QuaternionBase< OtherDerived > &

other

)

const [inline]

Returns:

the angle (in radian) between two rotations

See also:

dot()

Definition at line 652 of file Geometry.

template<class Derived>

template<typename NewScalarType >

internal::cast_return_type<Derived,Quaternion<NewScalarType> >::type Eigen::QuaternionBase< Derived >::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 184 of file Geometry.

template<class Derived>

const internal::traits<Derived>::Coefficients& Eigen::QuaternionBase< Derived >::coeffs

(

)

const [inline]

Returns:

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

Reimplemented in Eigen::Quaternion< _Scalar, _Options >, Eigen::Map< const Quaternion< _Scalar >, _Options >, and Eigen::Map< Quaternion< _Scalar >, _Options >.

Definition at line 92 of file Geometry.

template<class Derived>

internal::traits<Derived>::Coefficients& Eigen::QuaternionBase< Derived >::coeffs

(

)

[inline]

Returns:

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

Reimplemented in Eigen::Quaternion< _Scalar, _Options >, and Eigen::Map< Quaternion< _Scalar >, _Options >.

Definition at line 95 of file Geometry.

template<class Derived >

Quaternion< typename internal::traits< Derived >::Scalar > Eigen::QuaternionBase< Derived >::conjugate

(

)

const [inline]

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()

Definition at line 641 of file Geometry.

const Derived& Eigen::RotationBase< Derived, _Dim >::derived

(

)

const [inline, inherited]

Definition at line 55 of file Geometry.

Derived& Eigen::RotationBase< Derived, _Dim >::derived

(

)

[inline, inherited]

Definition at line 56 of file Geometry.

template<class Derived>

template<class OtherDerived >

Scalar Eigen::QuaternionBase< Derived >::dot

(

const QuaternionBase< OtherDerived > &

other

)

const [inline]

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.

template<class Derived>

static Quaternion<Scalar> Eigen::QuaternionBase< Derived >::Identity

(

)

[inline, static]

Returns:

a quaternion representing an identity rotation

See also:

MatrixBase::Identity()

Definition at line 113 of file Geometry.

template<class Derived >

Quaternion< typename internal::traits< Derived >::Scalar > Eigen::QuaternionBase< Derived >::inverse

(

)

const [inline]

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< Derived, 3 >.

Definition at line 620 of file Geometry.

template<class Derived>

template<class OtherDerived >

bool Eigen::QuaternionBase< Derived >::isApprox	(	const QuaternionBase< OtherDerived > &	other,
		RealScalar	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 172 of file Geometry.

RotationMatrixType Eigen::RotationBase< Derived, _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.

template<class Derived>

Scalar Eigen::QuaternionBase< Derived >::norm

(

)

const [inline]

Returns:

the norm of the quaternion's coefficients

See also:

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

Definition at line 127 of file Geometry.

template<class Derived>

void Eigen::QuaternionBase< Derived >::normalize

(

)

[inline]

Normalizes the quaternion *this.

See also:

normalized(), MatrixBase::normalize()

Definition at line 131 of file Geometry.

template<class Derived>

Quaternion<Scalar> Eigen::QuaternionBase< Derived >::normalized

(

)

const [inline]

Returns:

a normalized copy of *this

See also:

normalize(), MatrixBase::normalized()

Definition at line 134 of file Geometry.

EIGEN_STRONG_INLINE internal::rotation_base_generic_product_selector<Derived,OtherDerived,OtherDerived::IsVectorAtCompileTime>::ReturnType Eigen::RotationBase< Derived, _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.

RotationMatrixType Eigen::RotationBase< Derived, _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.

Transform<Scalar,Dim,Mode> Eigen::RotationBase< Derived, _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.

template<class Derived >

template<class OtherDerived >

EIGEN_STRONG_INLINE Quaternion< typename internal::traits< Derived >::Scalar > Eigen::QuaternionBase< Derived >::operator*

(

const QuaternionBase< OtherDerived > &

other

)

const

Returns:

the concatenation of two rotations as a quaternion-quaternion product

Definition at line 445 of file Geometry.

Transform<Scalar,Dim,Isometry> Eigen::RotationBase< Derived, _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.

template<class Derived >

template<class OtherDerived >

EIGEN_STRONG_INLINE Derived & Eigen::QuaternionBase< Derived >::operator*=

(

const QuaternionBase< OtherDerived > &

other

)

See also:

operator*(Quaternion)

Definition at line 457 of file Geometry.

template<class Derived>

template<class OtherDerived >

Derived& Eigen::QuaternionBase< Derived >::operator=

(

const MatrixBase< OtherDerived > &

m

)

template<class Derived>

template<class MatrixDerived >

Derived& Eigen::QuaternionBase< Derived >::operator=

(

const MatrixBase< MatrixDerived > &

xpr

)

[inline]

Set *this from the expression xpr:

• if xpr is a 4x1 vector, then xpr is assumed to be a quaternion
• if xpr is a 3x3 matrix, then xpr is assumed to be rotation matrix and xpr is converted to a quaternion

Definition at line 518 of file Geometry.

template<class Derived >

template<class OtherDerived >

EIGEN_STRONG_INLINE Derived & Eigen::QuaternionBase< Derived >::operator=

(

const QuaternionBase< OtherDerived > &

other

)

Definition at line 493 of file Geometry.

template<class Derived>

EIGEN_STRONG_INLINE QuaternionBase< Derived > & Eigen::QuaternionBase< Derived >::operator=

(

const QuaternionBase< Derived > &

other

)

Definition at line 485 of file Geometry.

template<class Derived>

EIGEN_STRONG_INLINE Derived & Eigen::QuaternionBase< Derived >::operator=

(

const AngleAxisType &

aa

)

Set *this from an angle-axis aa and returns a reference to *this.

Definition at line 502 of file Geometry.

template<class Derived >

template<typename Derived1 , typename Derived2 >

Derived & Eigen::QuaternionBase< Derived >::setFromTwoVectors	(	const MatrixBase< Derived1 > &	a,
		const MatrixBase< Derived2 > &	b
	)		[inline]

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.

Definition at line 577 of file Geometry.

template<class Derived>

QuaternionBase& Eigen::QuaternionBase< Derived >::setIdentity

(

)

[inline]

See also:

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

Definition at line 117 of file Geometry.

template<class Derived >

template<class OtherDerived >

Quaternion< typename internal::traits< Derived >::Scalar > Eigen::QuaternionBase< Derived >::slerp	(	Scalar	t,
		const QuaternionBase< OtherDerived > &	other
	)		const

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

Definition at line 667 of file Geometry.

template<class Derived>

Scalar Eigen::QuaternionBase< Derived >::squaredNorm

(

)

const [inline]

Returns:

the squared norm of the quaternion's coefficients

See also:

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

Definition at line 122 of file Geometry.

template<class Derived >

QuaternionBase< Derived >::Matrix3 Eigen::QuaternionBase< Derived >::toRotationMatrix

(

void

)

const [inline]

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< Derived, 3 >.

Definition at line 531 of file Geometry.

template<class Derived>

const VectorBlock<const Coefficients,3> Eigen::QuaternionBase< Derived >::vec

(

)

const [inline]

Returns:

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

Definition at line 86 of file Geometry.

template<class Derived>

VectorBlock<Coefficients,3> Eigen::QuaternionBase< Derived >::vec

(

)

[inline]

Returns:

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

Definition at line 89 of file Geometry.

template<class Derived>

Scalar& Eigen::QuaternionBase< Derived >::w

(

)

[inline]

Returns:

a reference to the w coefficient

Definition at line 83 of file Geometry.

template<class Derived>

Scalar Eigen::QuaternionBase< Derived >::w

(

)

const [inline]

Returns:

the w coefficient

Definition at line 74 of file Geometry.

template<class Derived>

Scalar Eigen::QuaternionBase< Derived >::x

(

)

const [inline]

Returns:

the x coefficient

Definition at line 68 of file Geometry.

template<class Derived>

Scalar& Eigen::QuaternionBase< Derived >::x

(

)

[inline]

Returns:

a reference to the x coefficient

Definition at line 77 of file Geometry.

template<class Derived>

Scalar& Eigen::QuaternionBase< Derived >::y

(

)

[inline]

Returns:

a reference to the y coefficient

Definition at line 79 of file Geometry.

template<class Derived>

Scalar Eigen::QuaternionBase< Derived >::y

(

)

const [inline]

Returns:

the y coefficient

Definition at line 70 of file Geometry.

template<class Derived>

Scalar& Eigen::QuaternionBase< Derived >::z

(

)

[inline]

Returns:

a reference to the z coefficient

Definition at line 81 of file Geometry.

template<class Derived>

Scalar Eigen::QuaternionBase< Derived >::z

(

)

const [inline]

Returns:

the z coefficient

Definition at line 72 of file Geometry.

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Friends And Related Function Documentation

RotationMatrixType operator*	(	const EigenBase< OtherDerived > &	l,
		const Derived &	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 Derived &	r
	)		[friend, inherited]

Returns:

the concatenation of a scaling l with the rotation r

Definition at line 94 of file Geometry.