QuaternionBase< Derived > Class Template Reference

Base class for quaternion expressions. More...

#include <Quaternion.h>

Inheritance diagram for QuaternionBase< Derived >:

List of all members.

Public Types
typedef AngleAxis< Scalar >	AngleAxisType
typedef Matrix< Scalar, 3, 3 >	Matrix3
typedef Matrix< Scalar, Dim, Dim >	RotationMatrixType
typedef internal::traits < Derived >::Scalar	Scalar
typedef Matrix< Scalar, 3, 1 >	Vector3
Public Member Functions
Vector3	_transformVector (Vector3 v) const
template<class OtherDerived >
Scalar	angularDistance (const QuaternionBase< OtherDerived > &other) const
template<typename NewScalarType >
internal::cast_return_type < Derived, Quaternion < NewScalarType > >::type	cast () const
const internal::traits < Derived >::Coefficients &	coeffs () const
internal::traits< Derived > ::Coefficients &	coeffs ()
Quaternion< Scalar >	conjugate () const
template<class OtherDerived >
Scalar	dot (const QuaternionBase< OtherDerived > &other) const
Quaternion< Scalar >	inverse () const
template<class OtherDerived >
bool	isApprox (const QuaternionBase< OtherDerived > &other, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const
RotationMatrixType	matrix () const
Scalar	norm () const
void	normalize ()
Quaternion< Scalar >	normalized () const
Transform< Scalar, Dim, Isometry >	operator* (const Translation< Scalar, Dim > &t) const
RotationMatrixType	operator* (const UniformScaling< Scalar > &s) const
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
template<class OtherDerived >
Quaternion< Scalar >	operator* (const QuaternionBase< OtherDerived > &q) const
template<class OtherDerived >
Derived &	operator*= (const QuaternionBase< OtherDerived > &q)
Derived &	operator= (const AngleAxisType &aa)
template<class MatrixDerived >
Derived &	operator= (const MatrixBase< MatrixDerived > &xpr)
template<typename Derived1 , typename Derived2 >
Derived &	setFromTwoVectors (const MatrixBase< Derived1 > &a, const MatrixBase< Derived2 > &b)
QuaternionBase &	setIdentity ()
template<class OtherDerived >
Quaternion< Scalar >	slerp (Scalar t, const QuaternionBase< OtherDerived > &other) const
Scalar	squaredNorm () const
Matrix3	toRotationMatrix () const
const VectorBlock< const Coefficients, 3 >	vec () const
VectorBlock< Coefficients, 3 >	vec ()
Scalar	w () const
Scalar &	w ()
Scalar	x () const
Scalar &	x ()
Scalar	y () const
Scalar &	y ()
Scalar	z () const
Scalar &	z ()
Static Public Member Functions
static Quaternion< Scalar >	Identity ()
Friends
RotationMatrixType	operator* (const EigenBase< OtherDerived > &l, const Derived &r)
Transform< Scalar, Dim, Affine >	operator* (const DiagonalMatrix< Scalar, Dim > &l, const Derived &r)

---

Detailed Description

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

Base class for quaternion expressions.

This is defined in the Geometry module.

 #include <Eigen/Geometry> 

Template Parameters:

Derived

derived type (CRTP)

See also:

class Quaternion

---

Member Typedef Documentation

typedef AngleAxis<Scalar> AngleAxisType

the equivalent angle-axis type

Reimplemented in Quaternion< _Scalar, _Options >.

typedef Matrix<Scalar,3,3> Matrix3

the equivalent rotation matrix type

typedef Matrix<Scalar,Dim,Dim> RotationMatrixType [inherited]

corresponding linear transformation matrix type

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

the scalar type of the coefficients

Reimplemented from RotationBase< Derived, 3 >.

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

typedef Matrix<Scalar,3,1> Vector3

the type of a 3D vector

---

Member Function Documentation

QuaternionBase< Derived >::Vector3 _transformVector

(

Vector3

v

)

const [inline]

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

internal::traits< Derived >::Scalar angularDistance

(

const QuaternionBase< OtherDerived > &

other

)

const [inline]

Returns:

the angle (in radian) between two rotations

See also:

dot()

References abs().

internal::cast_return_type<Derived,Quaternion<NewScalarType> >::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 internal::traits<Derived>::Coefficients& coeffs

(

)

const [inline]

Returns:

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

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

Referenced by QuaternionBase< Quaternion< _Scalar, _Options > >::dot(), QuaternionBase< Quaternion< _Scalar, _Options > >::isApprox(), QuaternionBase< Quaternion< _Scalar, _Options > >::norm(), QuaternionBase< Quaternion< _Scalar, _Options > >::normalize(), QuaternionBase< Quaternion< _Scalar, _Options > >::normalized(), QuaternionBase< Quaternion< _Scalar, _Options > >::setIdentity(), QuaternionBase< Derived >::slerp(), QuaternionBase< Quaternion< _Scalar, _Options > >::squaredNorm(), and QuaternionBase< Quaternion< _Scalar, _Options > >::vec().

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

(

)

[inline]

Returns:

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

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

Quaternion< typename internal::traits< Derived >::Scalar > 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()

Scalar 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()

static Quaternion<Scalar> Identity

(

)

[inline, static]

Returns:

a quaternion representing an identity rotation

See also:

MatrixBase::Identity()

Quaternion< typename internal::traits< Derived >::Scalar > 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 RotationBase< Derived, 3 >.

bool 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()

RotationMatrixType matrix

(

)

const [inline, inherited]

Returns:

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

Scalar norm

(

)

const [inline]

Returns:

the norm of the quaternion's coefficients

See also:

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

void normalize

(

void

)

[inline]

Normalizes the quaternion *this

See also:

normalized(), MatrixBase::normalize()

Quaternion<Scalar> normalized

(

)

const [inline]

Returns:

a normalized copy of *this

See also:

normalize(), MatrixBase::normalized()

Transform<Scalar,Dim,Isometry> operator*

(

const Translation< Scalar, Dim > &

t

)

const [inline, inherited]

Returns:

the concatenation of the rotation *this with a translation t

RotationMatrixType operator*

(

const UniformScaling< Scalar > &

s

)

const [inline, inherited]

Returns:

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

References RotationBase< Derived, _Dim >::toRotationMatrix().

internal::rotation_base_generic_product_selector<Derived,OtherDerived,OtherDerived::IsVectorAtCompileTime>::ReturnType 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

References EigenBase< Derived >::derived().

Transform<Scalar,Dim,Mode> operator*

(

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

t

)

const [inline, inherited]

Returns:

the concatenation of the rotation *this with a transformation t

References RotationBase< Derived, _Dim >::toRotationMatrix().

Quaternion< typename internal::traits< Derived >::Scalar > operator*

(

const QuaternionBase< OtherDerived > &

other

)

const [inline]

Returns:

the concatenation of two rotations as a quaternion-quaternion product

Derived & operator*=

(

const QuaternionBase< OtherDerived > &

other

)

[inline]

See also:

operator*(Quaternion)

Derived & operator=

(

const AngleAxisType &

aa

)

[inline]

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

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

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

Returns:

the quaternion which transform a into b through a rotation

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

References Eigen::ComputeFullV, JacobiSVD< _MatrixType, QRPreconditioner >::matrixV(), and MatrixBase< Derived >::normalized().

Referenced by Quaternion< _Scalar, _Options >::FromTwoVectors().

QuaternionBase& setIdentity

(

)

[inline]

See also:

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

Quaternion< typename internal::traits< Derived >::Scalar > 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

References abs(), and QuaternionBase< Derived >::coeffs().

Scalar squaredNorm

(

)

const [inline]

Returns:

the squared norm of the quaternion's coefficients

See also:

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

QuaternionBase< Derived >::Matrix3 toRotationMatrix

(

void

)

const [inline]

Returns:

an equivalent 3x3 rotation matrix

Convert the quaternion to a 3x3 rotation matrix. The quaternion is required to be normalized, otherwise the result is undefined.

Reimplemented from RotationBase< Derived, 3 >.

const VectorBlock<const Coefficients,3> vec

(

)

const [inline]

Returns:

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

Referenced by AngleAxis< _Scalar >::operator=().

VectorBlock<Coefficients,3> vec

(

)

[inline]

Returns:

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

Scalar w

(

)

const [inline]

Returns:

the w coefficient

Referenced by AngleAxis< _Scalar >::operator=().

Scalar& w

(

)

[inline]

Returns:

a reference to the w coefficient

Scalar x

(

)

const [inline]

Returns:

the x coefficient

Scalar& x

(

)

[inline]

Returns:

a reference to the x coefficient

Scalar y

(

)

const [inline]

Returns:

the y coefficient

Scalar& y

(

)

[inline]

Returns:

a reference to the y coefficient

Scalar z

(

)

const [inline]

Returns:

the z coefficient

Scalar& z

(

)

[inline]

Returns:

a reference to the z coefficient

---

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

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

---

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

• Quaternion.h