QuaternionBase< Derived > Class Template Reference

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

Inheritance diagram for QuaternionBase< Derived >:

Public Types
typedef AngleAxis< Scalar >	AngleAxisType
typedef Matrix< Scalar, 3, 3 >	Matrix3
typedef Matrix< Scalar, Dim, Dim >	RotationMatrixType
typedef Matrix< Scalar, Dim, Dim >	RotationMatrixType
typedef Matrix< Scalar, 3, 1 >	Vector3

Public Member Functions
Vector3	_transformVector (const Vector3 &v) const
template<class OtherDerived>
internal::traits< Derived >::Scalar	angularDistance (const QuaternionBase< OtherDerived > &other) const
template<typename NewScalarType>
internal::cast_return_type< Derived, Quaternion< NewScalarType > >::type	cast () const
internal::traits< Derived >::Coefficients &	coeffs ()
const internal::traits< Derived >::Coefficients &	coeffs () const
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, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
RotationMatrixType	matrix () const
RotationMatrixType	matrix () const
Scalar	norm () const
void	normalize ()
Quaternion< Scalar >	normalized () const
internal::rotation_base_generic_product_selector< Derived, OtherDerived, OtherDerived::IsVectorAtCompileTime >::ReturnType	operator* (const EigenBase< OtherDerived > &e) const
template<class OtherDerived>
Quaternion< typename internal::traits< Derived >::Scalar >	operator* (const QuaternionBase< OtherDerived > &other) const
Transform< Scalar, Dim, Mode >	operator* (const Transform< Scalar, Dim, Mode, Options > &t) const
Transform< Scalar, Dim, Isometry >	operator* (const Translation< Scalar, Dim > &t) const
RotationMatrixType	operator* (const UniformScaling< Scalar > &s) 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< typename internal::traits< Derived >::Scalar >	slerp (const Scalar &t, const QuaternionBase< OtherDerived > &other) const
Scalar	squaredNorm () const
Matrix3	toRotationMatrix () const
VectorBlock< Coefficients, 3 >	vec ()
const VectorBlock< const Coefficients, 3 >	vec () const
Scalar &	w ()
Scalar	w () const
Scalar &	x ()
Scalar	x () const
Scalar &	y ()
Scalar	y () const
Scalar &	z ()
Scalar	z () const

Static Public Member Functions
static Quaternion< Scalar >	Identity ()

Member Typedef Documentation

AngleAxisType

template<class Derived>

typedef AngleAxis<Scalar> AngleAxisType

the equivalent angle-axis type

Matrix3

template<class Derived>

typedef Matrix<Scalar,3,3> Matrix3

the equivalent rotation matrix type

RotationMatrixType [1/2]

typedef Matrix<Scalar,Dim,Dim> RotationMatrixType

inherited

corresponding linear transformation matrix type

RotationMatrixType [2/2]

typedef Matrix<Scalar,Dim,Dim> RotationMatrixType

inherited

corresponding linear transformation matrix type

Vector3

template<class Derived>

typedef Matrix<Scalar,3,1> Vector3

the type of a 3D vector

Member Function Documentation

_transformVector()

template<class Derived>

QuaternionBase< Derived >::Vector3 _transformVector ( const 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

References vec(), and w().

angularDistance()

template<class Derived>

template<class OtherDerived>

internal::traits< Derived >::Scalar angularDistance ( const QuaternionBase< OtherDerived > & other ) const

inline

Returns

the angle (in radian) between two rotations

See also

dot()

cast()

template<class Derived>

template<typename NewScalarType>

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.

coeffs() [1/2]

template<class Derived>

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

inline

Returns

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

coeffs() [2/2]

template<class Derived>

const internal::traits< Derived >::Coefficients & coeffs ( ) const

inline

Returns

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

Referenced by QuaternionBase< Quaternion< _Scalar, _Options > >::dot(), inverse(), 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< Quaternion< _Scalar, _Options > >::slerp(), QuaternionBase< Quaternion< _Scalar, _Options > >::squaredNorm(), QuaternionBase< Quaternion< _Scalar, _Options > >::vec(), and QuaternionBase< Quaternion< _Scalar, _Options > >::vec().

conjugate()

template<class Derived>

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()

References w(), x(), y(), and z().

Referenced by QuaternionBase< Quaternion< _Scalar, _Options > >::angularDistance(), and inverse().

dot()

template<class Derived>

template<class OtherDerived>

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()

Identity()

template<class Derived>

static Quaternion< Scalar > Identity ( )

inlinestatic

Returns

a quaternion representing an identity rotation

See also

MatrixBase::Identity()

inverse()

template<class Derived>

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()

References coeffs(), conjugate(), and squaredNorm().

isApprox()

template<class Derived>

template<class OtherDerived>

bool isApprox ( const QuaternionBase< OtherDerived > & other, const 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()

matrix() [1/2]

RotationMatrixType matrix ( ) const

inlineinherited

Returns

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

matrix() [2/2]

RotationMatrixType matrix ( ) const

inlineinherited

Returns

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

norm()

template<class Derived>

Scalar norm ( ) const

inline

Returns

the norm of the quaternion's coefficients

See also

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

normalize()

template<class Derived>

void normalize ( )

inline

Normalizes the quaternion *this

See also

normalized(), MatrixBase::normalize()

normalized()

template<class Derived>

Quaternion< Scalar > normalized ( ) const

inline

Returns

a normalized copy of *this

See also

normalize(), MatrixBase::normalized()

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

operator*() [1/5]

template<class Derived>

internal::rotation_base_generic_product_selector< Derived, OtherDerived, OtherDerived::IsVectorAtCompileTime >::ReturnType operator* ( const EigenBase< OtherDerived > & e ) const

inline

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

operator*() [2/5]

template<class Derived>

template<class OtherDerived>

Quaternion< typename internal::traits< Derived >::Scalar > operator* ( const QuaternionBase< OtherDerived > & other ) const

inline

Returns

the concatenation of two rotations as a quaternion-quaternion product

operator*() [3/5]

template<class Derived>

Transform< Scalar, Dim, Mode > operator* ( const Transform< Scalar, Dim, Mode, Options > & t ) const

inline

Returns

the concatenation of the rotation *this with a transformation t

operator*() [4/5]

template<class Derived>

Transform< Scalar, Dim, Isometry > operator* ( const Translation< Scalar, Dim > & t ) const

inline

Returns

the concatenation of the rotation *this with a translation t

operator*() [5/5]

template<class Derived>

RotationMatrixType operator* ( const UniformScaling< Scalar > & s ) const

inline

Returns

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

operator*=()

template<class Derived>

template<class OtherDerived>

Derived & operator*= ( const QuaternionBase< OtherDerived > & other )

inline

See also

operator*(Quaternion)

operator=() [1/2]

template<class Derived>

Derived & operator= ( const AngleAxisType & aa )

inline

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

References AngleAxis< _Scalar >::angle(), AngleAxis< _Scalar >::axis(), vec(), and w().

operator=() [2/2]

template<class Derived>

template<class MatrixDerived>

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

setFromTwoVectors()

template<class Derived>

template<typename Derived1, typename Derived2>

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 MatrixBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::col(), Eigen::ComputeFullV, MatrixBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::cross(), MatrixBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::dot(), JacobiSVD< _MatrixType, QRPreconditioner >::matrixV(), MatrixBase< Derived >::normalized(), MatrixBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::transpose(), vec(), and w().

Referenced by Quaternion< Scalar >::FromTwoVectors().

setIdentity()

template<class Derived>

QuaternionBase & setIdentity ( )

inline

See also

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

slerp()

template<class Derived>

template<class OtherDerived>

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

Returns

the spherical linear interpolation between the two quaternions *this and other at the parameter t in [0;1].

This represents an interpolation for a constant motion between *this and other, see also http://en.wikipedia.org/wiki/Slerp.

squaredNorm()

template<class Derived>

Scalar squaredNorm ( ) const

inline

Returns

the squared norm of the quaternion's coefficients

See also

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

Referenced by inverse().

toRotationMatrix()

template<class Derived>

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.

References w(), x(), y(), and z().

vec() [1/2]

template<class Derived>

VectorBlock< Coefficients, 3 > vec ( )

inline

Returns

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

vec() [2/2]

template<class Derived>

const VectorBlock< const Coefficients, 3 > vec ( ) const

inline

Returns

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

Referenced by _transformVector(), QuaternionBase< Quaternion< _Scalar, _Options > >::angularDistance(), AngleAxis< float >::operator=(), operator=(), and setFromTwoVectors().

w() [1/2]

template<class Derived>

Scalar & w ( )

inline

Returns

a reference to the w coefficient

w() [2/2]

template<class Derived>

Scalar w ( ) const

inline

Returns

the w coefficient

Referenced by _transformVector(), QuaternionBase< Quaternion< _Scalar, _Options > >::angularDistance(), conjugate(), AngleAxis< float >::operator=(), operator=(), setFromTwoVectors(), and toRotationMatrix().

x() [1/2]

template<class Derived>

Scalar & x ( )

inline

Returns

a reference to the x coefficient

x() [2/2]

template<class Derived>

Scalar x ( ) const

inline

Returns

the x coefficient

Referenced by conjugate(), and toRotationMatrix().

y() [1/2]

template<class Derived>

Scalar & y ( )

inline

Returns

a reference to the y coefficient

y() [2/2]

template<class Derived>

Scalar y ( ) const

inline

Returns

the y coefficient

Referenced by conjugate(), and toRotationMatrix().

z() [1/2]

template<class Derived>

Scalar & z ( )

inline

Returns

a reference to the z coefficient

z() [2/2]

template<class Derived>

Scalar z ( ) const

inline

Returns

the z coefficient

Referenced by conjugate(), and toRotationMatrix().

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

• ForwardDeclarations.h
• Quaternion.h