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Eigen::QuaternionBase< Derived > Class Template Reference

Detailed Description

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

Base class for quaternion expressions.

This is defined in the Geometry module.

#include <Eigen/Geometry>
Template Parameters
Derivedderived type (CRTP)
See Also
class Quaternion
+ Inheritance diagram for Eigen::QuaternionBase< Derived >:

Public Types

typedef AngleAxis< Scalar > AngleAxisType
 
typedef Matrix< Scalar, 3, 3 > Matrix3
 
typedef Matrix< Scalar, 3, 1 > Vector3
 
- Public Types inherited from Eigen::RotationBase< Derived, 3 >
typedef Matrix< Scalar, Dim, Dim > RotationMatrixType
 
typedef internal::traits
< Derived >::Scalar 
Scalar
 

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
 
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, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
 
Scalar norm () const
 
void normalize ()
 
Quaternion< Scalar > normalized () const
 
template<class OtherDerived >
Quaternion< typename
internal::traits< Derived >
::Scalar > 
operator* (const QuaternionBase< OtherDerived > &other) 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)
 
QuaternionBasesetIdentity ()
 
template<class OtherDerived >
Quaternion< typename
internal::traits< Derived >
::Scalar > 
slerp (const Scalar &t, const QuaternionBase< OtherDerived > &other) const
 
Scalar squaredNorm () const
 
Matrix3 toRotationMatrix () const
 
const VectorBlock< const
Coefficients, 3 > 
vec () const
 
VectorBlock< Coefficients, 3 > vec ()
 
CoeffReturnType w () const
 
NonConstCoeffReturnType w ()
 
CoeffReturnType x () const
 
NonConstCoeffReturnType x ()
 
CoeffReturnType y () const
 
NonConstCoeffReturnType y ()
 
CoeffReturnType z () const
 
NonConstCoeffReturnType z ()
 
- Public Member Functions inherited from Eigen::RotationBase< Derived, 3 >
Derived inverse () const
 
RotationMatrixType matrix () 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
 
RotationMatrixType toRotationMatrix () const
 

Static Public Member Functions

static Quaternion< Scalar > Identity ()
 

Member Typedef Documentation

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

the equivalent angle-axis type

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

the equivalent rotation matrix type

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

the type of a 3D vector

Member Function Documentation

template<class Derived >
QuaternionBase< Derived >::Vector3 Eigen::QuaternionBase< Derived >::_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
template<typename 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()
template<typename 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.

template<typename 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)
template<typename Derived>
internal::traits<Derived>::Coefficients& Eigen::QuaternionBase< Derived >::coeffs ( )
inline
Returns
a vector expression of the coefficients (x,y,z,w)
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()
template<typename 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()
template<typename Derived>
static Quaternion<Scalar> Eigen::QuaternionBase< Derived >::Identity ( )
inlinestatic
Returns
a quaternion representing an identity rotation
See Also
MatrixBase::Identity()
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()
template<typename Derived>
template<class OtherDerived >
bool Eigen::QuaternionBase< Derived >::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()
template<typename Derived>
Scalar Eigen::QuaternionBase< Derived >::norm ( ) const
inline
Returns
the norm of the quaternion's coefficients
See Also
QuaternionBase::squaredNorm(), MatrixBase::norm()
template<typename Derived>
void Eigen::QuaternionBase< Derived >::normalize ( void  )
inline

Normalizes the quaternion *this

See Also
normalized(), MatrixBase::normalize()
template<typename Derived>
Quaternion<Scalar> Eigen::QuaternionBase< Derived >::normalized ( ) const
inline
Returns
a normalized copy of *this
See Also
normalize(), MatrixBase::normalized()
template<typename Derived>
template<class OtherDerived >
Quaternion<typename internal::traits<Derived>::Scalar> Eigen::QuaternionBase< Derived >::operator* ( const QuaternionBase< OtherDerived > &  other) const
inline
Returns
the concatenation of two rotations as a quaternion-quaternion product
template<class Derived >
template<class OtherDerived >
Derived & Eigen::QuaternionBase< Derived >::operator*= ( const QuaternionBase< OtherDerived > &  other)
inline
See Also
operator*(Quaternion)
template<class Derived>
Derived & Eigen::QuaternionBase< Derived >::operator= ( const AngleAxisType aa)
inline

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

template<typename 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
template<class Derived >
template<typename Derived1 , typename Derived2 >
Derived & Eigen::QuaternionBase< 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.

template<typename Derived>
QuaternionBase& Eigen::QuaternionBase< Derived >::setIdentity ( )
inline
template<typename Derived>
template<class OtherDerived >
Quaternion<typename internal::traits<Derived>::Scalar> Eigen::QuaternionBase< Derived >::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.

template<typename Derived>
Scalar Eigen::QuaternionBase< Derived >::squaredNorm ( ) const
inline
Returns
the squared norm of the quaternion's coefficients
See Also
QuaternionBase::norm(), MatrixBase::squaredNorm()
template<class Derived >
QuaternionBase< Derived >::Matrix3 Eigen::QuaternionBase< Derived >::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.

template<typename 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)
template<typename Derived>
VectorBlock<Coefficients,3> Eigen::QuaternionBase< Derived >::vec ( )
inline
Returns
a vector expression of the imaginary part (x,y,z)
template<typename Derived>
CoeffReturnType Eigen::QuaternionBase< Derived >::w ( ) const
inline
Returns
the w coefficient
template<typename Derived>
NonConstCoeffReturnType Eigen::QuaternionBase< Derived >::w ( )
inline
Returns
a reference to the w coefficient (if Derived is a non-const lvalue)
template<typename Derived>
CoeffReturnType Eigen::QuaternionBase< Derived >::x ( ) const
inline
Returns
the x coefficient
template<typename Derived>
NonConstCoeffReturnType Eigen::QuaternionBase< Derived >::x ( )
inline
Returns
a reference to the x coefficient (if Derived is a non-const lvalue)
template<typename Derived>
CoeffReturnType Eigen::QuaternionBase< Derived >::y ( ) const
inline
Returns
the y coefficient
template<typename Derived>
NonConstCoeffReturnType Eigen::QuaternionBase< Derived >::y ( )
inline
Returns
a reference to the y coefficient (if Derived is a non-const lvalue)
template<typename Derived>
CoeffReturnType Eigen::QuaternionBase< Derived >::z ( ) const
inline
Returns
the z coefficient
template<typename Derived>
NonConstCoeffReturnType Eigen::QuaternionBase< Derived >::z ( )
inline
Returns
a reference to the z coefficient (if Derived is a non-const lvalue)

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