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QuaternionBase< Derived > Class Template Reference
Public Types | Public Member Functions | Static Public Member Functions | Friends

QuaternionBase< Derived > Class Template Reference
[Geometry module]

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#include <Quaternion.h>

Inherits RotationBase< Derived, 3 >.

Public Types

typedef internal::traits
< Derived >::Scalar 		Scalar
 the scalar type of the 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
typedef Matrix< Scalar, Dim, Dim > RotationMatrixType
 corresponding linear transformation matrix type

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 ()
Derived & operator= (const AngleAxisType &aa)
 Set *this from an angle-axis aa and returns a reference to *this.
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 (const Scalar &t, const QuaternionBase< OtherDerived > &other) const
template<class OtherDerived >
bool isApprox (const QuaternionBase< OtherDerived > &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
EIGEN_STRONG_INLINE Vector3 _transformVector (const 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:

  • 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.

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

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

Template Parameters:
Derivedderived type (CRTP)
See also:
class Quaternion

Definition at line 35 of file Quaternion.h.

Member Typedef Documentation

typedef AngleAxis<Scalar> AngleAxisType

the equivalent angle-axis type

Reimplemented in Quaternion< _Scalar, _Options >.

Definition at line 55 of file Quaternion.h.

typedef Matrix<Scalar,3,3> Matrix3

the equivalent rotation matrix type

Definition at line 53 of file Quaternion.h.

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

corresponding linear transformation matrix type

Definition at line 37 of file RotationBase.h.

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

the scalar type of the coefficients

Reimplemented from RotationBase< Derived, 3 >.

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

Definition at line 42 of file Quaternion.h.

typedef Matrix<Scalar,3,1> Vector3

the type of a 3D vector

Definition at line 51 of file Quaternion.h.

Member Function Documentation

EIGEN_STRONG_INLINE QuaternionBase< Derived >::Vector3 _transformVector ( const 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 464 of file Quaternion.h.

internal::traits< Derived >::Scalar angularDistance ( const QuaternionBase< OtherDerived > &  other ) const
Returns:
the angle (in radian) between two rotations
See also:
dot()

Definition at line 668 of file Quaternion.h.

internal::cast_return_type<Derived,Quaternion<NewScalarType> >::type cast (  ) const
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 172 of file Quaternion.h.

const internal::traits<Derived>::Coefficients& coeffs (  ) const
Returns:
a read-only vector expression of the coefficients (x,y,z,w)

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

Definition at line 84 of file Quaternion.h.

internal::traits<Derived>::Coefficients& coeffs (  )
Returns:
a vector expression of the coefficients (x,y,z,w)

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

Definition at line 87 of file Quaternion.h.

Quaternion< typename internal::traits< Derived >::Scalar > conjugate (  ) const
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 657 of file Quaternion.h.

Scalar dot ( const QuaternionBase< OtherDerived > &  other ) const
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 133 of file Quaternion.h.

static Quaternion<Scalar> Identity (  ) [static]
Returns:
a quaternion representing an identity rotation
See also:
MatrixBase::Identity()

Definition at line 105 of file Quaternion.h.

Quaternion< typename internal::traits< Derived >::Scalar > inverse (  ) const
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 >.

Definition at line 636 of file Quaternion.h.

bool isApprox ( const QuaternionBase< OtherDerived > &  other,
const RealScalar &  prec = NumTraits<Scalar>::dummy_precision() 
) const
Returns:
true if *this is approximately equal to other, within the precision determined by prec.
See also:
MatrixBase::isApprox()

Definition at line 160 of file Quaternion.h.

RotationMatrixType matrix (  ) const [inherited]
Returns:
an equivalent rotation matrix This function is added to be conform with the Transform class' naming scheme.

Definition at line 50 of file RotationBase.h.

Scalar norm (  ) const
Returns:
the norm of the quaternion's coefficients
See also:
QuaternionBase::squaredNorm(), MatrixBase::norm()

Definition at line 119 of file Quaternion.h.

void normalize ( void   )

Normalizes the quaternion *this.

See also:
normalized(), MatrixBase::normalize()

Definition at line 123 of file Quaternion.h.

Quaternion<Scalar> normalized (  ) const
Returns:
a normalized copy of *this
See also:
normalize(), MatrixBase::normalized()

Definition at line 126 of file Quaternion.h.

EIGEN_STRONG_INLINE internal::rotation_base_generic_product_selector<Derived,OtherDerived,OtherDerived::IsVectorAtCompileTime>::ReturnType operator* ( const EigenBase< OtherDerived > &  e ) const [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 71 of file RotationBase.h.

RotationMatrixType operator* ( const UniformScaling< Scalar > &  s ) const [inherited]
Returns:
the concatenation of the rotation *this with a uniform scaling s

Definition at line 60 of file RotationBase.h.

Transform<Scalar,Dim,Mode> operator* ( const Transform< Scalar, Dim, Mode, Options > &  t ) const [inherited]
Returns:
the concatenation of the rotation *this with a transformation t

Definition at line 89 of file RotationBase.h.

EIGEN_STRONG_INLINE Quaternion< typename internal::traits< Derived >::Scalar > operator* ( const QuaternionBase< OtherDerived > &  other ) const
Returns:
the concatenation of two rotations as a quaternion-quaternion product

Definition at line 437 of file Quaternion.h.

Transform<Scalar,Dim,Isometry> operator* ( const Translation< Scalar, Dim > &  t ) const [inherited]
Returns:
the concatenation of the rotation *this with a translation t

Definition at line 56 of file RotationBase.h.

EIGEN_STRONG_INLINE Derived & operator*= ( const QuaternionBase< OtherDerived > &  other )
See also:
operator*(Quaternion)

Definition at line 449 of file Quaternion.h.

Derived& operator= ( const MatrixBase< MatrixDerived > &  xpr )

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 512 of file Quaternion.h.

EIGEN_STRONG_INLINE Derived & operator= ( const AngleAxisType &  aa )

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

Definition at line 494 of file Quaternion.h.

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.

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 571 of file Quaternion.h.

QuaternionBase& setIdentity (  )
See also:
QuaternionBase::Identity(), MatrixBase::setIdentity()

Definition at line 109 of file Quaternion.h.

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.

Definition at line 687 of file Quaternion.h.

Scalar squaredNorm (  ) const
Returns:
the squared norm of the quaternion's coefficients
See also:
QuaternionBase::norm(), MatrixBase::squaredNorm()

Definition at line 114 of file Quaternion.h.

QuaternionBase< Derived >::Matrix3 toRotationMatrix ( void   ) const

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 RotationBase< Derived, 3 >.

Definition at line 525 of file Quaternion.h.

const VectorBlock<const Coefficients,3> vec (  ) const
Returns:
a read-only vector expression of the imaginary part (x,y,z)

Definition at line 78 of file Quaternion.h.

VectorBlock<Coefficients,3> vec (  )
Returns:
a vector expression of the imaginary part (x,y,z)

Definition at line 81 of file Quaternion.h.

Scalar& w (  )
Returns:
a reference to the w coefficient

Definition at line 75 of file Quaternion.h.

Scalar w (  ) const
Returns:
the w coefficient

Definition at line 66 of file Quaternion.h.

Scalar x (  ) const
Returns:
the x coefficient

Definition at line 60 of file Quaternion.h.

Scalar& x (  )
Returns:
a reference to the x coefficient

Definition at line 69 of file Quaternion.h.

Scalar& y (  )
Returns:
a reference to the y coefficient

Definition at line 71 of file Quaternion.h.

Scalar y (  ) const
Returns:
the y coefficient

Definition at line 62 of file Quaternion.h.

Scalar& z (  )
Returns:
a reference to the z coefficient

Definition at line 73 of file Quaternion.h.

Scalar z (  ) const
Returns:
the z coefficient

Definition at line 64 of file Quaternion.h.

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 76 of file RotationBase.h.

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 80 of file RotationBase.h.

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