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Map< Quaternion< _Scalar >, _Options > Class Template Reference
Public Types | Public Member Functions | Static Public Member Functions | Friends

Map< Quaternion< _Scalar >, _Options > Class Template Reference
[Geometry module]

Expression of a quaternion from a memory buffer. More...

#include <Quaternion.h>

Inherits QuaternionBase< Map< Quaternion< _Scalar >, _Options > >.

Public Types

typedef _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

EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Map)
using Base EIGEN_STRONG_INLINE 		Map (Scalar *coeffs)
 Constructs a Mapped Quaternion object from the pointer coeffs.
Coefficients & coeffs ()
const Coefficients & coeffs () const
Scalar x () const
Scalar & x ()
Scalar y () const
Scalar & y ()
Scalar z () const
Scalar & z ()
Scalar w () const
Scalar & w ()
const VectorBlock< const
Coefficients, 3 > 		vec () const
VectorBlock< Coefficients, 3 > vec ()
QuaternionBase & setIdentity ()
Scalar squaredNorm () const
Scalar norm () const
void normalize ()
 Normalizes the quaternion *this.
Quaternion< Scalar > normalized () const
Scalar dot (const QuaternionBase< OtherDerived > &other) const
Matrix3 toRotationMatrix () const
Map< Quaternion< _Scalar >
, _Options > & 		setFromTwoVectors (const MatrixBase< Derived1 > &a, const MatrixBase< Derived2 > &b)
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
< Map< Quaternion< _Scalar >
, _Options >, OtherDerived,
OtherDerived::IsVectorAtCompileTime >
::ReturnType 		operator* (const EigenBase< OtherDerived > &e) const
Transform< Scalar, Dim, Mode > operator* (const Transform< Scalar, Dim, Mode, Options > &t) const
Quaternion< Scalar > inverse () const
Quaternion< Scalar > conjugate () const
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
internal::cast_return_type
< Map< Quaternion< _Scalar >
, _Options >, Quaternion
< NewScalarType > >::type 		cast () const
RotationMatrixType matrix () const

Static Public Member Functions

static Quaternion< Scalar > Identity ()

Friends

RotationMatrixType operator* (const EigenBase< OtherDerived > &l, const Map< Quaternion< _Scalar >, _Options > &r)
Transform< Scalar, Dim, Affine > operator* (const DiagonalMatrix< Scalar, Dim > &l, const Map< Quaternion< _Scalar >, _Options > &r)

Detailed Description

template<typename _Scalar, int _Options>
class Eigen::Map< Quaternion< _Scalar >, _Options >

Expression of a quaternion from a memory buffer.

Template Parameters:
_Scalarthe type of the Quaternion coefficients
_Optionssee class Map

This is a specialization of class Map for Quaternion. This class allows to view a 4 scalar memory buffer as an Eigen's Quaternion object.

See also:
class Map, class Quaternion, class QuaternionBase

Definition at line 373 of file Quaternion.h.

Member Typedef Documentation

typedef AngleAxis<Scalar> AngleAxisType [inherited]

the equivalent angle-axis type

Definition at line 55 of file Quaternion.h.

typedef Matrix<Scalar,3,3> Matrix3 [inherited]

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 _Scalar Scalar

the scalar type of the coefficients

Reimplemented from QuaternionBase< Map< Quaternion< _Scalar >, _Options > >.

Definition at line 379 of file Quaternion.h.

typedef Matrix<Scalar,3,1> Vector3 [inherited]

the type of a 3D vector

Definition at line 51 of file Quaternion.h.

Constructor & Destructor Documentation

EIGEN_INHERIT_ASSIGNMENT_OPERATORS (Map) using Base EIGEN_STRONG_INLINE Map ( Scalar *  coeffs )

Constructs a Mapped Quaternion object from the pointer coeffs.

The pointer coeffs must reference the four coefficients of Quaternion in the following order: 

 *coeffs  == {x , y , z , w }

If the template parameter _Options is set to Aligned, then the pointer coeffs must be aligned.

Definition at line 390 of file Quaternion.h.

Member Function Documentation

EIGEN_STRONG_INLINE Vector3 _transformVector ( const Vector3 &  v ) const [inherited]

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::cast_return_type<Map< Quaternion< _Scalar >, _Options > ,Quaternion<NewScalarType> >::type cast (  ) const [inherited]
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.

Coefficients& coeffs (  )
Returns:
a vector expression of the coefficients (x,y,z,w)

Reimplemented from QuaternionBase< Map< Quaternion< _Scalar >, _Options > >.

Definition at line 392 of file Quaternion.h.

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

Reimplemented from QuaternionBase< Map< Quaternion< _Scalar >, _Options > >.

Definition at line 393 of file Quaternion.h.

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

Definition at line 105 of file Quaternion.h.

Quaternion<Scalar> inverse (  ) const [inherited]
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< Map< Quaternion< _Scalar >, _Options >, 3 >.

bool isApprox ( const QuaternionBase< OtherDerived > &  other,
const RealScalar &  prec = NumTraits<Scalar>::dummy_precision() 
) const [inherited]
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 [inherited]
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   ) [inherited]

Normalizes the quaternion *this.

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

Definition at line 123 of file Quaternion.h.

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

Definition at line 126 of file Quaternion.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.

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.

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.

EIGEN_STRONG_INLINE internal::rotation_base_generic_product_selector<Map< Quaternion< _Scalar >, _Options > ,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.

Map< Quaternion< _Scalar >, _Options > & setFromTwoVectors ( const MatrixBase< Derived1 > &  a,
const MatrixBase< Derived2 > &  b 
) [inherited]

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.

QuaternionBase& setIdentity (  ) [inherited]
See also:
QuaternionBase::Identity(), MatrixBase::setIdentity()

Definition at line 109 of file Quaternion.h.

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

Definition at line 114 of file Quaternion.h.

Matrix3 toRotationMatrix ( void   ) const [inherited]

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< Map< Quaternion< _Scalar >, _Options >, 3 >.

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

Definition at line 81 of file Quaternion.h.

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

Definition at line 78 of file Quaternion.h.

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

Definition at line 75 of file Quaternion.h.

Scalar w (  ) const [inherited]
Returns:
the w coefficient

Definition at line 66 of file Quaternion.h.

Scalar x (  ) const [inherited]
Returns:
the x coefficient

Definition at line 60 of file Quaternion.h.

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

Definition at line 69 of file Quaternion.h.

Scalar y (  ) const [inherited]
Returns:
the y coefficient

Definition at line 62 of file Quaternion.h.

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

Definition at line 71 of file Quaternion.h.

Scalar z (  ) const [inherited]
Returns:
the z coefficient

Definition at line 64 of file Quaternion.h.

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

Definition at line 73 of file Quaternion.h.

Friends And Related Function Documentation

RotationMatrixType operator* ( const EigenBase< OtherDerived > &  l,
const Map< Quaternion< _Scalar >, _Options > &  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 Map< Quaternion< _Scalar >, _Options > &  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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